Pseudospectral Optimal Control of Constrained Nonlinear Systems

This chapter presents a unified pseudospectral computational framework for accurately and efficiently solving optimal control problems (OCPs). Any continuous-time OCP is converted into a nonlinear programming (NLP) problem via pseudospectral transformation. Through using pseudospectral method, both states and controls are approximated by global Lagrange interpolating polynomials at Legendre–Gauss–Lobatto (LGL) collocation points. The mapping relationship between the costates of OCP and the KKT multipliers of NLP is derived for checking the optimality of solutions. Besides, a quasi-Newton iterative algorithm is integrated to accurately calculate the LGL points for engineering practice, and a multi-phase preprocessing strategy is proposed to handle non-smooth problems. We use a general solver called Pseudospectral Optimal control Problem Solver (POPS), which is developed in Matlab environment to implement the computational framework. The classic vehicle automation problem, i.e., optimal path planning in an overtaking scenario, is formulated to demonstrate the effectiveness of POPS.