API

abstract type AbstractConstraintsModel

abstract type AbstractControlModel

abstract type AbstractDualModel

abstract type AbstractModel

abstract type AbstractObjectiveModel

abstract type AbstractSolution

abstract type AbstractSolverInfos

abstract type AbstractStateModel

abstract type AbstractTimeGridModel

abstract type AbstractTimeModel

abstract type AbstractTimesModel

abstract type AbstractVariableModel

struct BolzaObjectiveModel{TM<:Function, TL<:Function} <: CTModels.AbstractObjectiveModel

Fields

• mayer::Function

• lagrange::Function

• criterion::Symbol

struct ConstraintsModel{TP<:Tuple, TB<:Tuple, TS<:Tuple, TC<:Tuple, TV<:Tuple, TC_ALL<:Dict{Symbol, Tuple{Symbol, Union{Function, OrdinalRange{<:Int64}}, AbstractVector{<:Real}, AbstractVector{<:Real}}}} <: CTModels.AbstractConstraintsModel

Fields

• path_nl::Tuple

• boundary_nl::Tuple

• state_box::Tuple

• control_box::Tuple

• variable_box::Tuple

• dict::Dict{Symbol, Tuple{Symbol, Union{Function, OrdinalRange{<:Int64}}, AbstractVector{<:Real}, AbstractVector{<:Real}}}

struct ControlModel <: CTModels.AbstractControlModel

Fields

• name::String

• components::Vector{String}

struct ControlModelSolution{TS<:Function} <: CTModels.AbstractControlModel

Fields

• name::String

• components::Vector{String}

• value::Function

struct DualModel{PC<:Function, PC_Dual<:Function, BC<:(AbstractVector{<:Real}), BC_Dual<:(AbstractVector{<:Real}), SC_LB_Dual<:Function, SC_UB_Dual<:Function, CC_LB_Dual<:Function, CC_UB_Dual<:Function, VC_LB_Dual<:(AbstractVector{<:Real}), VC_UB_Dual<:(AbstractVector{<:Real})} <: CTModels.AbstractDualModel

Fields

• path_constraints::Function

• path_constraints_dual::Function

• boundary_constraints::AbstractVector{<:Real}

• boundary_constraints_dual::AbstractVector{<:Real}

• state_constraints_lb_dual::Function

• state_constraints_ub_dual::Function

• control_constraints_lb_dual::Function

• control_constraints_ub_dual::Function

• variable_constraints_lb_dual::AbstractVector{<:Real}

• variable_constraints_ub_dual::AbstractVector{<:Real}

struct EmptyTimeGridModel <: CTModels.AbstractTimeGridModel

Fields

struct EmptyVariableModel <: CTModels.AbstractVariableModel

Fields

struct FixedTimeModel{T<:Real} <: CTModels.AbstractTimeModel

Fields

• time::Real

• name::String

struct FreeTimeModel <: CTModels.AbstractTimeModel

Fields

• index::Int64

• name::String

Initial guess for OCP, contains

• functions of time for the state and control variables
• vector for optimization variables

Initialization data for each field can be left to default or:

• vector for optimization variables
• constant / vector / function for state and control
• existing solution ('warm start') for all fields

Constructors:

• Init(): default initialization
• Init(state, control, variable, time): constant vector, function handles and / or matrices / vectors interpolated along given time grid
• Init(sol): from existing solution

Examples

julia> init = Init()
julia> init = Init(state=[0.1, 0.2], control=0.3)
julia> init = Init(state=[0.1, 0.2], control=0.3, variable=0.5)
julia> init = Init(state=[0.1, 0.2], controlt=t->sin(t), variable=0.5)
julia> init = Init(state=[[0, 0], [1, 2], [5, -1]], time=[0, .3, 1.], controlt=t->sin(t))
julia> init = Init(sol)

struct LagrangeObjectiveModel{TL<:Function} <: CTModels.AbstractObjectiveModel

Fields

• lagrange::Function

• criterion::Symbol

struct MayerObjectiveModel{TM<:Function} <: CTModels.AbstractObjectiveModel

Fields

• mayer::Function

• criterion::Symbol

struct Model{TimesModelType<:CTModels.AbstractTimesModel, StateModelType<:CTModels.AbstractStateModel, ControlModelType<:CTModels.AbstractControlModel, VariableModelType<:CTModels.AbstractVariableModel, DynamicsModelType<:Function, ObjectiveModelType<:CTModels.AbstractObjectiveModel, ConstraintsModelType<:CTModels.AbstractConstraintsModel} <: CTModels.AbstractModel

Fields

• times::CTModels.AbstractTimesModel

• state::CTModels.AbstractStateModel

• control::CTModels.AbstractControlModel

• variable::CTModels.AbstractVariableModel

• dynamics::Function

• objective::CTModels.AbstractObjectiveModel

• constraints::CTModels.AbstractConstraintsModel

• definition::Expr

mutable struct PreModel <: CTModels.AbstractModel

Fields

• times::Union{Nothing, CTModels.AbstractTimesModel}: Default: nothing

• state::Union{Nothing, CTModels.AbstractStateModel}: Default: nothing

• control::Union{Nothing, CTModels.AbstractControlModel}: Default: nothing

• variable::CTModels.AbstractVariableModel: Default: EmptyVariableModel()

