Types

abstract type AbstractHamiltonian{time_dependence, variable_dependence}

Abstract type for hamiltonians.

abstract type Autonomous <: TimeDependence

struct BoundaryConstraint{variable_dependence}

Fields

• f::Function

The default value for variable_dependence is Fixed.

Constructor

The constructor BoundaryConstraint returns a BoundaryConstraint of a function. The function must take 2 or 3 arguments (x0, xf) or (x0, xf, v), if the function is variable, it must be specified. Dependencies are specified with a boolean, variable, false by default or with a DataType, NonFixed/Fixed, Fixed by default.

Examples

julia> B = BoundaryConstraint((x0, xf) -> [xf[2]-x0[1], 2xf[1]+x0[2]^2])
julia> B = BoundaryConstraint((x0, xf, v) -> [v[3]+xf[2]-x0[1], v[1]-v[2]+2xf[1]+x0[2]^2], variable=true)
julia> B = BoundaryConstraint((x0, xf, v) -> [v[3]+xf[2]-x0[1], v[1]-v[2]+2xf[1]+x0[2]^2], NonFixed)

Call

The call returns the evaluation of the BoundaryConstraint for given values. If a variable is given for a non variable dependent boundary constraint, it will be ignored.

Examples

julia> B = BoundaryConstraint((x0, xf) -> [xf[2]-x0[1], 2xf[1]+x0[2]^2])
julia> B([0, 0], [1, 1])
[1, 2]
julia> B = BoundaryConstraint((x0, xf) -> [xf[2]-x0[1], 2xf[1]+x0[2]^2])
julia> B([0, 0], [1, 1],Real[])
[1, 2]
julia> B = BoundaryConstraint((x0, xf, v) -> [v[3]+xf[2]-x0[1], v[1]-v[2]+2xf[1]+x0[2]^2], variable=true)
julia> B([0, 0], [1, 1], [1, 2, 3])
[4, 1]

struct ControlConstraint{time_dependence, variable_dependence}

Fields

• f::Function

Similar to VectorField in the usage, but the dimension of the output of the function f is arbitrary.

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor ControlConstraint returns a ControlConstraint of a function. The function must take 1 to 3 arguments, u to (t, u, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> IncorrectArgument ControlConstraint(u -> [u[1]^2, 2u[2]], Int64)
julia> IncorrectArgument ControlConstraint(u -> [u[1]^2, 2u[2]], Int64)
julia> C = ControlConstraint(u -> [u[1]^2, 2u[2]], Autonomous, Fixed)
julia> C = ControlConstraint((u, v) -> [u[1]^2, 2u[2]+v[3]], Autonomous, NonFixed)
julia> C = ControlConstraint((t, u) -> [t+u[1]^2, 2u[2]], NonAutonomous, Fixed)
julia> C = ControlConstraint((t, u, v) -> [t+u[1]^2, 2u[2]+v[3]], NonAutonomous, NonFixed)
julia> C = ControlConstraint(u -> [u[1]^2, 2u[2]], autonomous=true, variable=false)
julia> C = ControlConstraint((u, v) -> [u[1]^2, 2u[2]+v[3]], autonomous=true, variable=true)
julia> C = ControlConstraint((t, u) -> [t+u[1]^2, 2u[2]], autonomous=false, variable=false)
julia> C = ControlConstraint((t, u, v) -> [t+u[1]^2, 2u[2]+v[3]], autonomous=false, variable=true)

Call

The call returns the evaluation of the ControlConstraint for given values.

Examples

julia> C = ControlConstraint(u -> [u[1]^2, 2u[2]], autonomous=true, variable=false)
julia> C([1, -1])
[1, -2]
julia> t = 1
julia> v = Real[]
julia> C(t, [1, -1], v)
[1, -2]
julia> C = ControlConstraint((u, v) -> [u[1]^2, 2u[2]+v[3]], autonomous=true, variable=true)
julia> C([1, -1], [1, 2, 3])
[1, 1]
julia> C(t, [1, -1], [1, 2, 3])
[1, 1]
julia> C = ControlConstraint((t, u) -> [t+u[1]^2, 2u[2]], autonomous=false, variable=false)
julia> C(1, [1, -1])
[2, -2]
julia> C(1, [1, -1], v)
[2, -2]
julia> C = ControlConstraint((t, u, v) -> [t+u[1]^2, 2u[2]+v[3]], autonomous=false, variable=true)
julia> C(1, [1, -1], [1, 2, 3])
[2, 1]

struct ControlLaw{time_dependence, variable_dependence}

Fields

• f::Function

Similar to Hamiltonian in the usage, but the dimension of the output of the function f is arbitrary.

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor ControlLaw returns a ControlLaw of a function. The function must take 2 to 4 arguments, (x, p) to (t, x, p, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> ControlLaw((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> ControlLaw((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> u = ControlLaw((x, p) -> x[1]^2+2p[2], Autonomous, Fixed)
julia> u = ControlLaw((x, p, v) -> x[1]^2+2p[2]+v[3], Autonomous, NonFixed)
julia> u = ControlLaw((t, x, p) -> t+x[1]^2+2p[2], NonAutonomous, Fixed)
julia> u = ControlLaw((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], NonAutonomous, NonFixed)
julia> u = ControlLaw((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> u = ControlLaw((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> u = ControlLaw((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> u = ControlLaw((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)

Call

The call returns the evaluation of the ControlLaw for given values.

Examples

julia> u = ControlLaw((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> u([1, 0], [0, 1])
3
julia> t = 1
julia> v = Real[]
julia> u(t, [1, 0], [0, 1])
MethodError
julia> u([1, 0], [0, 1], v)
MethodError
julia> u(t, [1, 0], [0, 1], v)
3
julia> u = ControlLaw((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> u([1, 0], [0, 1], [1, 2, 3])
6
julia> u(t, [1, 0], [0, 1], [1, 2, 3])
6
julia> u = ControlLaw((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> u(1, [1, 0], [0, 1])
4
julia> u(1, [1, 0], [0, 1], v)
4
julia> u = ControlLaw((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)
julia> u(1, [1, 0], [0, 1], [1, 2, 3])
7

struct Dynamics{time_dependence, variable_dependence}

Fields

• f::Function

The default value for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor Dynamics returns a Dynamics of a function. The function must take 2 to 4 arguments, (x, u) to (t, x, u, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> Dynamics((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> Dynamics((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> D = Dynamics((x, u) -> [2x[2]-u^2, x[1]], Autonomous, Fixed)
julia> D = Dynamics((x, u, v) -> [2x[2]-u^2+v[3], x[1]], Autonomous, NonFixed)
julia> D = Dynamics((t, x, u) -> [t+2x[2]-u^2, x[1]], NonAutonomous, Fixed)
julia> D = Dynamics((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], NonAutonomous, NonFixed)
julia> D = Dynamics((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> D = Dynamics((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> D = Dynamics((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> D = Dynamics((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)

Call

The call returns the evaluation of the Dynamics for given values.

