A new spectral method for the nonlinear optimal control systems
Chen Xuesong, Li Xingke, Zhang Lili, Cai Shuting · 2017
A new spectral method based on Galerkin approximation solutions of the nonlinear optimal control systems is proposed in this paper. Galerkin approximation with Chebyshev polynomials (GACP) is firstly used to solve the generalized Hamilton-Jacobi-Bellman (GHJB) equation for the nonlinear optimal control systems. The proposed GACP method employs some Chebyshev global polynomials as the trial functions for discretization of GHJB equation on a well-defined region of attraction. A stable optimal solution of a nonlinear control system is finally obtained. Numerical example shows that the proposed method can efficiently solve the nonlinear optimal control problem and therefore is promising.