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

• objective::Union{Nothing, CTModels.AbstractObjectiveModel}: Default: nothing

• constraints::Dict{Symbol, Tuple{Symbol, Union{Function, OrdinalRange{<:Int64}}, AbstractVector{<:Real}, AbstractVector{<:Real}}}: Default: ConstraintsDictType()

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

struct Solution{TimeGridModelType<:CTModels.AbstractTimeGridModel, TimesModelType<:CTModels.AbstractTimesModel, StateModelType<:CTModels.AbstractStateModel, ControlModelType<:CTModels.AbstractControlModel, VariableModelType<:CTModels.AbstractVariableModel, CostateModelType<:Function, ObjectiveValueType<:Real, DualModelType<:CTModels.AbstractDualModel, SolverInfosType<:CTModels.AbstractSolverInfos} <: CTModels.AbstractSolution

Fields

• time_grid::CTModels.AbstractTimeGridModel

• times::CTModels.AbstractTimesModel

• state::CTModels.AbstractStateModel

• control::CTModels.AbstractControlModel

• variable::CTModels.AbstractVariableModel

• costate::Function

• objective::Real

• dual::CTModels.AbstractDualModel

• solver_infos::CTModels.AbstractSolverInfos

struct SolverInfos{TI<:Dict{Symbol, Any}} <: CTModels.AbstractSolverInfos

Fields

• iterations::Int64

• stopping::Symbol

• message::String

• success::Bool

• constraints_violation::Float64

• infos::Dict{Symbol, Any}

struct StateModel <: CTModels.AbstractStateModel

Fields

• name::String

• components::Vector{String}

struct StateModelSolution{TS<:Function} <: CTModels.AbstractStateModel

Fields

• name::String

• components::Vector{String}

• value::Function

struct TimeGridModel{T<:Union{StepRangeLen, AbstractVector{<:Real}}} <: CTModels.AbstractTimeGridModel

Fields

• value::Union{StepRangeLen, AbstractVector{<:Real}}

struct TimesModel{TI<:CTModels.AbstractTimeModel, TF<:CTModels.AbstractTimeModel} <: CTModels.AbstractTimesModel

Fields

• initial::CTModels.AbstractTimeModel

• final::CTModels.AbstractTimeModel

• time_name::String

struct VariableModel <: CTModels.AbstractVariableModel

Fields

• name::String

• components::Vector{String}

struct VariableModelSolution{TS<:Union{Real, AbstractVector{<:Real}}} <: CTModels.AbstractVariableModel

Fields

• name::String

• components::Vector{String}

• value::Union{Real, AbstractVector{<:Real}}

isempty(model::CTModels.ConstraintsModel) -> Bool

Return if the constraints model is not empty.

show(
    io::IO,
    _::MIME{Symbol("text/plain")},
    ocp::CTModels.Model
)

Print the optimal control problem.

show(
    io::IO,
    _::MIME{Symbol("text/plain")},
    ocp::CTModels.PreModel
)

Print the optimal control problem.

show(
    io::IO,
    _::MIME{Symbol("text/plain")},
    sol::CTModels.Solution
)

Prints the solution.

__constraint!(
    ocp_constraints::Dict{Symbol, Tuple{Symbol, Union{Function, OrdinalRange{<:Int64}}, AbstractVector{<:Real}, AbstractVector{<:Real}}},
    type::Symbol,
    n::Int64,
    m::Int64,
    q::Int64;
    rg,
    f,
    lb,
    ub,
    label
)

Add a constraint to a dictionary of constraints.

__constraint_label() -> Symbol

Used to set the default value of the label of a constraint. A unique value is given to each constraint using the gensym function and prefixing by :unamed.

__control_components(
    m::Int64,
    name::String
) -> Vector{String}

Used to set the default value of the names of the controls. The default value is ["u"] for a one dimensional control, and ["u₁", "u₂", ...] for a multi dimensional control.

__control_name() -> String

Used to set the default value of the names of the control. The default value is "u".

__criterion_type() -> Symbol

Used to set the default value of the type of criterion. Either :min or :max. The default value is :min. The other possible criterion type is :max.

__is_consistent(ocp::CTModels.PreModel) -> Bool

__is_control_set(ocp::CTModels.Model) -> Bool

__is_control_set(ocp::CTModels.PreModel) -> Bool

__is_definition_set(ocp::CTModels.Model) -> Bool

__is_definition_set(ocp::CTModels.PreModel) -> Bool

__is_dynamics_set(ocp::CTModels.Model) -> Bool

__is_dynamics_set(ocp::CTModels.PreModel) -> Bool

__is_empty(ocp::CTModels.PreModel) -> Bool

__is_objective_set(ocp::CTModels.Model) -> Bool

__is_objective_set(ocp::CTModels.PreModel) -> Bool

__is_state_set(ocp::CTModels.Model) -> Bool

__is_state_set(ocp::CTModels.PreModel) -> Bool

__is_times_set(ocp::CTModels.Model) -> Bool

__is_times_set(ocp::CTModels.PreModel) -> Bool

__is_variable_set(ocp::CTModels.Model) -> Bool

__is_variable_set(ocp::CTModels.PreModel) -> Bool

__state_components(n::Int64, name::String) -> Vector{String}

Used to set the default value of the names of the states. The default value is ["x"] for a one dimensional state, and ["x₁", "x₂", ...] for a multi dimensional state.

