A probabilistic solution of robust control problem with scaled matrices

R. Xie and J.Y. Gong

International Journal of Systems Science, 2016, vol. 47, issue 10, 2264-2271

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.

Date: 2016
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DOI: 10.1080/00207721.2014.984360

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