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ISA Trans. 2017 May;68:335-352. doi: 10.1016/j.isatra.2017.02.018. Epub 2017 Mar 16.

A symplectic pseudospectral method for nonlinear optimal control problems with inequality constraints.

Author information

1
Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial, Equipment, Dalian University of Technology, Dalian, Liaoning 116024, China.
2
Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial, Equipment, Dalian University of Technology, Dalian, Liaoning 116024, China. Electronic address: hjpeng@dlut.edu.cn.

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.

KEYWORDS:

inequality constraints; linear complementary problem; nonlinear optimal control; parametric variational principle; quasilinearization

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