Examples

julia> D = Dynamics((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> D([1, 0], 1)
[-1, 1]
julia> t = 1
julia> v = Real[]
julia> D(t, [1, 0], 1, v)
[-1, 1]
julia> D = Dynamics((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> D([1, 0], 1, [1, 2, 3])
[2, 1]
julia> D(t, [1, 0], 1, [1, 2, 3])
[2, 1]
julia> D = Dynamics((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> D(1, [1, 0], 1)
[0, 1]
julia> D(1, [1, 0], 1, v)
[0, 1]
julia> D = Dynamics((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)
julia> D(1, [1, 0], 1, [1, 2, 3])
[3, 1]

struct FeedbackControl{time_dependence, variable_dependence}

Fields

• f::Function

Similar to VectorField in the usage, but the dimension of the output of the function f is arbitrary.

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor FeedbackControl returns a FeedbackControl of a function. The function must take 1 to 3 arguments, x to (t, x, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> FeedbackControl(x -> x[1]^2+2x[2], Int64)
IncorrectArgument
julia> FeedbackControl(x -> x[1]^2+2x[2], Int64)
IncorrectArgument
julia> u = FeedbackControl(x -> x[1]^2+2x[2], Autonomous, Fixed)
julia> u = FeedbackControl((x, v) -> x[1]^2+2x[2]+v[3], Autonomous, NonFixed)
julia> u = FeedbackControl((t, x) -> t+x[1]^2+2x[2], NonAutonomous, Fixed)
julia> u = FeedbackControl((t, x, v) -> t+x[1]^2+2x[2]+v[3], NonAutonomous, NonFixed)
julia> u = FeedbackControl(x -> x[1]^2+2x[2], autonomous=true, variable=false)
julia> u = FeedbackControl((x, v) -> x[1]^2+2x[2]+v[3], autonomous=true, variable=true)
julia> u = FeedbackControl((t, x) -> t+x[1]^2+2x[2], autonomous=false, variable=false)
julia> u = FeedbackControl((t, x, v) -> t+x[1]^2+2x[2]+v[3], autonomous=false, variable=true)

Call

The call returns the evaluation of the FeedbackControl for given values.

Examples

julia> u = FeedbackControl(x -> x[1]^2+2x[2], autonomous=true, variable=false)
julia> u([1, 0])
1
julia> t = 1
julia> v = Real[]
julia> u(t, [1, 0])
MethodError
julia> u([1, 0], v)
MethodError
julia> u(t, [1, 0], v)
1
julia> u = FeedbackControl((x, v) -> x[1]^2+2x[2]+v[3], autonomous=true, variable=true)
julia> u([1, 0], [1, 2, 3])
4
julia> u(t, [1, 0], [1, 2, 3])
4
julia> u = FeedbackControl((t, x) -> t+x[1]^2+2x[2], autonomous=false, variable=false)
julia> u(1, [1, 0])
2
julia> u(1, [1, 0], v)
2
julia> u = FeedbackControl((t, x, v) -> t+x[1]^2+2x[2]+v[3], autonomous=false, variable=true)
julia> u(1, [1, 0], [1, 2, 3])
5

abstract type Fixed <: VariableDependence

struct Hamiltonian{time_dependence, variable_dependence} <: AbstractHamiltonian{time_dependence, variable_dependence}

Fields

• f::Function

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor Hamiltonian returns a Hamiltonian of a function. The function must take 2 to 4 arguments, (x, p) to (t, x, p, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> Hamiltonian((x, p) -> x + p, Int64)
IncorrectArgument 
julia> Hamiltonian((x, p) -> x + p, Int64)
IncorrectArgument
julia> H = Hamiltonian((x, p) -> x[1]^2+2p[2])
julia> H = Hamiltonian((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3]], autonomous=false, variable=true)
julia> H = Hamiltonian((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3]], NonAutonomous, NonFixed)

Call

The call returns the evaluation of the Hamiltonian for given values.

Examples

julia> H = Hamiltonian((x, p) -> [x[1]^2+2p[2]]) # autonomous=true, variable=false
julia> H([1, 0], [0, 1])
MethodError # H must return a scalar
julia> H = Hamiltonian((x, p) -> x[1]^2+2p[2])
julia> H([1, 0], [0, 1])
3
julia> t = 1
julia> v = Real[]
julia> H(t, [1, 0], [0, 1])
MethodError
julia> H([1, 0], [0, 1], v)
MethodError 
julia> H(t, [1, 0], [0, 1], v)
3
julia> H = Hamiltonian((x, p, v) -> x[1]^2+2p[2]+v[3], variable=true)
julia> H([1, 0], [0, 1], [1, 2, 3])
6
julia> H(t, [1, 0], [0, 1], [1, 2, 3])
6
julia> H = Hamiltonian((t, x, p) -> t+x[1]^2+2p[2], autonomous=false)
julia> H(1, [1, 0], [0, 1])
4
julia> H(1, [1, 0], [0, 1], v)
4
julia> H = Hamiltonian((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)
julia> H(1, [1, 0], [0, 1], [1, 2, 3])
7

struct HamiltonianLift{time_dependence, variable_dependence} <: AbstractHamiltonian{time_dependence, variable_dependence}

Lifts

• X::VectorField

The values for time_dependence and variable_dependence are deternimed by the values of those for the VectorField.

Constructor

The constructor HamiltonianLift returns a HamiltonianLift of a VectorField.

Examples

julia> H = HamiltonianLift(VectorField(x -> [x[1]^2, 2x[2]]))
julia> H = HamiltonianLift(VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], variable=true))
julia> H = HamiltonianLift(VectorField((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false))
julia> H = HamiltonianLift(VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true))
julia> H = HamiltonianLift(VectorField(x -> [x[1]^2, 2x[2]]))
julia> H = HamiltonianLift(VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], NonFixed))
julia> H = HamiltonianLift(VectorField((t, x) -> [t+x[1]^2, 2x[2]], NonAutonomous))
julia> H = HamiltonianLift(VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], NonAutonomous, NonFixed))

Call

The call returns the evaluation of the HamiltonianLift for given values.

Examples

julia> H = HamiltonianLift(VectorField(x -> [x[1]^2, 2x[2]]))
julia> H([1, 2], [1, 1])
5
julia> t = 1
julia> v = Real[]
julia> H(t, [1, 0], [0, 1])
MethodError
julia> H([1, 0], [0, 1], v)
MethodError 
julia> H(t, [1, 0], [0, 1], v)
5
julia> H = HamiltonianLift(VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], variable=true))
julia> H([1, 0], [0, 1], [1, 2, 3])
3
julia> H(t, [1, 0], [0, 1], [1, 2, 3])
3
julia> H = HamiltonianLift(VectorField((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false))
julia> H(1, [1, 2], [1, 1])
6
julia> H(1, [1, 0], [0, 1], v)
6
julia> H = HamiltonianLift(VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true))
julia> H(1, [1, 0], [0, 1], [1, 2, 3])
3

Alternatively, it is possible to construct the HamiltonianLift from a Function being the VectorField.

julia> HL1 = HamiltonianLift((x, v) -> [x[1]^2,x[2]^2+v], autonomous=true, variable=true)
julia> HL2 = HamiltonianLift(VectorField((x, v) -> [x[1]^2,x[2]^2+v], autonomous=true, variable=true))
julia> HL1([1, 0], [0, 1], 1) == HL2([1, 0], [0, 1], 1)
true

struct HamiltonianVectorField{time_dependence, variable_dependence} <: CTBase.AbstractVectorField{time_dependence, variable_dependence}

Fields

• f::Function

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor HamiltonianVectorField returns a HamiltonianVectorField of a function. The function must take 2 to 4 arguments, (x, p) to (t, x, p, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2], Int64)
IncorrectArgument
julia> HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2], Int64)
IncorrectArgument
julia> Hv = HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2]) # autonomous=true, variable=false
julia> Hv = HamiltonianVectorField((x, p, v) -> [x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], variable=true)
julia> Hv = HamiltonianVectorField((t, x, p) -> [t+x[1]^2+2p[2], x[2]-3p[2]^2], autonomous=false)
julia> Hv = HamiltonianVectorField((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], autonomous=false, variable=true)
julia> Hv = HamiltonianVectorField((x, p, v) -> [x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], NonFixed)
julia> Hv = HamiltonianVectorField((t, x, p) -> [t+x[1]^2+2p[2], x[2]-3p[2]^2], NonAutonomous)
julia> Hv = HamiltonianVectorField((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], NonAutonomous, NonFixed)

Call

The call returns the evaluation of the HamiltonianVectorField for given values.

