Add a problem

To add a new problem to OptimalControlProblems, you should follow these steps:

1. Create a new file in the ext/MetaData directory with the name of your problem, containing the required information about the problem in a dictionary. For example, if your problem is called new_problem, create a file named new_problem.jl. The dictionary should follow the template:

new_problem_meta = OrderedDict(
    :name => "new_problem",             # Problem name
    :N => 100,                          # Number of steps
    :minimise => true,                  # Whether the objective is minimised (true) or maximised (false)
    :state_name => ["x1", "x2"],        # Names of the state components
    :costate_name => ["∂x1", "∂x2"],    # Names of the costate components (dual variables of the dynamics constraints)
    :control_name => ["u"],             # Names of the control components
    :variable_name => ["v"],            # Names of the optimisation variables
    :final_time => (:fixed, 1),         # Final time information
)

2. Define the DOCP OptimalControl model of the problem in a file named new_problem.jl in the ext/OptimalControlModels directory.

"""
    Documentation of the method
"""
function OptimalControlProblems.new_problem(::OptimalControlBackend, description::Symbol...; N::Int=steps_number_data(:new_problem), kwargs...)

    # if tf is fixed
    tf = final_time_data(:new_problem)

    # model
    @def ocp begin
        # Define the problem here
        # ...
    end

    # initial guess for the problem
    init = () 

    # DOCP and NLP
        docp = direct_transcription(
        ocp, 
        description...; 
        lagrange_to_mayer=false,
        init=init, 
        grid_size=N, 
        disc_method=:trapeze, 
        kwargs...
    )

    return docp

end

3. Define the NLP JuMP model of the problem in a file named new_problem.jl in the ext/JuMPModels directory.

"""
    Documentation of the method
"""
function OptimalControlProblems.new_problem(::JuMPBackend, args...; N::Int=steps_number_data(:new_problem), kwargs...)

    # if tf is fixed
    tf = final_time_data(:new_problem)

    # model
    model = JuMP.Model(args...; kwargs...)

    # Define the problem here
    # ...

    return model
end

4. Describe the problem in a file named new_problem.jl in the ext/Descriptions directory.