Model

mutable struct OptimalControlModel{time_dependence<:TimeDependence, variable_dependence<:VariableDependence} <: CTBase.AbstractOptimalControlModel

Fields

• model_expression::Union{Nothing, Expr}: Default: nothing

• initial_time::Union{Nothing, Index, Real}: Default: nothing

• initial_time_name::Union{Nothing, String}: Default: nothing

• final_time::Union{Nothing, Index, Real}: Default: nothing

• final_time_name::Union{Nothing, String}: Default: nothing

• time_name::Union{Nothing, String}: Default: nothing

• control_dimension::Union{Nothing, Integer}: Default: nothing

• control_components_names::Union{Nothing, Vector{String}}: Default: nothing

• control_name::Union{Nothing, String}: Default: nothing

• state_dimension::Union{Nothing, Integer}: Default: nothing

• state_components_names::Union{Nothing, Vector{String}}: Default: nothing

• state_name::Union{Nothing, String}: Default: nothing

• variable_dimension::Union{Nothing, Integer}: Default: nothing

• variable_components_names::Union{Nothing, Vector{String}}: Default: nothing

• variable_name::Union{Nothing, String}: Default: nothing

• lagrange::Union{Nothing, Lagrange}: Default: nothing

• mayer::Union{Nothing, Mayer}: Default: nothing

• criterion::Union{Nothing, Symbol}: Default: nothing

• dynamics::Union{Nothing, Dynamics}: Default: nothing

• constraints::Dict{Symbol, Tuple}: Default: Dict{Symbol, Tuple{Vararg{Any}}}()

• dim_control_constraints::Union{Nothing, Integer}: Default: nothing

• dim_state_constraints::Union{Nothing, Integer}: Default: nothing

• dim_mixed_constraints::Union{Nothing, Integer}: Default: nothing

• dim_boundary_constraints::Union{Nothing, Integer}: Default: nothing

• dim_variable_constraints::Union{Nothing, Integer}: Default: nothing

• dim_control_range::Union{Nothing, Integer}: Default: nothing

• dim_state_range::Union{Nothing, Integer}: Default: nothing

• dim_variable_range::Union{Nothing, Integer}: Default: nothing

constraint(
    ocp::OptimalControlModel{T<:TimeDependence, V<:VariableDependence},
    label::Symbol
) -> Union{Nothing, VariableConstraint, BoundaryConstraint, ControlConstraint, MixedConstraint, StateConstraint}

Retrieve a labeled constraint. The result is a function associated with the constraint computation (not taking into account provided value / bounds).

Example

julia> constraint!(ocp, :initial, 0, :c0)
julia> c = constraint(ocp, :c0)
julia> c(1)
1

constraints_labels(
    ocp::OptimalControlModel
) -> Base.KeySet{Symbol, Dict{Symbol, Tuple}}

Return the labels of the constraints as a Base.keys.

control_components_names(
    ocp::OptimalControlModel
) -> Union{Nothing, Vector{String}}

Return the names of the components of the control of the optimal control problem or nothing.

control_dimension(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimention of the control of the optimal control problem or nothing.

control_name(
    ocp::OptimalControlModel
) -> Union{Nothing, String}

Return the name of the control of the optimal control problem or nothing.

criterion(
    ocp::OptimalControlModel
) -> Union{Nothing, Symbol}

Return the criterion (:min or :max) of the optimal control problem or nothing.

dim_boundary_constraints(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of the boundary constraints (nothing if not knonw). Information is updated after nlp_constraints! is called.

dim_control_constraints(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of nonlinear control constraints (nothing if not knonw). Information is updated after nlp_constraints! is called.

dim_control_range(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of range constraints on control (nothing if not knonw). Information is updated after nlp_constraints! is called.

dim_mixed_constraints(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of nonlinear mixed constraints (nothing if not knonw). Information is updated after nlp_constraints! is called.

