Certain investigations on improving the robustness of linear quadratic regulator applied to multivariable systems

Abstract

Linear Quadratic Regulator (LQR), milestone of modern optimal control theory has attracted considerable attention over decades, due to its inherent robustness and stability properties. In LQR the system dynamics are represented by linear differential equations and the cost function is described by a quadratic function. The performance of LQR is purely dependent on the proper selection of Q and R weighting matrices. However, the choice of these matrices are done using trial and error method or through experience. This tedious job is more cumbersome and time consuming. As a measure to overcome this problem, Particle Swarm Optimization (PSO) algorithm is proposed for the optimal selection of weighting matrices. PSO is a meta-heuristic algorithm that optimizes a problem by iteratively trying to improve a candidate solution with respect to a given measure of quality. However, PSO has two undesirable characteristics that limit its wide applications. One is the premature convergence of particles and the other is the inability to strike a balance between global exploration and local search exploitation. These demerits shed light on the exploration of the following versions of PSO towards the optimal selection of weighting matrices. and#1048766; Space Transformation Search PSO (STS-PSO) and#1048766; Hybrid PSO (HPSO) and#1048766; Adaptive PSO (APSO) The above mentioned versions are utilized to find the optimal weighting matrices of LQR. In STS-PSO a convergence monitor is introduced, incorporating a disturbing factor in the particle positions at the newline