Examples

julia> Hv = HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2]) # autonomous=true, variable=false
julia> Hv([1, 0], [0, 1])
[3, -3]
julia> t = 1
julia> v = Real[]
julia> Hv(t, [1, 0], [0, 1])
MethodError
julia> Hv([1, 0], [0, 1], v)
MethodError
julia> Hv(t, [1, 0], [0, 1], v)
[3, -3]
julia> Hv = HamiltonianVectorField((x, p, v) -> [x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], variable=true)
julia> Hv([1, 0], [0, 1], [1, 2, 3, 4])
[6, -3]
julia> Hv(t, [1, 0], [0, 1], [1, 2, 3, 4])
[6, -3]
julia> Hv = HamiltonianVectorField((t, x, p) -> [t+x[1]^2+2p[2], x[2]-3p[2]^2], autonomous=false)
julia> Hv(1, [1, 0], [0, 1])
[4, -3]
julia> Hv(1, [1, 0], [0, 1], v)
[4, -3]
julia> Hv = HamiltonianVectorField((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], autonomous=false, variable=true)
julia> Hv(1, [1, 0], [0, 1], [1, 2, 3, 4])
[7, -3]

mutable struct Index

Fields

• val::Int64

struct Lagrange{time_dependence, variable_dependence}

Fields

• f::Function

The default value for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor Lagrange returns a Lagrange cost of a function. The function must take 2 to 4 arguments, (x, u) to (t, x, u, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> Lagrange((x, u) -> 2x[2]-u[1]^2, Int64)
IncorrectArgument
julia> Lagrange((x, u) -> 2x[2]-u[1]^2, Int64)
IncorrectArgument
julia> L = Lagrange((x, u) -> [2x[2]-u[1]^2], autonomous=true, variable=false)
julia> L = Lagrange((x, u) -> 2x[2]-u[1]^2, autonomous=true, variable=false)
julia> L = Lagrange((x, u, v) -> 2x[2]-u[1]^2+v[3], autonomous=true, variable=true)
julia> L = Lagrange((t, x, u) -> t+2x[2]-u[1]^2, autonomous=false, variable=false)
julia> L = Lagrange((t, x, u, v) -> t+2x[2]-u[1]^2+v[3], autonomous=false, variable=true)
julia> L = Lagrange((x, u) -> [2x[2]-u[1]^2], Autonomous, Fixed)
julia> L = Lagrange((x, u) -> 2x[2]-u[1]^2, Autonomous, Fixed)
julia> L = Lagrange((x, u, v) -> 2x[2]-u[1]^2+v[3], Autonomous, NonFixed)
julia> L = Lagrange((t, x, u) -> t+2x[2]-u[1]^2, autonomous=false, Fixed)
julia> L = Lagrange((t, x, u, v) -> t+2x[2]-u[1]^2+v[3], autonomous=false, NonFixed)

Call

The call returns the evaluation of the Lagrange cost for given values.

Examples

julia> L = Lagrange((x, u) -> [2x[2]-u[1]^2], autonomous=true, variable=false)
julia> L([1, 0], [1])
MethodError
julia> L = Lagrange((x, u) -> 2x[2]-u[1]^2, autonomous=true, variable=false)
julia> L([1, 0], [1])
-1
julia> t = 1
julia> v = Real[]
julia> L(t, [1, 0], [1])
MethodError
julia> L([1, 0], [1], v)
MethodError
julia> L(t, [1, 0], [1], v)
-1
julia> L = Lagrange((x, u, v) -> 2x[2]-u[1]^2+v[3], autonomous=true, variable=true)
julia> L([1, 0], [1], [1, 2, 3])
2
julia> L(t, [1, 0], [1], [1, 2, 3])
2
julia> L = Lagrange((t, x, u) -> t+2x[2]-u[1]^2, autonomous=false, variable=false)
julia> L(1, [1, 0], [1])
0
julia> L(1, [1, 0], [1], v)
0
julia> L = Lagrange((t, x, u, v) -> t+2x[2]-u[1]^2+v[3], autonomous=false, variable=true)
julia> L(1, [1, 0], [1], [1, 2, 3])
3

struct Mayer{variable_dependence}

Fields

• f::Function

The default value for variable_dependence is Fixed.

Constructor

The constructor Mayer returns a Mayer cost of a function. The function must take 2 or 3 arguments (x0, xf) or (x0, xf, v), if the function is variable, it must be specified. Dependencies are specified with a boolean, variable, false by default or with a DataType, NonFixed/Fixed, Fixed by default.

Examples

julia> G = Mayer((x0, xf) -> xf[2]-x0[1])
julia> G = Mayer((x0, xf, v) -> v[3]+xf[2]-x0[1], variable=true)
julia> G = Mayer((x0, xf, v) -> v[3]+xf[2]-x0[1], NonFixed)

Call

The call returns the evaluation of the Mayer cost for given values. If a variable is given for a non variable dependent Mayer cost, it will be ignored.

Examples

julia> G = Mayer((x0, xf) -> xf[2]-x0[1])
julia> G([0, 0], [1, 1])
1
julia> G = Mayer((x0, xf) -> xf[2]-x0[1])
julia> G([0, 0], [1, 1],Real[])
1
julia> G = Mayer((x0, xf, v) -> v[3]+xf[2]-x0[1], variable=true)
julia> G([0, 0], [1, 1], [1, 2, 3])
4

struct MixedConstraint{time_dependence, variable_dependence}

Fields

• f::Function

Similar to Lagrange in the usage, but the dimension of the output of the function f is arbitrary.

The default value for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor MixedConstraint returns a MixedConstraint of a function. The function must take 2 to 4 arguments, (x, u) to (t, x, u, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> M = MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Autonomous, Fixed)
julia> M = MixedConstraint((x, u, v) -> [2x[2]-u^2+v[3], x[1]], Autonomous, NonFixed)
julia> M = MixedConstraint((t, x, u) -> [t+2x[2]-u^2, x[1]], NonAutonomous, Fixed)
julia> M = MixedConstraint((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], NonAutonomous, NonFixed)
julia> M = MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> M = MixedConstraint((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> M = MixedConstraint((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> M = MixedConstraint((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)

Call

The call returns the evaluation of the MixedConstraint for given values.

