Design of robust quadratic-optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

This paper discusses the robust-optimal state feedback controller design problems of linear singular systems under the structured (elemental) parameter uncertainties by using the orthogonal function approach (OFA) and the hybrid Taguchi genetic algorithm (HTGA). A sufficient condition is proposed to ensure that the linear singular systems with the structured parameter uncertainties are regular, impulse free, and asymptotically stable. Based on the OFA, an algorithm only involving algebraic computation is derived in this paper and then is integrated with the HTGA to design the robust-optimal state feedback controller of linear uncertain singular systems subject to robust stability constraint and the minimization of a quadratic performance index. A design example of a two degree of freedom mass-spring-damper system is given to demonstrate the applicability of the proposed approach. Copyright (C) 2008 John Wiley & Sons, Ltd.