A Multi-Stage Linear Gauss Pseudospectral Successive Convex Method with Costate Information for Solving Optimal Control Problems

This paper presents an algorithm for solving multistage nonlinear optimal control problems with terminal constraints and path constraints. Based on the framework of successive convex optimization, the algorithm generates nominal state trajectories through integrating nominal control sequences. By linearizing the dynamic equations around the nominal states and controls, we formulate a linearized convex optimization subproblem. Subsequently, the Gauss pseudospectral discretization technique is employed to convert the problem into a discrete convex optimization subproblem. The analytical derivation of the constraints between the costate variables, state variables, and control variables is incorporated into the subproblem formulation, thereby enabling more accurate and stable control corrections. This approach enhances the convergence of the algorithm and yields subproblem solutions that more closely approximate the solution to the original problem. Finally, numerical simulations demonstrate that the proposed method exhibits strong stability, fast convergence, and high optimality.