dim_path_constraints(ocp::OptimalControlModel) -> Any

Return the dimension of nonlinear path (state + control + mixed) constraints (nothing if one of them is not knonw). Information is updated after nlp_constraints! is called.

dim_state_constraints(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of nonlinear state constraints (nothing if not knonw). Information is updated after nlp_constraints! is called.

dim_state_range(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of range constraints on state (nothing if not knonw). Information is updated after nlp_constraints! is called.

dim_variable_constraints(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of nonlinear variable constraints (nothing if not knonw). Information is updated after nlp_constraints! is called.

dim_variable_range(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of range constraints on variable (nothing if not knonw). Information is updated after nlp_constraints! is called.

dynamics(
    ocp::OptimalControlModel
) -> Union{Nothing, Dynamics}

Return the dynamics of the optimal control problem or nothing.

final_time(
    ocp::OptimalControlModel
) -> Union{Nothing, Index, Real}

Return the final time of the optimal control problem or nothing.

final_time_name(
    ocp::OptimalControlModel
) -> Union{Nothing, String}

Return the name of the final time of the optimal control problem or nothing.

has_free_final_time(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined with free final time.

has_free_initial_time(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined with free initial time.

has_lagrange_cost(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined with lagrange cost.

has_mayer_cost(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined with mayer cost.

initial_time(
    ocp::OptimalControlModel
) -> Union{Nothing, Index, Real}

Return the initial time of the optimal control problem or nothing.

initial_time_name(
    ocp::OptimalControlModel
) -> Union{Nothing, String}

Return the name of the initial time of the optimal control problem or nothing.

is_autonomous(ocp::OptimalControlModel{Autonomous}) -> Bool

Return true if the model is autonomous.

is_fixed(
    ocp::OptimalControlModel{<:TimeDependence, Fixed}
) -> Bool

Return true if the model is fixed (= has no variable).

is_max(ocp::OptimalControlModel) -> Bool

Return true if the criterion type of ocp is :max.

is_min(ocp::OptimalControlModel) -> Bool

Return true if the criterion type of ocp is :min.

is_time_dependent(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined as time dependent.

is_time_independent(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined as time independent.

is_variable_dependent(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined as variable dependent.

is_variable_independent(ocp::OptimalControlModel) -> Bool

Return true if the model has been defined as variable independent.

lagrange(
    ocp::OptimalControlModel
) -> Union{Nothing, Lagrange}

Return the Lagrange part of the cost of the optimal control problem or nothing.

mayer(ocp::OptimalControlModel) -> Union{Nothing, Mayer}

Return the Mayer part of the cost of the optimal control problem or nothing.

model_expression(
    ocp::OptimalControlModel
) -> Union{Nothing, Expr}

Return the model expression of the optimal control problem or nothing.

nlp_constraints!(
    ocp::OptimalControlModel
) -> Tuple{Tuple{Any, CTBase.var"#ξ#41", Vector{Real}}, Tuple{Any, CTBase.var"#η#42", Vector{Real}}, Tuple{Any, CTBase.var"#ψ#43", Vector{Real}}, Tuple{Any, CTBase.var"#ϕ#44", Vector{Real}}, Tuple{Any, CTBase.var"#θ#45", Vector{Real}}, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}}

Return a 6-tuple of tuples:

• (ξl, ξ, ξu) are control constraints
• (ηl, η, ηu) are state constraints
• (ψl, ψ, ψu) are mixed constraints
• (ϕl, ϕ, ϕu) are boundary constraints
• (θl, θ, θu) are variable constraints
• (ul, uind, uu) are control linear constraints of a subset of indices
• (xl, xind, xu) are state linear constraints of a subset of indices
• (vl, vind, vu) are variable linear constraints of a subset of indices

and update information about constraints dimensions of ocp.