Examples

julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> M = MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> M([1, 0], 1)
[-1, 1]
julia> t = 1
julia> v = Real[]
julia> MethodError M(t, [1, 0], 1)
julia> MethodError M([1, 0], 1, v)
julia> M(t, [1, 0], 1, v)
[-1, 1]
julia> M = MixedConstraint((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> M([1, 0], 1, [1, 2, 3])
[2, 1]
julia> M(t, [1, 0], 1, [1, 2, 3])
[2, 1]
julia> M = MixedConstraint((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> M(1, [1, 0], 1)
[0, 1]
julia> M(1, [1, 0], 1, v)
[0, 1]
julia> M = MixedConstraint((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)
julia> M(1, [1, 0], 1, [1, 2, 3])
[3, 1]

struct Multiplier{time_dependence, variable_dependence}

Fields

• f::Function

Similar to ControlLaw in the usage.

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor Multiplier returns a Multiplier of a function. The function must take 2 to 4 arguments, (x, p) to (t, x, p, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> Multiplier((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> Multiplier((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> μ = Multiplier((x, p) -> x[1]^2+2p[2], Autonomous, Fixed)
julia> μ = Multiplier((x, p, v) -> x[1]^2+2p[2]+v[3], Autonomous, NonFixed)
julia> μ = Multiplier((t, x, p) -> t+x[1]^2+2p[2], NonAutonomous, Fixed)
julia> μ = Multiplier((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], NonAutonomous, NonFixed)
julia> μ = Multiplier((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> μ = Multiplier((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> μ = Multiplier((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> μ = Multiplier((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)

Call

The call returns the evaluation of the Multiplier for given values.

Examples

julia> μ = Multiplier((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> μ([1, 0], [0, 1])
3
julia> t = 1
julia> v = Real[]
julia> μ(t, [1, 0], [0, 1])
MethodError
julia> μ([1, 0], [0, 1], v)
MethodError
julia> μ(t, [1, 0], [0, 1], v)
3
julia> μ = Multiplier((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> μ([1, 0], [0, 1], [1, 2, 3])
6
julia> μ(t, [1, 0], [0, 1], [1, 2, 3])
6
julia> μ = Multiplier((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> μ(1, [1, 0], [0, 1])
4
julia> μ(1, [1, 0], [0, 1], v)
4
julia> μ = Multiplier((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)
julia> μ(1, [1, 0], [0, 1], [1, 2, 3])
7

abstract type NonAutonomous <: TimeDependence

abstract type NonFixed <: VariableDependence

struct StateConstraint{time_dependence, variable_dependence}

Fields

• f::Function

Similar to VectorField in the usage, but the dimension of the output of the function f is arbitrary.

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor StateConstraint returns a StateConstraint of a function. The function must take 1 to 3 arguments, x to (t, x, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> S = StateConstraint(x -> [x[1]^2, 2x[2]], Autonomous, Fixed)
julia> S = StateConstraint((x, v) -> [x[1]^2, 2x[2]+v[3]], Autonomous, NonFixed)
julia> S = StateConstraint((t, x) -> [t+x[1]^2, 2x[2]], NonAutonomous, Fixed)
julia> S = StateConstraint((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], NonAutonomous, NonFixed)
julia> S = StateConstraint(x -> [x[1]^2, 2x[2]], autonomous=true, variable=false)
julia> S = StateConstraint((x, v) -> [x[1]^2, 2x[2]+v[3]], autonomous=true, variable=true)
julia> S = StateConstraint((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false, variable=false)
julia> S = StateConstraint((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)

Call

The call returns the evaluation of the StateConstraint for given values.

Examples

julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> S = StateConstraint(x -> [x[1]^2, 2x[2]], autonomous=true, variable=false)
julia> S([1, -1])
[1, -2]
julia> t = 1
julia> v = Real[]
julia> S(t, [1, -1], v)
[1, -2]
julia> S = StateConstraint((x, v) -> [x[1]^2, 2x[2]+v[3]], autonomous=true, variable=true)
julia> S([1, -1], [1, 2, 3])
[1, 1]
julia> S(t, [1, -1], [1, 2, 3])
[1, 1]
julia> S = StateConstraint((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false, variable=false)
julia>  S(1, [1, -1])
[2, -2]
julia>  S(1, [1, -1], v)
[2, -2]
julia> S = StateConstraint((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)
julia>  S(1, [1, -1], [1, 2, 3])
[2, 1]

abstract type TimeDependence

struct VariableConstraint

Fields

• f::Function

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor VariableConstraint returns a VariableConstraint of a function. The function must take 1 argument, v.

Examples

julia> V = VariableConstraint(v -> [v[1]^2, 2v[2]])

Call

The call returns the evaluation of the VariableConstraint for given values.

Examples

julia> V = VariableConstraint(v -> [v[1]^2, 2v[2]])
julia> V([1, -1])
[1, -2]

abstract type VariableDependence

struct VectorField{time_dependence, variable_dependence} <: CTBase.AbstractVectorField{time_dependence, variable_dependence}

Fields

• f::Function

The default values for time_dependence and variable_dependence are Autonomous and Fixed respectively.

Constructor

The constructor VectorField returns a VectorField of a function. The function must take 1 to 3 arguments, x to (t, x, v), if the function is variable or non autonomous, it must be specified. Dependencies are specified either with :

• booleans, autonomous and variable, respectively true and false by default
• DataType, Autonomous/NonAutonomous and NonFixed/Fixed, respectively Autonomous and Fixed by default.

Examples

julia> VectorField(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> VectorField(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> V = VectorField(x -> [x[1]^2, 2x[2]]) # autonomous=true, variable=false
julia> V = VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], variable=true)
julia> V = VectorField((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false)
julia> V = VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)
julia> V = VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], NonFixed)
julia> V = VectorField((t, x) -> [t+x[1]^2, 2x[2]], NonAutonomous)
julia> V = VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], NonAutonomous, NonFixed)

Call

The call returns the evaluation of the VectorField for given values.

Examples

julia> V = VectorField(x -> [x[1]^2, 2x[2]]) # autonomous=true, variable=false
julia> V([1, -1])
[1, -2]
julia> t = 1
julia> v = Real[]
julia> V(t, [1, -1])
MethodError
julia> V([1, -1], v)
MethodError
julia> V(t, [1, -1], v)
[1, -2]
julia> V = VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], variable=true)
julia> V([1, -1], [1, 2, 3])
[1, 1]
julia> V(t, [1, -1], [1, 2, 3])
[1, 1]
julia> V = VectorField((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false)
julia> V(1, [1, -1])
[2, -2]
julia> V(1, [1, -1], v)
[2, -2]
julia> V = VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)
julia> V(1, [1, -1], [1, 2, 3])
[2, 1]

BoundaryConstraint(
    f::Function,
    dependencies::DataType...
) -> BoundaryConstraint{Fixed}

Return a BoundaryConstraint of a function. Dependencies are specified with a DataType, NonFixed/Fixed, Fixed by default.

julia> B = BoundaryConstraint((x0, xf) -> [xf[2]-x0[1], 2xf[1]+x0[2]^2])
julia> B = BoundaryConstraint((x0, xf, v) -> [v[3]+xf[2]-x0[1], v[1]-v[2]+2xf[1]+x0[2]^2], NonFixed)

BoundaryConstraint(
    f::Function;
    variable
) -> BoundaryConstraint{Fixed}

Return a BoundaryConstraint of a function. Dependencies are specified with a boolean, variable, false by default.