__state_name() -> String

Used to set the default value of the name of the state. The default value is "x".

__time_name() -> String

Used to set the default value of the name of the time. The default value is t.

__variable_components(
    q::Int64,
    name::String
) -> Vector{String}

Used to set the default value of the names of the variables. The default value is ["v"] for a one dimensional variable, and ["v₁", "v₂", ...] for a multi dimensional variable.

__variable_name(q::Int64) -> String

Used to set the default value of the names of the variables. The default value is "v".

boundary_constraints(
    sol::CTModels.Solution
) -> AbstractVector{<:Real}

Return the boundary constraints of the optimal control solution.

boundary_constraints_dual(
    sol::CTModels.Solution
) -> AbstractVector{<:Real}

Return the dual of the boundary constraints of the optimal control solution.

boundary_constraints_nl(
    model::CTModels.ConstraintsModel{<:Tuple, TB}
) -> Any

Get the nonlinear boundary constraints from the model.

boundary_constraints_nl(
    ocp::CTModels.Model{<:CTModels.TimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.AbstractObjectiveModel, <:CTModels.ConstraintsModel{<:Tuple, TB<:Tuple}}
) -> Any

Get the nonlinear boundary constraints from the model.

buildFunctionalInit(data, time, dim) -> CTModels.var"#14#15"

Build functional initialization: general interpolation case

buildFunctionalInit(
    data::Function,
    time,
    dim
) -> CTModels.var"#16#17"{<:Function}

Build functional initialization: function case

buildFunctionalInit(
    data::Nothing,
    time,
    dim
) -> CTModels.var"#14#15"

Build functional initialization: default case

buildFunctionalInit(
    data::Union{Real, AbstractVector{<:Real}},
    time,
    dim
) -> Union{CTModels.var"#18#20", CTModels.var"#19#21"}

Build functional initialization: constant / 1D interpolation

buildVectorInit(data, dim) -> Any

Build vector initialization: default / vector case

build_constraints(
    constraints::Dict{Symbol, Tuple{Symbol, Union{Function, OrdinalRange{<:Int64}}, AbstractVector{<:Real}, AbstractVector{<:Real}}}
) -> CTModels.ConstraintsModel{TP, TB, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Dict{Symbol, Tuple{Symbol, Union{Function, OrdinalRange{<:Int64}}, AbstractVector{<:Real}, AbstractVector{<:Real}}}} where {TP<:Tuple{Vector{Real}, Any, Vector{Real}}, TB<:Tuple{Vector{Real}, Any, Vector{Real}}}

Build a concrete type constraints model from a dictionary of constraints.

build_model(
    pre_ocp::CTModels.PreModel
) -> CTModels.Model{TimesModelType, StateModelType, ControlModelType, VariableModelType, DynamicsModelType, ObjectiveModelType, ConstraintsModelType} where {TimesModelType<:CTModels.AbstractTimesModel, StateModelType<:CTModels.AbstractStateModel, ControlModelType<:CTModels.AbstractControlModel, VariableModelType<:CTModels.AbstractVariableModel, DynamicsModelType<:Function, ObjectiveModelType<:CTModels.AbstractObjectiveModel, ConstraintsModelType<:(CTModels.ConstraintsModel{TP, TB, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Tuple{Vector{Real}, Vector{Int64}, Vector{Real}}, Dict{Symbol, Tuple{Symbol, Union{Function, OrdinalRange{<:Int64}}, AbstractVector{<:Real}, AbstractVector{<:Real}}}} where {TP<:Tuple{Vector{Real}, Any, Vector{Real}}, TB<:Tuple{Vector{Real}, Any, Vector{Real}}})}

Build a concrete type model from a pre-model.

build_solution(
    ocp::CTModels.Model,
    T::Vector{Float64},
    X::Union{Function, Matrix{Float64}},
    U::Union{Function, Matrix{Float64}},
    v::Vector{Float64},
    P::Union{Function, Matrix{Float64}};
    objective,
    iterations,
    constraints_violation,
    message,
    stopping,
    success,
    path_constraints,
    path_constraints_dual,
    boundary_constraints,
    boundary_constraints_dual,
    state_constraints_lb_dual,
    state_constraints_ub_dual,
    control_constraints_lb_dual,
    control_constraints_ub_dual,
    variable_constraints_lb_dual,
    variable_constraints_ub_dual
)

Build a solution from the optimal control problem, the time grid, the state, control, variable, and dual variables.

