NUMERICAL ALGORITHM OF OPTIMAL CONTROL BASED ON A GAUSS PSEUDOSPECTRAL METHOD AND ITS APPLICATION
基于高斯伪谱的最优控制求解及其应用

A numerical computation of constrained optimal control problem (OCP) is discussed based on Gauss Pseudospectral Method. The state evolvement and control rules are approximated by using some parameterized polynomials, and the differential equations are approximated by using orthogonal polynomials. After such approximation, the OCP-solving problem can be turned to a nonlinear programming problem (NLP) with inequality constraints. The effectiveness of this approximation is expressed in detail. As an application of this numerical method, the optimal path generating (OPG) problem for a robot in an environment with some obstacles is studied. The OPG is firstly modeled as a constrained OCP, and then solved by using proposed numerical method. Some simulation results are given in the paper.