A symplectic pseudospectral method for nonlinear optimal control problems with inequality constraints. (May 2017)

• Record Type: Journal Article
• Authors: Wang, Xinwei; Peng, Haijun; Zhang, Sheng; Chen, Biaosong; Zhong, Wanxie
• Is Part Of: ISA transactions. Volume 68(2017:May)
• Page Start: 335
• Page End: 352
• Publication Date: 2017-05
• Subjects: nonlinear optimal control -- inequality constraints -- quasilinearization -- parametric variational principle -- linear complementary problem; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2017.02.018
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency. Highlights: A novel symplectic hp pseudospectral method is proposed. The pure state constraints along with pure control constraints and the state-control mixed constraints can be treated in a uniform formulation. No extra estimation of costates are required. Boundary conditions can be strictly satisfied. Numerical simulations demonstrate that the proposed method is of high precision and efficiency comparing to other algorithms.