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Optimal control for a chaotic system by means of Gauss pseudospectral method

Cao Xiao-Qun

Optimal control for a chaotic system by means of Gauss pseudospectral method

Cao Xiao-Qun
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Publishing process
  • Received Date:  30 July 2013
  • Accepted Date:  06 September 2013
  • Published Online:  05 December 2013

Optimal control for a chaotic system by means of Gauss pseudospectral method

  • 1. School of Computer Science, National University of Defense Technology, Changsha 410073, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 41105063, 41375105).

Abstract: A new numerical method is presented to solve optimal control problem of a chaotic system based on Gauss pseudospectral method (GPM). Firstly, the Lagrange interpolation polynomials are constructed on Legendre-Gauss nodes and used to parameterize the state and control the trajectories in optimal control of the chaotic system. Then, the chaotic optimal control problem in the continuous space is transformed into a nonlinear programming (NLP) problem through GPM. Furthermore, the NLP problem is solved by the sequential quadratic programming algorithm. Finally, the proposed method is applied to the optimal control of the typical Lorenz, Chen, and Liu chaotic systems respectively. The simulation processes indicate that the GPM is effective, fast and feasible for solving optimal control problems of chaotic systems.

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