Arguments

• ocp::Model: the optimal control problem.
• T::Vector{Float64}: the time grid.
• X::Matrix{Float64}: the state trajectory.
• U::Matrix{Float64}: the control trajectory.
• v::Vector{Float64}: the variable trajectory.
• P::Matrix{Float64}: the costate trajectory.
• objective::Float64: the objective value.
• iterations::Int: the number of iterations.
• constraints_violation::Float64: the constraints violation.
• message::String: the message associated to the stopping criterion.
• stopping::Symbol: the stopping criterion.
• success::Bool: the success status.
• path_constraints::Matrix{Float64}: the path constraints.
• path_constraints_dual::Matrix{Float64}: the dual of the path constraints.
• boundary_constraints::Vector{Float64}: the boundary constraints.
• boundary_constraints_dual::Vector{Float64}: the dual of the boundary constraints.
• state_constraints_lb_dual::Matrix{Float64}: the lower bound dual of the state constraints.
• state_constraints_ub_dual::Matrix{Float64}: the upper bound dual of the state constraints.
• control_constraints_lb_dual::Matrix{Float64}: the lower bound dual of the control constraints.
• control_constraints_ub_dual::Matrix{Float64}: the upper bound dual of the control constraints.
• variable_constraints_lb_dual::Vector{Float64}: the lower bound dual of the variable constraints.
• variable_constraints_ub_dual::Vector{Float64}: the upper bound dual of the variable constraints.

Returns

• sol::Solution: the optimal control solution.

checkDim(actual_dim, target_dim)

Check if actual dimension is equal to target dimension, error otherwise

components(
    model::CTModels.ControlModelSolution
) -> Vector{String}

Get the components names of the control from the model solution.

components(model::CTModels.ControlModel) -> Vector{String}

Get the components names of the control from the model.

components(_::CTModels.EmptyVariableModel) -> Vector{String}

Get the components names of the variable from the empty variable model. Return an empty vector.

components(
    model::CTModels.StateModelSolution
) -> Vector{String}

Get the components names of the state from the state model solution.

components(model::CTModels.StateModel) -> Vector{String}

Get the components names of the state from the state model.

components(
    model::CTModels.VariableModelSolution
) -> Vector{String}

Get the components names of the variable from the variable model solution.

components(model::CTModels.VariableModel) -> Vector{String}

Get the components names of the variable from the variable model.

constraint!(
    ocp::CTModels.PreModel,
    type::Symbol;
    rg,
    f,
    lb,
    ub,
    label
)

Add a constraint to a pre-model.

constraint(ocp::CTModels.Model, label::Symbol) -> Tuple

Get a labelled constraint from the model.

constraints(
    ocp::CTModels.Model{<:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.AbstractObjectiveModel, C<:CTModels.AbstractConstraintsModel}
) -> CTModels.AbstractConstraintsModel

Get the constraints from the model.

constraints_violation(sol::CTModels.Solution) -> Float64

Return the constraints violation of the optimal control solution.

control!(ocp::CTModels.PreModel, m::Int64)
control!(
    ocp::CTModels.PreModel,
    m::Int64,
    name::Union{String, Symbol}
)
control!(
    ocp::CTModels.PreModel,
    m::Int64,
    name::Union{String, Symbol},
    components_names::Array{T2<:Union{String, Symbol}, 1}
)

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

Examples

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

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

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

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

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

julia> control!(ocp, 2, "v", ["a", "b"])
julia> control_dimension(ocp)
2
julia> control_components(ocp)
["a", "b"]

julia> control!(ocp, 2, "v", [:a, :b])
julia> control_dimension(ocp)
2
julia> control_components(ocp)
["a", "b"]

control(
    ocp::CTModels.Model{<:CTModels.TimesModel, <:CTModels.AbstractStateModel, T<:CTModels.AbstractControlModel}
) -> CTModels.AbstractControlModel

Get the control from the model.

control(
    sol::CTModels.Solution{<:CTModels.AbstractTimeGridModel, <:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.ControlModelSolution{TS<:Function}}
) -> Function

Return the control (function of time) of the optimal control solution.

julia> t0 = time_grid(sol)[1]
julia> u  = control(sol)
julia> u0 = u(t0) # control at initial time

control_components(ocp::CTModels.Model) -> Vector{String}

Get the components names of the control from the model.

control_components(sol::CTModels.Solution) -> Vector{String}

Return the names of the components of the control of the optimal control solution.

control_constraints_box(
    model::CTModels.ConstraintsModel{<:Tuple, <:Tuple, <:Tuple, TC}
) -> Any

Get the control box constraints from the model.

control_constraints_box(
    ocp::CTModels.Model{<:CTModels.TimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.AbstractObjectiveModel, <:CTModels.ConstraintsModel{<:Tuple, <:Tuple, <:Tuple, TC<:Tuple}}
) -> Any

Get the box constraints on control from the model.

control_constraints_lb_dual(
    sol::CTModels.Solution
) -> Function

Return the lower bound dual of the control constraints of the optimal control solution.

control_constraints_ub_dual(
    sol::CTModels.Solution
) -> Function

Return the upper bound dual of the control constraints of the optimal control solution.

control_dimension(ocp::CTModels.Model) -> Int64

Get the control dimension from the model.

control_dimension(sol::CTModels.Solution) -> Int64

Return the dimension of the control of the optimal control solution.

control_discretized(sol::CTModels.Solution) -> Any

Return the control values at times time_grid(sol) of the optimal control solution or nothing.

julia> u  = control_discretized(sol)
julia> u0 = u[1] # control at initial time

control_name(ocp::CTModels.Model) -> String

Get the name of the control from the model.

control_name(sol::CTModels.Solution) -> String

Return the name of the control of the optimal control solution.