Example

julia> (ξl, ξ, ξu), (ηl, η, ηu), (ψl, ψ, ψu), (ϕl, ϕ, ϕu), (θl, θ, θu),
    (ul, uind, uu), (xl, xind, xu), (vl, vind, vu) = nlp_constraints!(ocp)

state_components_names(
    ocp::OptimalControlModel
) -> Union{Nothing, Vector{String}}

Return the names of the components of the state of the optimal control problem or nothing.

state_dimension(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of the state of the optimal control problem or nothing.

state_name(
    ocp::OptimalControlModel
) -> Union{Nothing, String}

Return the name of the state of the optimal control problem or nothing.

time_name(
    ocp::OptimalControlModel
) -> Union{Nothing, String}

Return the name of the time component of the optimal control problem or nothing.

variable_components_names(
    ocp::OptimalControlModel
) -> Union{Nothing, Vector{String}}

Return the names of the components of the variable of the optimal control problem or nothing.

variable_dimension(
    ocp::OptimalControlModel
) -> Union{Nothing, Integer}

Return the dimension of the variable of the optimal control problem or nothing.

variable_name(
    ocp::OptimalControlModel
) -> Union{Nothing, String}

Return the name of the variable of the optimal control problem or nothing.

Model(
    dependencies::DataType...
) -> OptimalControlModel{Autonomous, Fixed}

Return a new OptimalControlModel instance, that is a model of an optimal control problem.

The model is defined by the following argument:

• dependencies: either Autonomous or NonAutonomous. Default is Autonomous. And either NonFixed or Fixed. Default is Fixed.

Examples

julia> ocp = Model()
julia> ocp = Model(NonAutonomous)
julia> ocp = Model(Autonomous, NonFixed)

Model(
;
    autonomous,
    variable
) -> OptimalControlModel{Autonomous, Fixed}

Return a new OptimalControlModel instance, that is a model of an optimal control problem.

The model is defined by the following optional keyword argument:

• autonomous: either true or false. Default is true.
• variable: either true or false. Default is false.

Examples

julia> ocp = Model()
julia> ocp = Model(autonomous=false)
julia> ocp = Model(autonomous=false, variable=true)

constraint!(
    ocp::OptimalControlModel{T<:TimeDependence, V<:VariableDependence},
    type::Symbol;
    rg,
    f,
    lb,
    ub,
    val,
    label
)

Add a constraint to an optimal control problem, denoted ocp.

You can add an :initial, :final, :control, :state or :variable box constraint (whole range).

Range constraint on the state, control or variable

You can add an :initial, :final, :control, :state or :variable box constraint on a range of it, that is only on some components. If not range is specified, then the constraint is on the whole range. We denote by x, u and v respectively the state, control and variable. We denote by n, m and q respectively the dimension of the state, control and variable. The range of the constraint must be contained in 1:n if the constraint is on the state, or 1:m if the constraint is on the control, or 1:q if the constraint is on the variable.

Examples

julia> constraint!(ocp, :initial; rg=1:2:5, lb=[ 0, 0, 0 ], ub=[ 1, 2, 1 ])
julia> constraint!(ocp, :initial; rg=2:3, lb=[ 0, 0 ], ub=[ 1, 2 ])
julia> constraint!(ocp, :final; rg=1, lb=0, ub=2)
julia> constraint!(ocp, :control; rg=1, lb=0, ub=2)
julia> constraint!(ocp, :state; rg=2:3, lb=[ 0, 0 ], ub=[ 1, 2 ])
julia> constraint!(ocp, :variable; rg=1:2, lb=[ 0, 0 ], ub=[ 1, 2 ])
julia> constraint!(ocp, :initial; lb=[ 0, 0, 0 ])                 # [ 0, 0, 0 ] ≤ x(t0),                          dim(x) = 3
julia> constraint!(ocp, :initial; lb=[ 0, 0, 0 ], ub=[ 1, 2, 1 ]) # [ 0, 0, 0 ] ≤ x(t0) ≤ [ 1, 2, 1 ],            dim(x) = 3
julia> constraint!(ocp, :final; lb=-1, ub=1)                      #          -1 ≤ x(tf) ≤ 1,                      dim(x) = 1
julia> constraint!(ocp, :control; lb=0, ub=2)                     #           0 ≤ u(t)  ≤ 2,        t ∈ [t0, tf], dim(u) = 1
julia> constraint!(ocp, :state; lb=[ 0, 0 ], ub=[ 1, 2 ])         #    [ 0, 0 ] ≤ x(t)  ≤ [ 1, 2 ], t ∈ [t0, tf], dim(x) = 2
julia> constraint!(ocp, :variable; lb=[ 0, 0 ], ub=[ 1, 2 ])      #    [ 0, 0 ] ≤    v  ≤ [ 1, 2 ],               dim(v) = 2

