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A probabilistic solution of robust control problem with scaled matrices

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  • R. Xie
  • J.Y. Gong

Abstract

This paper addresses the robust H∞ control problem with scaled matrices. It is difficult to find a global optimal solution for this non-convex optimisation problem. A probabilistic solution, which can achieve globally optimal robust performance within any pre-specified tolerance, is obtained by using the proposed method based on randomised algorithm. In the proposed method, the scaled H∞ control problem is divided into two parts: (1) assume the scaled matrices be random variables, the scaled H∞ control problem is converted to a convex optimisation problem for the fixed sample of the scaled matrix and a optimal solution corresponding to the fixed sample is obtained; (2) a probabilistic optimal solution is obtained by using the randomised algorithm based on a finite number N optimal solutions, which are obtained in part (1). The analysis shows that the worst case complexity of proposed method is a polynomial.

Suggested Citation

  • R. Xie & J.Y. Gong, 2016. "A probabilistic solution of robust control problem with scaled matrices," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2264-2271, July.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:10:p:2264-2271
    DOI: 10.1080/00207721.2014.984360
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