costate(
    sol::CTModels.Solution{<:CTModels.AbstractTimeGridModel, <:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, Co<:Function}
) -> Function

Return the costate of the optimal control solution.

julia> t0 = time_grid(sol)[1]
julia> p  = costate(sol)
julia> p0 = p(t0)

costate_discretized(sol::CTModels.Solution) -> Any

Return the costate values at times time_grid(sol) of the optimal control solution or nothing.

julia> p  = costate_discretized(sol)
julia> p0 = p[1] # costate at initial time

criterion(model::CTModels.BolzaObjectiveModel) -> Symbol

Get the criterion (:min or :max) of the Bolza objective model.

criterion(model::CTModels.LagrangeObjectiveModel) -> Symbol

Get the criterion (:min or :max) of the Lagrange objective model.

criterion(model::CTModels.MayerObjectiveModel) -> Symbol

Get the criterion (:min or :max) of the Mayer objective model.

criterion(ocp::CTModels.Model) -> Symbol

Get the type of criterion (:min or :max) from the model.

ctinterpolate(x, f) -> Any

Return the interpolation of f at x.

definition!(ocp::CTModels.PreModel, definition::Expr)

Set the model definition of the optimal control problem.

definition(ocp::CTModels.Model) -> Expr

Return the model definition of the optimal control problem.

definition(ocp::CTModels.PreModel) -> Union{Nothing, Expr}

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

dim_boundary_constraints_nl(
    model::CTModels.ConstraintsModel
) -> Int64

Return the dimension of nonlinear boundary constraints.

dim_boundary_constraints_nl(ocp::CTModels.Model) -> Int64

Return the dimension of the boundary constraints.

dim_control_constraints_box(
    model::CTModels.ConstraintsModel
) -> Int64

Return the dimension of control box constraints.

dim_control_constraints_box(ocp::CTModels.Model) -> Int64

Return the dimension of box constraints on control.

dim_path_constraints_nl(
    model::CTModels.ConstraintsModel
) -> Int64

Return the dimension of nonlinear path constraints.

dim_path_constraints_nl(ocp::CTModels.Model) -> Int64

Return the dimension of nonlinear path constraints.

dim_state_constraints_box(
    model::CTModels.ConstraintsModel
) -> Int64

Return the dimension of state box constraints.

dim_state_constraints_box(ocp::CTModels.Model) -> Int64

Return the dimension of box constraints on state.

dim_variable_constraints_box(
    model::CTModels.ConstraintsModel
) -> Int64

Return the dimension of variable box constraints.

dim_variable_constraints_box(ocp::CTModels.Model) -> Int64

Return the dimension of box constraints on variable.

dimension(model::CTModels.ControlModelSolution) -> Int64

Get the control dimension from the model solution.

dimension(model::CTModels.ControlModel) -> Int64

Get the control dimension from the model.

dimension(_::CTModels.EmptyVariableModel) -> Int64

Get the variable dimension from the empty variable model. Return 0.

dimension(model::CTModels.StateModelSolution) -> Int64

Get the dimension of the state from the state model solution.

dimension(model::CTModels.StateModel) -> Int64

Get the dimension of the state from the state model.

dimension(model::CTModels.VariableModelSolution) -> Int64

Get the variable dimension from the variable model solution.

dimension(model::CTModels.VariableModel) -> Int64

Get the variable dimension from the variable model.

dynamics!(ocp::CTModels.PreModel, f::Function)

Set the dynamics of the optimal control problem, in a pre-model.

dynamics(
    ocp::CTModels.Model{<:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, D<:Function}
) -> Function

Get the dynamics from the model.

final(
    model::CTModels.TimesModel{<:CTModels.AbstractTimeModel, TF<:CTModels.AbstractTimeModel}
) -> CTModels.AbstractTimeModel

Get the final time from the times model.

final_time(
    ocp::CTModels.Model{<:CTModels.TimesModel{<:CTModels.AbstractTimeModel, CTModels.FixedTimeModel{T<:Real}}}
) -> Real

Get the final time from the model, for a fixed final time.

final_time(
    model::CTModels.TimesModel{<:CTModels.AbstractTimeModel, <:CTModels.FixedTimeModel{T<:Real}}
) -> Real

Get the final time from the times model, from a fixed final time model.

final_time(
    ocp::CTModels.Model{<:CTModels.TimesModel{<:CTModels.AbstractTimeModel, CTModels.FreeTimeModel}},
    variable::AbstractArray{T<:Real, 1}
) -> Any

Get the final time from the model, for a free final time.

final_time(
    model::CTModels.TimesModel{<:CTModels.AbstractTimeModel, CTModels.FreeTimeModel},
    variable::AbstractArray{T<:Real, 1}
) -> Any

Get the final time from the times model, from a free final time model.

final_time_name(ocp::CTModels.Model) -> String

Get the name of the final time from the model.

final_time_name(sol::CTModels.Solution) -> String

Return the name of the final time of the optimal control solution.

final_time_name(model::CTModels.TimesModel) -> String

Get the name of the final time from the times model.

formatData(data) -> Any

Convert matrix to vector of vectors (could be expanded)

formatTimeGrid(time) -> Any

Convert matrix time-grid to vector

has_fixed_final_time(ocp::CTModels.Model) -> Bool

Check if the final time is fixed.