julia> B = BoundaryConstraint((x0, xf) -> [xf[2]-x0[1], 2xf[1]+x0[2]^2])
julia> B = BoundaryConstraint((x0, xf, v) -> [v[3]+xf[2]-x0[1], v[1]-v[2]+2xf[1]+x0[2]^2], variable=true)

Return the evaluation of the BoundaryConstraint.

julia> B = BoundaryConstraint((x0, xf) -> [xf[2]-x0[1], 2xf[1]+x0[2]^2])
julia> B([0, 0], [1, 1])
[1, 2]
julia> B = BoundaryConstraint((x0, xf) -> [xf[2]-x0[1], 2xf[1]+x0[2]^2])
julia> B([0, 0], [1, 1],Real[])
[1, 2]
julia> B = BoundaryConstraint((x0, xf, v) -> [v[3]+xf[2]-x0[1], v[1]-v[2]+2xf[1]+x0[2]^2], variable=true)
julia> B([0, 0], [1, 1], [1, 2, 3])
[4, 1]

ControlConstraint(
    f::Function,
    dependencies::DataType...
) -> ControlConstraint{Autonomous, Fixed}

Return the StateConstraint of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> IncorrectArgument ControlConstraint(u -> [u[1]^2, 2u[2]], Int64)
julia> IncorrectArgument ControlConstraint(u -> [u[1]^2, 2u[2]], Int64)
julia> C = ControlConstraint(u -> [u[1]^2, 2u[2]], Autonomous, Fixed)
julia> C = ControlConstraint((u, v) -> [u[1]^2, 2u[2]+v[3]], Autonomous, NonFixed)
julia> C = ControlConstraint((t, u) -> [t+u[1]^2, 2u[2]], NonAutonomous, Fixed)
julia> C = ControlConstraint((t, u, v) -> [t+u[1]^2, 2u[2]+v[3]], NonAutonomous, NonFixed)

ControlConstraint(
    f::Function;
    autonomous,
    variable
) -> ControlConstraint{Autonomous, Fixed}

Return the ControlConstraint of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> C = ControlConstraint(u -> [u[1]^2, 2u[2]], autonomous=true, variable=false)
julia> C = ControlConstraint((u, v) -> [u[1]^2, 2u[2]+v[3]], autonomous=true, variable=true)
julia> C = ControlConstraint((t, u) -> [t+u[1]^2, 2u[2]], autonomous=false, variable=false)
julia> C = ControlConstraint((t, u, v) -> [t+u[1]^2, 2u[2]+v[3]], autonomous=false, variable=true)

Return the value of the ControlConstraint function.

julia> IncorrectArgument ControlConstraint(u -> [u[1]^2, 2u[2]], Int64)
julia> IncorrectArgument ControlConstraint(u -> [u[1]^2, 2u[2]], Int64)
julia> C = ControlConstraint(u -> [u[1]^2, 2u[2]], autonomous=true, variable=false)
julia> C([1, -1])
[1, -2]
julia> t = 1
julia> v = Real[]
julia> C(t, [1, -1], v)
[1, -2]
julia> C = ControlConstraint((u, v) -> [u[1]^2, 2u[2]+v[3]], autonomous=true, variable=true)
julia> C([1, -1], [1, 2, 3])
[1, 1]
julia> C(t, [1, -1], [1, 2, 3])
[1, 1]
julia> C = ControlConstraint((t, u) -> [t+u[1]^2, 2u[2]], autonomous=false, variable=false)
julia> C(1, [1, -1])
[2, -2]
julia> C(1, [1, -1], v)
[2, -2]
julia> C = ControlConstraint((t, u, v) -> [t+u[1]^2, 2u[2]+v[3]], autonomous=false, variable=true)
julia> C(1, [1, -1], [1, 2, 3])
[2, 1]

ControlLaw(
    f::Function,
    dependencies::DataType...
) -> ControlLaw{Autonomous, Fixed}

Return the ControlLaw of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> ControlLaw((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> ControlLaw((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> u = ControlLaw((x, p) -> x[1]^2+2p[2], Autonomous, Fixed)
julia> u = ControlLaw((x, p, v) -> x[1]^2+2p[2]+v[3], Autonomous, NonFixed)
julia> u = ControlLaw((t, x, p) -> t+x[1]^2+2p[2], NonAutonomous, Fixed)
julia> u = ControlLaw((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], NonAutonomous, NonFixed)

ControlLaw(
    f::Function;
    autonomous,
    variable
) -> ControlLaw{Autonomous, Fixed}

Return the ControlLaw of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> u = ControlLaw((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> u = ControlLaw((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> u = ControlLaw((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> u = ControlLaw((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)

Return the value of the ControlLaw function.

julia> ControlLaw((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> ControlLaw((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> u = ControlLaw((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> u([1, 0], [0, 1])
3
julia> t = 1
julia> v = Real[]
julia> u(t, [1, 0], [0, 1])
MethodError
julia> u([1, 0], [0, 1], v)
MethodError
julia> u(t, [1, 0], [0, 1], v)
3
julia> u = ControlLaw((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> u([1, 0], [0, 1], [1, 2, 3])
6
julia> u(t, [1, 0], [0, 1], [1, 2, 3])
6
julia> u = ControlLaw((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> u(1, [1, 0], [0, 1])
4
julia> u(1, [1, 0], [0, 1], v)
4
julia> u = ControlLaw((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)
julia> u(1, [1, 0], [0, 1], [1, 2, 3])
7

Dynamics(
    f::Function,
    dependencies::DataType...
) -> Dynamics{Autonomous, Fixed}

Return the Dynamics of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> Dynamics((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> Dynamics((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> D = Dynamics((x, u) -> [2x[2]-u^2, x[1]], Autonomous, Fixed)
julia> D = Dynamics((x, u, v) -> [2x[2]-u^2+v[3], x[1]], Autonomous, NonFixed)
julia> D = Dynamics((t, x, u) -> [t+2x[2]-u^2, x[1]], NonAutonomous, Fixed)
julia> D = Dynamics((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], NonAutonomous, NonFixed)

Dynamics(
    f::Function;
    autonomous,
    variable
) -> Dynamics{Autonomous, Fixed}

Return the Dynamics of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> D = Dynamics((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> D = Dynamics((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> D = Dynamics((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> D = Dynamics((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)

Return the value of the Dynamics function.

julia> D = Dynamics((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> D([1, 0], 1)
[-1, 1]
julia> t = 1
julia> v = Real[]
julia> D(t, [1, 0], 1, v)
[-1, 1]
julia> D = Dynamics((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> D([1, 0], 1, [1, 2, 3])
[2, 1]
julia> D(t, [1, 0], 1, [1, 2, 3])
[2, 1]
julia> D = Dynamics((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> D(1, [1, 0], 1)
[0, 1]
julia> D(1, [1, 0], 1, v)
[0, 1]
julia> D = Dynamics((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)
julia> D(1, [1, 0], 1, [1, 2, 3])
[3, 1]

FeedbackControl(
    f::Function,
    dependencies::DataType...
) -> FeedbackControl{Autonomous, Fixed}

Return the FeedbackControl of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> FeedbackControl(x -> x[1]^2+2x[2], Int64)
IncorrectArgument
julia> FeedbackControl(x -> x[1]^2+2x[2], Int64)
IncorrectArgument
julia> u = FeedbackControl(x -> x[1]^2+2x[2], Autonomous, Fixed)
julia> u = FeedbackControl((x, v) -> x[1]^2+2x[2]+v[3], Autonomous, NonFixed)
julia> u = FeedbackControl((t, x) -> t+x[1]^2+2x[2], NonAutonomous, Fixed)
julia> u = FeedbackControl((t, x, v) -> t+x[1]^2+2x[2]+v[3], NonAutonomous, NonFixed)

