POCP: a package for polynomial optimal control problems
Didier Henrion (LAAS, FEL-CVUT), Jean-Bernard Lasserre (LAAS, IMT),, Carlo Savorgnan (KUL)
TL;DR
POCP is a MATLAB package that simplifies solving polynomial optimal control problems by converting them into semidefinite programming problems, providing approximate solutions and optimal values.
Contribution
Introduces POCP, a MATLAB package that integrates with GloptiPoly 3 and YALMIP to efficiently solve polynomial optimal control problems.
Findings
Successfully computes approximate optimal control policies.
Demonstrates convergence of the hierarchy of semidefinite programs.
Provides numerical examples illustrating the package's capabilities.
Abstract
POCP is a new Matlab package running jointly with GloptiPoly 3 and, optionally, YALMIP. It is aimed at nonlinear optimal control problems for which all the problem data are polynomial, and provides an approximation of the optimal value as well as some control policy. Thanks to a user-friendly interface, POCP reformulates such control problems as generalized problems of moments, in turn converted by GloptiPoly 3 into a hierarchy of semidefinite programming problems whose associated sequence of optimal values converges to the optimal value of the polynomial optimal control problem. In this paper we describe the basic features of POCP and illustrate them with some numerical examples.
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