Functional constraint

You can add a :boundary, :control, :state, :mixed or :variable box functional constraint.

Examples

# variable independent ocp
julia> constraint!(ocp, :boundary; f = (x0, xf) -> x0[3]+xf[2], lb=0, ub=1)

# variable dependent ocp
julia> constraint!(ocp, :boundary; f = (x0, xf, v) -> x0[3]+xf[2]*v[1], lb=0, ub=1)

# time independent and variable independent ocp
julia> constraint!(ocp, :control; f = u -> 2u, lb=0, ub=1)
julia> constraint!(ocp, :state; f = x -> x-1, lb=[ 0, 0, 0 ], ub=[ 1, 2, 1 ])
julia> constraint!(ocp, :mixed; f = (x, u) -> x[1]-u, lb=0, ub=1)

# time dependent and variable independent ocp
julia> constraint!(ocp, :control; f = (t, u) -> 2u, lb=0, ub=1)
julia> constraint!(ocp, :state; f = (t, x) -> t * x, lb=[ 0, 0, 0 ], ub=[ 1, 2, 1 ])
julia> constraint!(ocp, :mixed; f = (t, x, u) -> x[1]-u, lb=0, ub=1)

# time independent and variable dependent ocp
julia> constraint!(ocp, :control; f = (u, v) -> 2u * v[1], lb=0, ub=1)
julia> constraint!(ocp, :state; f = (x, v) -> x * v[1], lb=[ 0, 0, 0 ], ub=[ 1, 2, 1 ])
julia> constraint!(ocp, :mixed; f = (x, u, v) -> x[1]-v[2]*u, lb=0, ub=1)

# time dependent and variable dependent ocp
julia> constraint!(ocp, :control; f = (t, u, v) -> 2u+v[2], lb=0, ub=1)
julia> constraint!(ocp, :state; f = (t, x, v) -> x-t*v[1], lb=[ 0, 0, 0 ], ub=[ 1, 2, 1 ])
julia> constraint!(ocp, :mixed; f = (t, x, u, v) -> x[1]*v[2]-u, lb=0, ub=1)

control!(ocp::OptimalControlModel, m::Integer)
control!(ocp::OptimalControlModel, m::Integer, name::String)
control!(
    ocp::OptimalControlModel,
    m::Integer,
    name::String,
    components_names::Vector{String}
)

Define the control dimension and possibly the names of each coordinate.

Examples

julia> control!(ocp, 1)
julia> ocp.control_dimension
1
julia> ocp.control_components_names
["u"]

julia> control!(ocp, 1, "v")
julia> ocp.control_dimension
1
julia> ocp.control_components_names
["v"]

julia> control!(ocp, 2)
julia> ocp.control_dimension
2
julia> ocp.control_components_names
["u₁", "u₂"]

julia> control!(ocp, 2, :v)
julia> ocp.control_dimension
2
julia> ocp.control_components_names
["v₁", "v₂"]

julia> control!(ocp, 2, "v")
julia> ocp.control_dimension
2
julia> ocp.control_components_names
["v₁", "v₂"]

dynamics!(
    ocp::OptimalControlModel{T<:TimeDependence, V<:VariableDependence},
    f::Function
)

Set the dynamics.