has_fixed_final_time(
    times::CTModels.TimesModel{<:CTModels.AbstractTimeModel, CTModels.FreeTimeModel}
) -> Bool

Check if the final time is free. Return false.

has_fixed_final_time(
    times::CTModels.TimesModel{<:CTModels.AbstractTimeModel, <:CTModels.FixedTimeModel{T<:Real}}
) -> Bool

Check if the final time is fixed. Return true.

has_fixed_initial_time(ocp::CTModels.Model) -> Bool

Check if the initial time is fixed.

has_fixed_initial_time(
    times::CTModels.TimesModel{CTModels.FreeTimeModel}
) -> Bool

Check if the initial time is free. Return false.

has_fixed_initial_time(
    times::CTModels.TimesModel{<:CTModels.FixedTimeModel{T<:Real}}
) -> Bool

Check if the initial time is fixed. Return true.

has_free_final_time(ocp::CTModels.Model) -> Bool

Check if the final time is free.

has_free_final_time(times::CTModels.TimesModel) -> Bool

Check if the final time is free.

has_free_initial_time(ocp::CTModels.Model) -> Bool

Check if the initial time is free.

has_free_initial_time(times::CTModels.TimesModel) -> Bool

Check if the final time is free.

has_lagrange_cost(
    model::CTModels.BolzaObjectiveModel
) -> Bool

Check if the Bolza objective model has a Lagrange function. Return true.

has_lagrange_cost(
    model::CTModels.LagrangeObjectiveModel
) -> Bool

Check if the Lagrange objective model has a Lagrange function. Return true.

has_lagrange_cost(
    model::CTModels.MayerObjectiveModel
) -> Bool

Check if the Mayer objective model has a Lagrange function. Return false.

has_lagrange_cost(ocp::CTModels.Model) -> Bool

Check if the model has a Lagrange cost.

has_mayer_cost(model::CTModels.BolzaObjectiveModel) -> Bool

Check if the Bolza objective model has a Mayer function. Return true.

has_mayer_cost(
    model::CTModels.LagrangeObjectiveModel
) -> Bool

Check if the Lagrange objective model has a Mayer function. Return false.

has_mayer_cost(model::CTModels.MayerObjectiveModel) -> Bool

Check if the Mayer objective model has a Mayer function. Return true.

has_mayer_cost(ocp::CTModels.Model) -> Bool

Check if the model has a Mayer cost.

index(model::CTModels.FreeTimeModel) -> Int64

Get the index of the time variable from the free time model.

infos(sol::CTModels.Solution) -> Dict{Symbol, Any}

Return a dictionary of additional infos depending on the solver or nothing.

initial(
    model::CTModels.TimesModel{TI<:CTModels.AbstractTimeModel}
) -> CTModels.AbstractTimeModel

Get the initial time from the times model.

initial_time(
    ocp::CTModels.Model{<:CTModels.TimesModel{CTModels.FixedTimeModel{T<:Real}}}
) -> Real

Get the initial time from the model, for a fixed initial time.

initial_time(
    model::CTModels.TimesModel{<:CTModels.FixedTimeModel{T<:Real}}
) -> Real

Get the initial time from the times model, from a fixed initial time model.

initial_time(
    ocp::CTModels.Model{<:CTModels.TimesModel{CTModels.FreeTimeModel}},
    variable::AbstractArray{T<:Real, 1}
) -> Any

Get the initial time from the model, for a free initial time.

initial_time(
    model::CTModels.TimesModel{CTModels.FreeTimeModel},
    variable::AbstractArray{T<:Real, 1}
) -> Any

Get the initial time from the times model, from a free initial time model.

initial_time_name(ocp::CTModels.Model) -> String

Get the name of the initial time from the model.

initial_time_name(sol::CTModels.Solution) -> String

Return the name of the initial time of the optimal control solution.

initial_time_name(model::CTModels.TimesModel) -> String

Get the name of the initial time from the times model.

is_empty_time_grid(sol::CTModels.Solution) -> Bool

Check if the time grid is empty from the solution.

isaVectVect(data) -> Bool

Return true if argument is a vector of vectors

isempty_constraints(ocp::CTModels.Model) -> Bool

Return if the constraints from the model are not empty.

iterations(sol::CTModels.Solution) -> Int64

Return the number of iterations (if solved by an iterative method) of the optimal control solution.

lagrange(
    model::CTModels.BolzaObjectiveModel{<:Function, L<:Function}
) -> Function

Get the Lagrange function of the Bolza objective model.

lagrange(
    model::CTModels.LagrangeObjectiveModel{L<:Function}
) -> Function

Get the Lagrange function of the Lagrange objective model.

lagrange(
    ocp::CTModels.Model{<:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.BolzaObjectiveModel{<:Function, L<:Function}}
) -> Any

Get the Lagrange cost from the model.

lagrange(
    ocp::CTModels.Model{<:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, CTModels.LagrangeObjectiveModel{L<:Function}}
) -> Function

Get the Lagrange cost from the model.

matrix2vec(x::Matrix{<:Real}) -> Vector{<:Vector{<:Real}}
matrix2vec(
    x::Matrix{<:Real},
    dim::Int64
) -> Vector{<:Vector{<:Real}}

Transforms x to a Vector{<:Vector{<:ctNumber}}.

