Private API

mutable struct DOCP{D<:CTDirect.Discretization, O<:CTModels.OCP.Model}

Struct representing a discretized optimal control problem (DOCP).

Fields

• discretization::D: The discretization scheme.
• ocp::O: The original OCP model.
• flags::DOCPFlags: Boolean flags describing problem structure.
• dims::DOCPdims: Problem dimensions.
• time::DOCPtime: Time discretization.
• bounds::DOCPbounds: Variable and constraint bounds.
• dim_NLP_variables::Int: Number of NLP variables.
• dim_NLP_constraints::Int: Number of NLP constraints.

Example

julia> DOCP(ocp, nlp_model_backend)
DOCP{...}(...)

struct DOCPFlags

Internal struct holding boolean flags that characterize properties of the discretized optimal control problem (DOCP).

Fields

• freet0::Bool: Whether the OCP has a free initial time.
• freetf::Bool: Whether the OCP has a free final time.
• lagrange::Bool: Whether the OCP includes a Lagrange cost.
• mayer::Bool: Whether the OCP includes a Mayer cost.
• max::Bool: Whether the OCP is a maximization problem.

Example

julia> DOCPFlags(true, false, true, true, false)
DOCPFlags(true, false, true, true, false)

DOCP_constraints!(c, xu, docp::CTDirect.DOCP) -> Any

Compute the nonlinear constraints of a DOCP.

The constraints are modeled as lb <= C(x) <= ub.

Arguments

• c: Preallocated constraint vector.
• xu: Vector of NLP decision variables.
• docp::DOCP: The discretized OCP.

Returns

• c: The filled constraint vector.

Example

julia> DOCP_constraints!(zeros(docp.dim_NLP_constraints), xu, docp)
[0.0, 0.1, …]

DOCP_initial_guess(
    docp::CTDirect.DOCP,
    init::CTModels.Init.InitialGuess
) -> Vector{Float64}

Build an initial guess vector for the discretized OCP.

Arguments

• docp::DOCP: The discretized OCP.
• init::CTModels.Init: Initialization settings (default: CTModels.Init()).

Returns

• NLP_X::Vector{Float64}: Initial guess vector.

Example

julia> DOCP_initial_guess(docp)
[0.1, 0.1, …]

DOCP_objective(xu, docp::CTDirect.DOCP) -> Any

Compute the objective value of a discretized OCP.

Arguments

• xu: Vector of NLP decision variables.
• docp::DOCP: The discretized OCP.

Returns

• obj::Float64: Objective function value.

Example

julia> DOCP_objective(xu, docp)
12.34

struct DOCPbounds

Internal struct holding variable and constraint bounds for a DOCP.

Fields

• var_l::Vector{Float64}: Lower bounds for NLP variables.
• var_u::Vector{Float64}: Upper bounds for NLP variables.
• con_l::Vector{Float64}: Lower bounds for NLP constraints.
• con_u::Vector{Float64}: Upper bounds for NLP constraints.

Example

julia> DOCPbounds([-1.0, -2.0], [1.0, 2.0], [0.0], [0.0])
DOCPbounds([-1.0, -2.0], [1.0, 2.0], [0.0], [0.0])

struct DOCPdims

Internal struct holding problem dimensions for a DOCP.

Fields

• NLP_x::Int: State dimension
• NLP_u::Int: Control dimension.
• NLP_v::Int: Variable dimension.
• path_cons::Int: Path constraints dimension.
• boundary_cons::Int: Boundary constraints dimension.

Example

julia> DOCPdims(4, 2, 1, 3, 2, 1)
DOCPdims(4, 2, 1, 3, 2, 1)

struct DOCPtime

Internal struct holding time grid information for a DOCP.

Fields

• steps::Int: Number of time steps.
• normalized_grid::Vector{Float64}: Normalized time grid in [0,1].
• fixed_grid::Vector{Float64}: Fixed time grid in [t0, tf].

Example

julia> DOCPtime(10, collect(0:0.1:1), collect(0.0:0.1:1.0))
DOCPtime(10, [0.0, 0.1, …, 1.0], [0.0, 0.1, …, 1.0])

