Global Optimization of Path-Constrained Optimal Control Problems via Semidefinite Programming Relaxations

Abstract

We consider a method for calculating global optimum for path-constrained OCPs (optimal control problems) with polynomial functions, i.e., the state equation, initial/final conditions, path constraints, and cost function, are all described by polynomials. Based on the formulation using occupation measures, a hierarchy of semidefinite programming relaxations of original nonconvex OCP is formulated. By solving the relaxed problems, reasonable approximations of the time histories of the state and control variables which achieves global optimum are obtained. The effectiveness of the proposed method is demonstrated through a simple kinematics problem of an aircraft.