An approximating pseudospectral method with state‐dependent coefficient optimization for nonlinear optimal control problem

Abstract

Abstract The approximating sequence Riccati equation method is an efficient approach for solving the nonlinear optimal control problems, but its neglect of nonlinear dynamics and necessary optimality condition makes the control law difficult to satisfy the optimality. In this paper, an approximating pseudospectral method with state‐dependent coefficient optimization algorithm is proposed to solve this defect. By introducing the approximating pseudospectral method, the original nonlinear problem is transformed into a sequence of linear subproblems, which preserves the nonlinearity of solution. Then a state‐dependent coefficient optimization algorithm based on the gradient projection technique is proposed, which ensures the optimality of the control law. A double‐layer optimization structure is designed to facilitate the coordination between the approximating method and the optimization algorithm. Theoretical analysis proves the convergence of the proposed method. Comparative case studies illustrate the effectiveness in reducing the performance index and ensuring the optimality of the control law.

Keywords

• convergence
• gradient methods
• matrix decomposition
• optimal control