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A symplectic local pseudospectral method for solving nonlinear state‐delayed optimal control problems with inequality constraints
Author(s) -
Wang Xinwei,
Peng Haijun,
Zhang Sheng,
Chen Biaosong,
Zhong Wanxie
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4003
Subject(s) - mathematics , gauss pseudospectral method , optimal control , nonlinear system , pseudospectral optimal control , linearization , symplectic geometry , mathematical optimization , pseudo spectral method , mathematical analysis , fourier analysis , physics , fourier transform , quantum mechanics
Summary In this paper, a symplectic local pseudospectral (PS) method for solving nonlinear state‐delayed optimal control problems with inequality constraints is proposed. We first convert the original nonlinear problem into a sequence of linear quadratic optimal control problems using quasi‐linearization techniques. Then, based on local Legendre‐Gauss‐Lobatto PS methods and the dual variational principle, a PS method to solve these converted linear quadratic constrained optimal control problems is developed. The developed method transforms the converted problems into a coupling of a system of linear algebraic equations and a linear complementarity problem. The coefficient matrix involved is sparse and symmetric due to the benefit of the dual variational principle. Converged solutions can be obtained with few iterations because of the local PS method and quasi‐linearization techniques are used. The proposed method can be applied to problems with fixed terminal states or free terminal states, and the boundary conditions and constraints are strictly satisfied. Numerical simulations show that the developed method is highly efficient and accurate.