A probabilistic solution of robust H∞ control problem with scaled matrices

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 usi...

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Bibliographic Details
Published in:International journal of systems science Vol. 47; no. 10; pp. 2264 - 2271
Main Authors: Xie, R., Gong, J.Y.
Format: Journal Article
Language:English
Published: Taylor & Francis 26.07.2016
Subjects:
bilinear matrix inequality
control
non-convex optimisation
probabilistic solution
randomised algorithms
scaled H
ISSN:0020-7721, 1464-5319
Online Access:Get full text
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Summary: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.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2014.984360