Note. dim ∈ {1, 2} is the dimension along which the matrix is transformed.

mayer(
    model::CTModels.BolzaObjectiveModel{M<:Function}
) -> Function

Get the Mayer function of the Bolza objective model.

mayer(
    model::CTModels.MayerObjectiveModel{M<:Function}
) -> Function

Get the Mayer function of the Mayer objective model.

mayer(
    ocp::CTModels.Model{<:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.BolzaObjectiveModel{M<:Function}}
) -> Any

Get the Mayer cost from the model.

mayer(
    ocp::CTModels.Model{<:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.MayerObjectiveModel{M<:Function}}
) -> Any

Get the Mayer cost from the model.

message(sol::CTModels.Solution) -> String

Return the message associated to the stopping criterion of the optimal control solution.

name(model::CTModels.ControlModelSolution) -> String

Get the name of the control from the model solution.

name(model::CTModels.ControlModel) -> String

Get the name of the control from the model.

name(_::CTModels.EmptyVariableModel) -> String

Get the variable name from the empty variable model. Return an empty string.

name(model::CTModels.FixedTimeModel) -> String

Get the name of the time from the fixed time model.

name(model::CTModels.FreeTimeModel) -> String

Get the name of the time from the free time model.

name(model::CTModels.StateModelSolution) -> String

Get the name of the state from the state model solution.

name(model::CTModels.StateModel) -> String

Get the name of the state from the state model.

name(model::CTModels.VariableModelSolution) -> String

Get the variable name from the variable model solution.

name(model::CTModels.VariableModel) -> String

Get the variable name from the variable model.

objective!(ocp::CTModels.PreModel; ...)
objective!(
    ocp::CTModels.PreModel,
    criterion::Symbol;
    mayer,
    lagrange
)

Set the objective of the optimal control problem.

Arguments

• ocp::PreModel: the optimal control problem.
• criterion::Symbol: the type of criterion. Either :min or :max. Default is :min.
• mayer::Union{Function, Nothing}: the Mayer function (inplace). Default is nothing.
• lagrange::Union{Function, Nothing}: the Lagrange function (inplace). Default is nothing.