FeedbackControl(
    f::Function;
    autonomous,
    variable
) -> FeedbackControl{Autonomous, Fixed}

Return the FeedbackControl of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> u = FeedbackControl(x -> x[1]^2+2x[2], autonomous=true, variable=false)
julia> u = FeedbackControl((x, v) -> x[1]^2+2x[2]+v[3], autonomous=true, variable=true)
julia> u = FeedbackControl((t, x) -> t+x[1]^2+2x[2], autonomous=false, variable=false)
julia> u = FeedbackControl((t, x, v) -> t+x[1]^2+2x[2]+v[3], autonomous=false, variable=true)

Return the value of the FeedbackControl function.

julia> FeedbackControl(x -> x[1]^2+2x[2], Int64)
IncorrectArgument
julia> FeedbackControl(x -> x[1]^2+2x[2], Int64)
IncorrectArgument
julia> u = FeedbackControl(x -> x[1]^2+2x[2], autonomous=true, variable=false)
julia> u([1, 0])
1
julia> t = 1
julia> v = Real[]
julia> u(t, [1, 0])
MethodError
julia> u([1, 0], v)
MethodError
julia> u(t, [1, 0], v)
1
julia> u = FeedbackControl((x, v) -> x[1]^2+2x[2]+v[3], autonomous=true, variable=true)
julia> u([1, 0], [1, 2, 3])
4
julia> u(t, [1, 0], [1, 2, 3])
4
julia> u = FeedbackControl((t, x) -> t+x[1]^2+2x[2], autonomous=false, variable=false)
julia> u(1, [1, 0])
2
julia> u(1, [1, 0], v)
2
julia> u = FeedbackControl((t, x, v) -> t+x[1]^2+2x[2]+v[3], autonomous=false, variable=true)
julia> u(1, [1, 0], [1, 2, 3])
5

Hamiltonian(
    f::Function,
    dependencies::DataType...
) -> Hamiltonian{Autonomous, Fixed}

Return an Hamiltonian of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> H = Hamiltonian((x, p) -> x[1]^2+2p[2])
julia> H = Hamiltonian((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3]], NonAutonomous, NonFixed)

Hamiltonian(
    f::Function;
    autonomous,
    variable
) -> Hamiltonian{Autonomous, Fixed}

Return an Hamiltonian of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> H = Hamiltonian((x, p) -> x[1]^2+2p[2])
julia> H = Hamiltonian((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3]], autonomous=false, variable=true)

Return the value of the Hamiltonian.

julia> Hamiltonian((x, p) -> x + p, Int64)
IncorrectArgument 
julia> Hamiltonian((x, p) -> x + p, Int64)
IncorrectArgument
julia> H = Hamiltonian((x, p) -> [x[1]^2+2p[2]]) # autonomous=true, variable=false
julia> H([1, 0], [0, 1])
MethodError # H must return a scalar
julia> H = Hamiltonian((x, p) -> x[1]^2+2p[2])
julia> H([1, 0], [0, 1])
3
julia> t = 1
julia> v = Real[]
julia> H(t, [1, 0], [0, 1])
MethodError
julia> H([1, 0], [0, 1], v)
MethodError 
julia> H(t, [1, 0], [0, 1], v)
3
julia> H = Hamiltonian((x, p, v) -> x[1]^2+2p[2]+v[3], variable=true)
julia> H([1, 0], [0, 1], [1, 2, 3])
6
julia> H(t, [1, 0], [0, 1], [1, 2, 3])
6
julia> H = Hamiltonian((t, x, p) -> t+x[1]^2+2p[2], autonomous=false)
julia> H(1, [1, 0], [0, 1])
4
julia> H(1, [1, 0], [0, 1], v)
4
julia> H = Hamiltonian((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)
julia> H(1, [1, 0], [0, 1], [1, 2, 3])
7

HamiltonianLift(
    f::Function,
    dependences::DataType...
) -> HamiltonianLift

Return an HamiltonianLift of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> HamiltonianLift(HamiltonianLift(VectorField(x -> [x[1]^2, 2x[2]], Int64))
IncorrectArgument 
julia> HL = HamiltonianLift(x -> [x[1]^2,x[2]^2], Autonomous, Fixed)
julia> HL = HamiltonianLift((x, v) -> [x[1]^2,x[2]^2+v], Autonomous, NonFixed)
julia> HL = HamiltonianLift((t, x) -> [t+x[1]^2,x[2]^2], NonAutonomous, Fixed)
julia> HL = HamiltonianLift((t, x, v) -> [t+x[1]^2,x[2]^2+v], NonAutonomous, NonFixed)

HamiltonianLift(
    f::Function;
    autonomous,
    variable
) -> HamiltonianLift

Return an HamiltonianLift of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> HL = HamiltonianLift(x -> [x[1]^2,x[2]^2], autonomous=true, variable=false)
julia> HL = HamiltonianLift((x, v) -> [x[1]^2,x[2]^2+v], autonomous=true, variable=true)
julia> HL = HamiltonianLift((t, x) -> [t+x[1]^2,x[2]^2], autonomous=false, variable=false)
julia> HL = HamiltonianLift((t, x, v) -> [t+x[1]^2,x[2]^2+v], autonomous=false, variable=true)

Return the value of the HamiltonianLift.

Examples

julia> HamiltonianLift(HamiltonianLift(VectorField(x -> [x[1]^2, 2x[2]], Int64))
IncorrectArgument 
julia> H = HamiltonianLift(VectorField(x -> [x[1]^2, 2x[2]]))
julia> H([1, 2], [1, 1])
5
julia> t = 1
julia> v = Real[]
julia> H(t, [1, 0], [0, 1])
MethodError
julia> H([1, 0], [0, 1], v)
MethodError 
julia> H(t, [1, 0], [0, 1], v)
5
julia> H = HamiltonianLift(VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], variable=true))
julia> H([1, 0], [0, 1], [1, 2, 3])
3
julia> H(t, [1, 0], [0, 1], [1, 2, 3])
3
julia> H = HamiltonianLift(VectorField((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false))
julia> H(1, [1, 2], [1, 1])
6
julia> H(1, [1, 0], [0, 1], v)
6
julia> H = HamiltonianLift(VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true))
julia> H(1, [1, 0], [0, 1], [1, 2, 3])
3

HamiltonianVectorField(
    f::Function,
    dependencies::DataType...
) -> HamiltonianVectorField{Autonomous, Fixed}

Return an HamiltonianVectorField of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2], Int64)
IncorrectArgument
julia> HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2], Int64)
IncorrectArgument
julia> Hv = HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2]) # autonomous=true, variable=false
julia> Hv = HamiltonianVectorField((x, p, v) -> [x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], NonFixed)
julia> Hv = HamiltonianVectorField((t, x, p) -> [t+x[1]^2+2p[2], x[2]-3p[2]^2], NonAutonomous)
julia> Hv = HamiltonianVectorField((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], NonAutonomous, NonFixed)

HamiltonianVectorField(
    f::Function;
    autonomous,
    variable
) -> HamiltonianVectorField{Autonomous, Fixed}

Return an HamiltonianVectorField of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> Hv = HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2]) # autonomous=true, variable=false
julia> Hv = HamiltonianVectorField((x, p, v) -> [x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], variable=true)
julia> Hv = HamiltonianVectorField((t, x, p) -> [t+x[1]^2+2p[2], x[2]-3p[2]^2], autonomous=false)
julia> Hv = HamiltonianVectorField((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], autonomous=false, variable=true)

Return the value of the HamiltonianVectorField.

