Harmony search optimization for robust pole assignment in union regions for synthesizing feedback control systems

Abstract

This paper is concerned with robust pole assignment optimization for synthesizing feedback control systems via state feedback or observer-based output feedback in specified union regions using the harmony search algorithm. By using exact pole placement theory and the harmony search algorithm, robust pole assignment for linear discrete-time systems or linear continuous-time systems in union regions can be converted into a global dynamical optimization problem. The robust measured indices are derived for robust union region stability constraints and a robust $H\infty$ performance. For the nonlinear, robust measured indices, a set of dynamic poles and the corresponding feedback controllers can be obtained by global dynamic optimization based on the harmony search algorithm and the idea of robust exact pole assignment. One key merit of the proposed approach is that the radius or the position of the sub-regions can be arbitrarily specified according to the transient performance request. Furthermore, the eigenstructure of the closed-loop system matrix can be optimized with better robustness for the proposed approach. Finally, the simulation results for a discrete-time system and a continuous-time system demonstrate the effectiveness and superiority of the proposed method.