Example

julia> dynamics!(ocp, f)

objective!(
    ocp::OptimalControlModel{T<:TimeDependence, V<:VariableDependence},
    type::Symbol,
    g::Function,
    f⁰::Function
)
objective!(
    ocp::OptimalControlModel{T<:TimeDependence, V<:VariableDependence},
    type::Symbol,
    g::Function,
    f⁰::Function,
    criterion::Symbol
)

Set the criterion to the function g and f⁰. Type can be :bolza. Criterion is :min or :max.

Example

julia> objective!(ocp, :bolza, (x0, xf) -> x0[1] + xf[2], (x, u) -> x[1]^2 + u^2) # the control is of dimension 1

objective!(
    ocp::OptimalControlModel{T<:TimeDependence, V<:VariableDependence},
    type::Symbol,
    f::Function
)
objective!(
    ocp::OptimalControlModel{T<:TimeDependence, V<:VariableDependence},
    type::Symbol,
    f::Function,
    criterion::Symbol
)

Set the criterion to the function f. Type can be :mayer or :lagrange. Criterion is :min or :max.

Examples

julia> objective!(ocp, :mayer, (x0, xf) -> x0[1] + xf[2])
julia> objective!(ocp, :lagrange, (x, u) -> x[1]^2 + u^2) # the control is of dimension 1

remove_constraint!(ocp::OptimalControlModel, label::Symbol)

Remove a labeled constraint.

Example

julia> remove_constraint!(ocp, :con)

state!(ocp::OptimalControlModel, n::Integer)
state!(ocp::OptimalControlModel, n::Integer, name::String)
state!(
    ocp::OptimalControlModel,
    n::Integer,
    name::String,
    components_names::Vector{String}
)

Define the state dimension and possibly the names of each component.

Examples

julia> state!(ocp, 1)
julia> ocp.state_dimension
1
julia> ocp.state_components_names
["x"]

julia> state!(ocp, 1, "y")
julia> ocp.state_dimension
1
julia> ocp.state_components_names
["y"]

julia> state!(ocp, 2)
julia> ocp.state_dimension
2
julia> ocp.state_components_names
["x₁", "x₂"]

julia> state!(ocp, 2, :y)
julia> ocp.state_dimension
2
julia> ocp.state_components_names
["y₁", "y₂"]

julia> state!(ocp, 2, "y")
julia> ocp.state_dimension
2
julia> ocp.state_components_names
["y₁", "y₂"]

time!(
    ocp::OptimalControlModel{<:TimeDependence, VT};
    t0,
    tf,
    ind0,
    indf,
    name
)

Set the initial and final times. We denote by t0 the initial time and tf the final time. The optimal control problem is denoted ocp. When a time is free, then one must provide the corresponding index of the ocp variable.

Examples

julia> time!(ocp, t0=0,   tf=1  ) # Fixed t0 and fixed tf
julia> time!(ocp, t0=0,   indf=2) # Fixed t0 and free  tf
julia> time!(ocp, ind0=2, tf=1  ) # Free  t0 and fixed tf
julia> time!(ocp, ind0=2, indf=3) # Free  t0 and free  tf

When you plot a solution of an optimal control problem, the name of the time variable appears. By default, the name is "t". Consider you want to set the name of the time variable to "s".

julia> time!(ocp, t0=0, tf=1, name="s") # name is a String
# or
julia> time!(ocp, t0=0, tf=1, name=:s ) # name is a Symbol  

variable!(ocp::OptimalControlModel, q::Integer)
variable!(
    ocp::OptimalControlModel,
    q::Integer,
    name::String
)
variable!(
    ocp::OptimalControlModel,
    q::Integer,
    name::String,
    components_names::Vector{String}
)

Define the variable dimension and possibly the names of each component.

Examples

julia> variable!(ocp, 1, "v")
julia> variable!(ocp, 2, "v", [ "v₁", "v₂" ])