Guaranteed Pseudospectral Sequential Convex Programming for Accurate Solutions to Constrained Optimal Control Problems

Abstract

This letter proposes an algorithm for solving finite-time nonlinear optimal control problems. The proposed method employs the Gauss pseudospectral method to transform the optimal control problem into a nonlinear programming problem, and sequential convex programming (SCP) to solve it. Furthermore, by applying the information of the solution obtained by SCP to the indirect shooting method, a more accurate optimal solution can be obtained. There was an attempt to solve a similar class of optimal control problems, but it was only applicable to a restrictive class of problems without state constraints. In contrast, the proposed method can solve a general class of optimal control problems, including those with state constraints, while ensuring the numerical stability of the algorithm. This objective is achieved without losing the numerical stability of the algorithm by introducing a slack variable and incorporating state constraints into the dynamics. Additionally, the proposed method guarantees quadratic convergence by appropriately limiting the update step size of the optimization variables. To demonstrate the effectiveness of the proposed method, we apply the proposed method to an $L^{1}/L^{2}$ -optimal control problem of a two-wheeled rover.