build_OCP_solution(
    docp::CTDirect.DOCP,
    nlp_solution::SolverCore.AbstractExecutionStats,
    T,
    objective,
    iterations,
    constraints_violation,
    message,
    status,
    successful;
    exa_getter
) -> Union{CTModels.OCP.Solution{TimeGridModelType, TimesModelType, StateModelType, ControlModelType, VariableModelType, ModelType, CostateModelType, Float64, DualModelType, CTModels.OCP.SolverInfos{Any, Dict{Symbol, Any}}} where {TimeGridModelType<:Union{CTModels.OCP.MultipleTimeGridModel, CTModels.OCP.UnifiedTimeGridModel{Vector{Float64}}}, TimesModelType<:CTModels.OCP.TimesModel, StateModelType<:Union{CTModels.OCP.StateModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.StateModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, ControlModelType<:Union{CTModels.OCP.ControlModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.ControlModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, VariableModelType<:Union{CTModels.OCP.VariableModelSolution{Vector{Float64}}, CTModels.OCP.VariableModelSolution{Float64}}, ModelType<:(CTModels.OCP.Model{<:CTModels.OCP.TimeDependence, T} where T<:CTModels.OCP.TimesModel), CostateModelType<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, DualModelType<:(CTModels.OCP.DualModel{PC_Dual, Nothing, SC_LB_Dual, SC_UB_Dual, CC_LB_Dual, CC_UB_Dual, Vector{Float64}, Vector{Float64}} where {PC_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, SC_LB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, SC_UB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, CC_LB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, CC_UB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}})}, CTModels.OCP.Solution{TimeGridModelType, TimesModelType, StateModelType, ControlModelType, VariableModelType, ModelType, CostateModelType, Float64, DualModelType, CTModels.OCP.SolverInfos{Any, Dict{Symbol, Any}}} where {TimeGridModelType<:Union{CTModels.OCP.MultipleTimeGridModel, CTModels.OCP.UnifiedTimeGridModel{Vector{Float64}}}, TimesModelType<:CTModels.OCP.TimesModel, StateModelType<:Union{CTModels.OCP.StateModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.StateModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, ControlModelType<:Union{CTModels.OCP.ControlModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.ControlModelSolution{TS} where TS<:CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, VariableModelType<:Union{CTModels.OCP.VariableModelSolution{Vector{Float64}}, CTModels.OCP.VariableModelSolution{Float64}}, ModelType<:(CTModels.OCP.Model{<:CTModels.OCP.TimeDependence, T} where T<:CTModels.OCP.TimesModel), CostateModelType<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, DualModelType<:(CTModels.OCP.DualModel{PC_Dual, Vector{Float64}, SC_LB_Dual, SC_UB_Dual, CC_LB_Dual, CC_UB_Dual, Vector{Float64}, Vector{Float64}} where {PC_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, SC_LB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, SC_UB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, CC_LB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}, CC_UB_Dual<:Union{CTModels.OCP.var"#_wrap_scalar_and_deepcopy##0#_wrap_scalar_and_deepcopy##1", CTModels.OCP.var"#_wrap_scalar_and_deepcopy##2#_wrap_scalar_and_deepcopy##3"}})}}

Build an OCP functional solution from a DOCP discrete solution given as a SolverCore.AbstractExecutionStats object.

Arguments

• docp: The discretized optimal control problem (DOCP).
• nlp_solution: A solver execution statistics object.

Returns

• solution::CTModels.Solution: A functional OCP solution containing trajectories, multipliers, and solver information.

Example

julia> build_OCP_solution(docp, nlp_solution)
CTModels.Solution(...)

build_bounds_block(
    dim_var,
    dim_box,
    box_triplet
) -> Tuple{Any, Any}

Build lower and upper bound vectors for state, control, or optimization variables.

Arguments

• dim_var::Int: Variable dimension.
• dim_box::Int: Number of box constraints.
• box_triplet: Triplet defining box constraints.

Returns

• (x_lb, x_ub)::Tuple{Vector{Float64},Vector{Float64}}: Lower and upper bounds.

Example

julia> build_bounds_block(3, 1, ([0.0], [2], [1.0]))
([-Inf, 0.0, -Inf], [Inf, 1.0, Inf])

constraints_bounds!(
    docp::CTDirect.DOCP
) -> Tuple{Vector{Float64}, Vector{Float64}}

Build lower and upper bounds vectors for the nonlinear constraints of a DOCP.

Arguments

• docp::DOCP: The discretized OCP.

Returns

• (lb, ub)::Tuple{Vector{Float64},Vector{Float64}}: Lower and upper bounds.

Example

julia> constraints_bounds!(docp)
([-1.0, …], [1.0, …])

disc_model(docp::CTDirect.DOCP) -> CTDirect.Discretization

Return the discretization model associated with a given discretized optimal control problem (DOCP).

Arguments

• docp::DOCP: The discretized optimal control problem.

Returns

• discretization::Any: The discretization model stored in docp.

Example

julia> disc_model(docp)
DiscretizationModel(...)

get_time_grid(xu, docp::CTDirect.DOCP) -> Any

Return the time grid for problems with free initial or final times. Note that this function can be called during optimization, not just for postprocessing

Arguments

• xu: Vector of NLP decision variables.
• docp::DOCP: The discretized OCP.

Returns

• grid::Vector{Float64}: Time grid corresponding to current NLP variables.

Example

julia> get_time_grid(xu, docp)
[0.0, 0.1, …, 1.0]

get_time_grid_exa(
    nlp_solution::SolverCore.AbstractExecutionStats,
    docp::CTDirect.DOCP,
    exa_getter
) -> Vector{Float64}

Retrieve the time grid from the given DOCP solution.

Arguments

• nlp_solution: The DOCP solution.
• docp: The DOCP.

Returns

• ::Vector{Float64}: The time grid.

is_empty(t) -> Any

Check whether a collection t is empty or not defined.

Arguments

• t: Any object that may be nothing or support length.

Returns

• ::Bool: true if t is nothing or has length zero, otherwise false.

Example

julia> is_empty([])
true

julia> is_empty([1, 2, 3])
false

julia> is_empty(nothing)
true

ocp_model(docp::CTDirect.DOCP) -> CTModels.OCP.Model

Return the continuous-time optimal control problem (OCP) model associated with a given discretized optimal control problem (DOCP).

Arguments

• docp::DOCP: The discretized optimal control problem.

Returns

• ocp::Any: The underlying OCP model stored in docp.

Example

julia> ocp_model(docp)
OCPModel(...)

variables_bounds!(
    docp::CTDirect.DOCP
) -> Tuple{Vector{Float64}, Vector{Float64}}

Build lower and upper bounds vectors for the variable box constraints of a DOCP.

Arguments

• docp::DOCP: The discretized OCP.

Returns

• (var_l, var_u)::Tuple{Vector{Float64},Vector{Float64}}: Lower and upper bounds for variables.

Example

julia> variables_bounds!(docp)
([-Inf, …], [Inf, …])