Examples

julia> HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2], Int64)
IncorrectArgument
julia> HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2], Int64)
IncorrectArgument
julia> Hv = HamiltonianVectorField((x, p) -> [x[1]^2+2p[2], x[2]-3p[2]^2]) # autonomous=true, variable=false
julia> Hv([1, 0], [0, 1])
[3, -3]
julia> t = 1
julia> v = Real[]
julia> Hv(t, [1, 0], [0, 1])
MethodError
julia> Hv([1, 0], [0, 1], v)
MethodError
julia> Hv(t, [1, 0], [0, 1], v)
[3, -3]
julia> Hv = HamiltonianVectorField((x, p, v) -> [x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], variable=true)
julia> Hv([1, 0], [0, 1], [1, 2, 3, 4])
[6, -3]
julia> Hv(t, [1, 0], [0, 1], [1, 2, 3, 4])
[6, -3]
julia> Hv = HamiltonianVectorField((t, x, p) -> [t+x[1]^2+2p[2], x[2]-3p[2]^2], autonomous=false)
julia> Hv(1, [1, 0], [0, 1])
[4, -3]
julia> Hv(1, [1, 0], [0, 1], v)
[4, -3]
julia> Hv = HamiltonianVectorField((t, x, p, v) -> [t+x[1]^2+2p[2]+v[3], x[2]-3p[2]^2+v[4]], autonomous=false, variable=true)
julia> Hv(1, [1, 0], [0, 1], [1, 2, 3, 4])
[7, -3]

Lagrange(
    f::Function,
    dependencies::DataType...
) -> Lagrange{Autonomous, Fixed}

Return a Lagrange cost of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> Lagrange((x, u) -> 2x[2]-u[1]^2, Int64)
IncorrectArgument
julia> Lagrange((x, u) -> 2x[2]-u[1]^2, Int64)
IncorrectArgument
julia> L = Lagrange((x, u) -> [2x[2]-u[1]^2], autonomous=true, variable=false)
julia> L = Lagrange((x, u) -> 2x[2]-u[1]^2, autonomous=true, variable=false)
julia> L = Lagrange((x, u, v) -> 2x[2]-u[1]^2+v[3], autonomous=true, variable=true)
julia> L = Lagrange((t, x, u) -> t+2x[2]-u[1]^2, autonomous=false, variable=false)
julia> L = Lagrange((t, x, u, v) -> t+2x[2]-u[1]^2+v[3], autonomous=false, variable=true)

Lagrange(
    f::Function;
    autonomous,
    variable
) -> Lagrange{Autonomous, Fixed}

Return a Lagrange cost of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> L = Lagrange((x, u) -> [2x[2]-u[1]^2], autonomous=true, variable=false)
julia> L = Lagrange((x, u) -> 2x[2]-u[1]^2, autonomous=true, variable=false)
julia> L = Lagrange((x, u, v) -> 2x[2]-u[1]^2+v[3], autonomous=true, variable=true)
julia> L = Lagrange((t, x, u) -> t+2x[2]-u[1]^2, autonomous=false, variable=false)
julia> L = Lagrange((t, x, u, v) -> t+2x[2]-u[1]^2+v[3], autonomous=false, variable=true)

Return the value of the Lagrange function.

Examples

julia> Lagrange((x, u) -> 2x[2]-u[1]^2, Int64)
IncorrectArgument
julia> Lagrange((x, u) -> 2x[2]-u[1]^2, Int64)
IncorrectArgument
julia> L = Lagrange((x, u) -> [2x[2]-u[1]^2], autonomous=true, variable=false)
julia> L([1, 0], [1])
MethodError
julia> L = Lagrange((x, u) -> 2x[2]-u[1]^2, autonomous=true, variable=false)
julia> L([1, 0], [1])
-1
julia> t = 1
julia> v = Real[]
julia> L(t, [1, 0], [1])
MethodError
julia> L([1, 0], [1], v)
MethodError
julia> L(t, [1, 0], [1], v)
-1
julia> L = Lagrange((x, u, v) -> 2x[2]-u[1]^2+v[3], autonomous=true, variable=true)
julia> L([1, 0], [1], [1, 2, 3])
2
julia> L(t, [1, 0], [1], [1, 2, 3])
2
julia> L = Lagrange((t, x, u) -> t+2x[2]-u[1]^2, autonomous=false, variable=false)
julia> L(1, [1, 0], [1])
0
julia> L(1, [1, 0], [1], v)
0
julia> L = Lagrange((t, x, u, v) -> t+2x[2]-u[1]^2+v[3], autonomous=false, variable=true)
julia> L(1, [1, 0], [1], [1, 2, 3])
3

Mayer(
    f::Function,
    dependencies::DataType...
) -> Mayer{Fixed}

Return a Mayer cost of a function. Dependencies are specified with a DataType, NonFixed/Fixed, Fixed by default.

julia> G = Mayer((x0, xf) -> xf[2]-x0[1])
julia> G = Mayer((x0, xf, v) -> v[3]+xf[2]-x0[1], NonFixed)

Mayer(f::Function; variable) -> Mayer{Fixed}

Return a Mayer cost of a function. Dependencies are specified with a boolean, variable, false by default.

julia> G = Mayer((x0, xf) -> xf[2]-x0[1])
julia> G = Mayer((x0, xf, v) -> v[3]+xf[2]-x0[1], variable=true)

Return the evaluation of the Mayer cost.

julia> G = Mayer((x0, xf) -> xf[2]-x0[1])
julia> G([0, 0], [1, 1])
1
julia> G = Mayer((x0, xf) -> xf[2]-x0[1])
julia> G([0, 0], [1, 1], Real[])
1
julia> G = Mayer((x0, xf, v) -> v[3]+xf[2]-x0[1], variable=true)
julia> G([0, 0], [1, 1], [1, 2, 3])
4

MixedConstraint(
    f::Function,
    dependencies::DataType...
) -> MixedConstraint{Autonomous, Fixed}

Return the MixedConstraint of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> M = MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Autonomous, Fixed)
julia> M = MixedConstraint((x, u, v) -> [2x[2]-u^2+v[3], x[1]], Autonomous, NonFixed)
julia> M = MixedConstraint((t, x, u) -> [t+2x[2]-u^2, x[1]], NonAutonomous, Fixed)
julia> M = MixedConstraint((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], NonAutonomous, NonFixed)

MixedConstraint(
    f::Function;
    autonomous,
    variable
) -> MixedConstraint{Autonomous, Fixed}

Return the MixedConstraint of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> M = MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> M = MixedConstraint((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> M = MixedConstraint((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> M = MixedConstraint((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)

Return the value of the MixedConstraint function.

julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], Int64)
IncorrectArgument
julia> M = MixedConstraint((x, u) -> [2x[2]-u^2, x[1]], autonomous=true, variable=false)
julia> M([1, 0], 1)
[-1, 1]
julia> t = 1
julia> v = Real[]
julia> MethodError M(t, [1, 0], 1)
julia> MethodError M([1, 0], 1, v)
julia> M(t, [1, 0], 1, v)
[-1, 1]
julia> M = MixedConstraint((x, u, v) -> [2x[2]-u^2+v[3], x[1]], autonomous=true, variable=true)
julia> M([1, 0], 1, [1, 2, 3])
[2, 1]
julia> M(t, [1, 0], 1, [1, 2, 3])
[2, 1]
julia> M = MixedConstraint((t, x, u) -> [t+2x[2]-u^2, x[1]], autonomous=false, variable=false)
julia> M(1, [1, 0], 1)
[0, 1]
julia> M(1, [1, 0], 1, v)
[0, 1]
julia> M = MixedConstraint((t, x, u, v) -> [t+2x[2]-u^2+v[3], x[1]], autonomous=false, variable=true)
julia> M(1, [1, 0], 1, [1, 2, 3])
[3, 1]

Multiplier(
    f::Function,
    dependencies::DataType...
) -> Multiplier{Autonomous, Fixed}

Return the Multiplier of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> Multiplier((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> Multiplier((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> μ = Multiplier((x, p) -> x[1]^2+2p[2], Autonomous, Fixed)
julia> μ = Multiplier((x, p, v) -> x[1]^2+2p[2]+v[3], Autonomous, NonFixed)
julia> μ = Multiplier((t, x, p) -> t+x[1]^2+2p[2], NonAutonomous, Fixed)
julia> μ = Multiplier((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], NonAutonomous, NonFixed)

Multiplier(
    f::Function;
    autonomous,
    variable
) -> Multiplier{Autonomous, Fixed}

Return the Multiplier of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> μ = Multiplier((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> μ = Multiplier((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> μ = Multiplier((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> μ = Multiplier((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)

Return the value of the Multiplier function.

julia> Multiplier((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> Multiplier((x, p) -> x[1]^2+2p[2], Int64)
IncorrectArgument
julia> μ = Multiplier((x, p) -> x[1]^2+2p[2], autonomous=true, variable=false)
julia> μ([1, 0], [0, 1])
3
julia> t = 1
julia> v = Real[]
julia> μ(t, [1, 0], [0, 1])
MethodError
julia> μ([1, 0], [0, 1], v)
MethodError
julia> μ(t, [1, 0], [0, 1], v)
3
julia> μ = Multiplier((x, p, v) -> x[1]^2+2p[2]+v[3], autonomous=true, variable=true)
julia> μ([1, 0], [0, 1], [1, 2, 3])
6
julia> μ(t, [1, 0], [0, 1], [1, 2, 3])
6
julia> μ = Multiplier((t, x, p) -> t+x[1]^2+2p[2], autonomous=false, variable=false)
julia> μ(1, [1, 0], [0, 1])
4
julia> μ(1, [1, 0], [0, 1], v)
4
julia> μ = Multiplier((t, x, p, v) -> t+x[1]^2+2p[2]+v[3], autonomous=false, variable=true)
julia> μ(1, [1, 0], [0, 1], [1, 2, 3])
7

StateConstraint(
    f::Function,
    dependencies::DataType...
) -> StateConstraint{Autonomous, Fixed}

Return the StateConstraint of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> S = StateConstraint(x -> [x[1]^2, 2x[2]], Autonomous, Fixed)
julia> S = StateConstraint((x, v) -> [x[1]^2, 2x[2]+v[3]], Autonomous, NonFixed)
julia> S = StateConstraint((t, x) -> [t+x[1]^2, 2x[2]], NonAutonomous, Fixed)
julia> S = StateConstraint((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], NonAutonomous, NonFixed)

StateConstraint(
    f::Function;
    autonomous,
    variable
) -> StateConstraint{Autonomous, Fixed}

Return the StateConstraint of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> S = StateConstraint(x -> [x[1]^2, 2x[2]], autonomous=true, variable=false)
julia> S = StateConstraint((x, v) -> [x[1]^2, 2x[2]+v[3]], autonomous=true, variable=true)
julia> S = StateConstraint((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false, variable=false)
julia> S = StateConstraint((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)

Return the value of the StateConstraint function.

julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> StateConstraint(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> S = StateConstraint(x -> [x[1]^2, 2x[2]], autonomous=true, variable=false)
julia> S([1, -1])
[1, -2]
julia> t = 1
julia> v = Real[]
julia> S(t, [1, -1], v)
[1, -2]
julia> S = StateConstraint((x, v) -> [x[1]^2, 2x[2]+v[3]], autonomous=true, variable=true)
julia> S([1, -1], [1, 2, 3])
[1, 1]
julia> S(t, [1, -1], [1, 2, 3])
[1, 1]
julia> S = StateConstraint((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false, variable=false)
julia>  S(1, [1, -1])
[2, -2]
julia>  S(1, [1, -1], v)
[2, -2]
julia> S = StateConstraint((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)
julia>  S(1, [1, -1], [1, 2, 3])
[2, 1]

Return the value of the VariableConstraint function.

julia> V = VariableConstraint(v -> [v[1]^2, 2v[2]])
julia> V([1, -1])
[1, -2]

VectorField(
    f::Function,
    dependencies::DataType...
) -> VectorField{Autonomous, Fixed}

Return a VectorField of a function. Dependencies are specified with DataType, Autonomous, NonAutonomous and Fixed, NonFixed.

julia> VectorField(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> VectorField(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> V = VectorField(x -> [x[1]^2, 2x[2]]) # autonomous=true, variable=false
julia> V = VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], NonFixed)
julia> V = VectorField((t, x) -> [t+x[1]^2, 2x[2]], NonAutonomous)
julia> V = VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], NonAutonomous, NonFixed)

VectorField(
    f::Function;
    autonomous,
    variable
) -> VectorField{Autonomous, Fixed}

Return a VectorField of a function. Dependencies are specified with a boolean, variable, false by default, autonomous, true by default.

julia> V = VectorField(x -> [x[1]^2, 2x[2]]) # autonomous=true, variable=false
julia> V = VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], variable=true)
julia> V = VectorField((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false)
julia> V = VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)

Return the value of the VectorField.

Examples

julia> VectorField(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> VectorField(x -> [x[1]^2, 2x[2]], Int64)
IncorrectArgument
julia> V = VectorField(x -> [x[1]^2, 2x[2]]) # autonomous=true, variable=false
julia> V([1, -1])
[1, -2]
julia> t = 1
julia> v = Real[]
julia> V(t, [1, -1])
MethodError
julia> V([1, -1], v)
MethodError
julia> V(t, [1, -1], v)
[1, -2]
julia> V = VectorField((x, v) -> [x[1]^2, 2x[2]+v[3]], variable=true)
julia> V([1, -1], [1, 2, 3])
[1, 1]
julia> V(t, [1, -1], [1, 2, 3])
[1, 1]
julia> V = VectorField((t, x) -> [t+x[1]^2, 2x[2]], autonomous=false)
julia> V(1, [1, -1])
[2, -2]
julia> V(1, [1, -1], v)
[2, -2]
julia> V = VectorField((t, x, v) -> [t+x[1]^2, 2x[2]+v[3]], autonomous=false, variable=true)
julia> V(1, [1, -1], [1, 2, 3])
[2, 1]