Optimal control problem formulations

Detailed Description

Data structures for different formulations of optimal control problems.

Files
file	conversion.hpp
	Conversion utilities for optimal control problems.
file	cyqlone-storage.hpp
	Data structure for optimal control problems where the initial states are eliminated.
file	ocp.hpp
	Data structure for optimal control problems.

Classes
struct	cyqlone::LinearOCPSparseQP
	Represents a sparse multiple shooting formulation of the standard optimal control problem. More...
struct	cyqlone::CyqloneStorage< T >
	Storage for a linear-quadratic OCP with the initial states x₀ eliminated. More...
struct	cyqlone::OCPDim
	Dimensions of an optimal control problem. More...
struct	cyqlone::LinearOCPStorage
	Storage for a linear-quadratic OCP of the form. More...

Functions
void	cyqlone::reference_to_gradient (const LinearOCPStorage &ocp, std::span< const real_t > ref, std::span< real_t > qr)
	Simply computes the gradient of the quadratic cost \( J(x, u) = \sum_{j=1}^{N-1} \ell_j(x^j, u^j) + \ell_N(x^N) \), with \( \ell_j(x, u) = \tfrac12 \left\| \begin{pmatrix} x - x^j_\text{ref} \\ u - u^j_\text{ref} \end{pmatrix} \right\|_{H_j}^2 \), with the Hessian \( H_j = \begin{pmatrix} Q_j & S_j^\top \\ S_j & R_j \end{pmatrix} \).
LinearOCPStorage	cyqlone::generate_random_ocp (OCPDim dim, uint_fast32_t seed=0)
	Generates a random linear OCP with the given dimensions and random seed.

Function Documentation

reference_to_gradient()

void cyqlone::reference_to_gradient	(	const LinearOCPStorage &	ocp,
		std::span< const real_t >	ref,
		std::span< real_t >	qr )

#include <cyqlone/conversion.hpp>

Simply computes the gradient of the quadratic cost \( J(x, u) = \sum_{j=1}^{N-1} \ell_j(x^j, u^j) + \ell_N(x^N) \), with \( \ell_j(x, u) = \tfrac12 \left\| \begin{pmatrix} x - x^j_\text{ref} \\ u - u^j_\text{ref} \end{pmatrix} \right\|_{H_j}^2 \), with the Hessian \( H_j = \begin{pmatrix} Q_j & S_j^\top \\ S_j & R_j \end{pmatrix} \).

Stores \( \nabla J(0, 0) \) to qr.

Definition at line 9 of file conversion.cpp.

generate_random_ocp()

LinearOCPStorage cyqlone::generate_random_ocp ( OCPDim dim, uint_fast32_t seed = 0 )

inline

#include <cyqlone/random-ocp.hpp>

Generates a random linear OCP with the given dimensions and random seed.

Definition at line 11 of file random-ocp.hpp.