Examples

```@example julia> function mayer(x0, xf, v) return x0[1] + xf[1] + v[1] end juila> function lagrange(t, x, u, v) return x[1] + u[1] + v[1] end julia> objective!(ocp, :min, mayer=mayer, lagrange=lagrange)

objective(
    ocp::CTModels.Model{<:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, O<:CTModels.AbstractObjectiveModel}
) -> CTModels.AbstractObjectiveModel

Get the objective from the model.

objective(
    sol::CTModels.Solution{<:CTModels.AbstractTimeGridModel, <:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, O<:Real}
) -> Real

Return the objective value of the optimal control solution.

path_constraints(sol::CTModels.Solution) -> Function

Return the path constraints of the optimal control solution.

path_constraints_dual(sol::CTModels.Solution) -> Function

Return the dual of the path constraints of the optimal control solution.

path_constraints_nl(
    model::CTModels.ConstraintsModel{TP}
) -> Any

Get the nonlinear path constraints from the model.

path_constraints_nl(
    ocp::CTModels.Model{<:CTModels.TimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.AbstractObjectiveModel, <:CTModels.ConstraintsModel{TP<:Tuple}}
) -> Any

Get the nonlinear path constraints from the model.

state!(ocp::CTModels.PreModel, n::Int64)
state!(
    ocp::CTModels.PreModel,
    n::Int64,
    name::Union{String, Symbol}
)
state!(
    ocp::CTModels.PreModel,
    n::Int64,
    name::Union{String, Symbol},
    components_names::Array{T2<:Union{String, Symbol}, 1}
)

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

Examples

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

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

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

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

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

julia> state!(ocp, 2, "y", ["u", "v"])
julia> state_dimension(ocp)
2
julia> state_components(ocp)
["u", "v"]

julia> state!(ocp, 2, "y", [:u, :v])
julia> state_dimension(ocp)
2
julia> state_components(ocp)
["u", "v"]

state(
    ocp::CTModels.Model{<:CTModels.TimesModel, T<:CTModels.AbstractStateModel}
) -> CTModels.AbstractStateModel

Get the state from the model.

state(
    sol::CTModels.Solution{<:CTModels.AbstractTimeGridModel, <:CTModels.AbstractTimesModel, <:CTModels.StateModelSolution{TS<:Function}}
) -> Function

Return the state (function of time) of the optimal control solution.

julia> t0 = time_grid(sol)[1]
julia> x  = state(sol)
julia> x0 = x(t0)

state_components(ocp::CTModels.Model) -> Vector{String}

Get the components names of the state from the model.

state_components(sol::CTModels.Solution) -> Vector{String}

Return the names of the components of the state of the optimal control solution.

state_constraints_box(
    model::CTModels.ConstraintsModel{<:Tuple, <:Tuple, TS}
) -> Any

Get the state box constraints from the model.

state_constraints_box(
    ocp::CTModels.Model{<:CTModels.TimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.AbstractObjectiveModel, <:CTModels.ConstraintsModel{<:Tuple, <:Tuple, TS<:Tuple}}
) -> Any

Get the box constraints on state from the model.

state_constraints_lb_dual(
    sol::CTModels.Solution
) -> Function

Return the lower bound dual of the state constraints of the optimal control solution.

state_constraints_ub_dual(
    sol::CTModels.Solution
) -> Function

Return the upper bound dual of the state constraints of the optimal control solution.

state_dimension(ocp::CTModels.Model) -> Int64

Get the state dimension from the model.

state_dimension(sol::CTModels.Solution) -> Int64

Return the dimension of the state of the optimal control solution.

state_discretized(sol::CTModels.Solution) -> Any

Return the state values at times time_grid(sol) of the optimal control solution or nothing.

julia> x  = state_discretized(sol)
julia> x0 = x[1] # state at initial time

state_name(ocp::CTModels.Model) -> String

Get the name of the state from the model.

state_name(sol::CTModels.Solution) -> String

Return the name of the state of the optimal control solution.

stopping(sol::CTModels.Solution) -> Symbol

Return the stopping criterion (a Symbol) of the optimal control solution.

success(sol::CTModels.Solution) -> Bool

Return the success status of the optimal control solution.

time!(ocp::CTModels.PreModel; t0, tf, ind0, indf, time_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  

time(model::CTModels.FixedTimeModel{T<:Real}) -> Real

Get the time from the fixed time model.

time(
    model::CTModels.FreeTimeModel,
    variable::AbstractArray{T<:Real, 1}
) -> Any

Get the time from the free time model.

Exceptions

• If the index of the time variable is not in [1, length(variable)], throw an error.

time_grid(
    sol::CTModels.Solution{<:CTModels.TimeGridModel{T<:Union{StepRangeLen, AbstractVector{<:Real}}}}
) -> Union{StepRangeLen, AbstractVector{<:Real}}

Return the time grid of the optimal control solution.

time_name(ocp::CTModels.Model) -> String

Get the name of the time from the model.

time_name(sol::CTModels.Solution) -> String

Return the name of the time component of the optimal control solution.

time_name(model::CTModels.TimesModel) -> String

Get the name of the time variable from the times model.

times(
    ocp::CTModels.Model{T<:CTModels.TimesModel}
) -> CTModels.TimesModel

Get the times from the model.

value(
    model::CTModels.ControlModelSolution{TS<:Function}
) -> Function

Get the control function value from the model solution.

value(
    model::CTModels.StateModelSolution{TS<:Function}
) -> Function

Get the state function from the state model solution.

value(
    model::CTModels.VariableModelSolution{TS<:Union{Real, AbstractVector{<:Real}}}
) -> Union{Real, AbstractVector{<:Real}}

Get the variable from the variable model solution.

variable!(ocp::CTModels.PreModel, q::Int64)
variable!(
    ocp::CTModels.PreModel,
    q::Int64,
    name::Union{String, Symbol}
)
variable!(
    ocp::CTModels.PreModel,
    q::Int64,
    name::Union{String, Symbol},
    components_names::Array{T2<:Union{String, Symbol}, 1}
)

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

Examples

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

variable(
    ocp::CTModels.Model{<:CTModels.TimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, T<:CTModels.AbstractVariableModel}
) -> CTModels.AbstractVariableModel

Get the variable from the model.

variable(
    sol::CTModels.Solution{<:CTModels.AbstractTimeGridModel, <:CTModels.AbstractTimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.VariableModelSolution{TS<:Union{Real, AbstractVector{<:Real}}}}
) -> Union{Real, AbstractVector{<:Real}}

Return the variable of the optimal control solution or nothing.

julia> v  = variable(sol)

variable_components(ocp::CTModels.Model) -> Vector{String}

Get the components names of the variable from the model.

variable_components(
    sol::CTModels.Solution
) -> Vector{String}

Return the names of the components of the variable of the optimal control solution.

variable_constraints_box(
    model::CTModels.ConstraintsModel{<:Tuple, <:Tuple, <:Tuple, <:Tuple, TV}
) -> Any

Get the variable box constraints from the model.

variable_constraints_box(
    ocp::CTModels.Model{<:CTModels.TimesModel, <:CTModels.AbstractStateModel, <:CTModels.AbstractControlModel, <:CTModels.AbstractVariableModel, <:Function, <:CTModels.AbstractObjectiveModel, <:CTModels.ConstraintsModel{<:Tuple, <:Tuple, <:Tuple, <:Tuple, TV<:Tuple}}
) -> Any

Get the box constraints on variable from the model.

variable_constraints_lb_dual(
    sol::CTModels.Solution
) -> AbstractVector{<:Real}

Return the lower bound dual of the variable constraints of the optimal control solution.

variable_constraints_ub_dual(
    sol::CTModels.Solution
) -> AbstractVector{<:Real}

Return the upper bound dual of the variable constraints of the optimal control solution.

variable_dimension(ocp::CTModels.Model) -> Int64

Get the variable dimension from the model.

variable_dimension(sol::CTModels.Solution) -> Int64

Return the dimension of the variable of the optimal control solution.

variable_name(ocp::CTModels.Model) -> String

Get the name of the variable from the model.

variable_name(sol::CTModels.Solution) -> String

Return the name of the variable of the optimal control solution.