Eco-Inspired Robust Control Design Algorithms For Linear Systems with Real Parameter Uncertainty

Abstract

This paper addresses the issue of robust control design of linear dynamical systems with real parameter uncertainty. It is well known that existing robust control design methodologies such as H-infinity and μ synthesis become very conservative when dealing with real parameter uncertainty. In robust control design methods that currently exist in the literature, which use Lyapunov and Riccati based methods, the control gains are functions of the perturbation data. The proposed robust control design algorithms in this paper differ from these in the sense that they focus on the control design to achieve a specific structure of the closed loop system matrix that guarantees as high stability robustness index as possible without the need for any information on the perturbation data. The proposed robust control design in which the structure of closed loop system matrix plays a central role, is inspired by the principles of ecology, wherein the desired closed loop matrix consists of self regulated species with predator-pray interactions among these species. A set of matrices labelled ‘Target Pseudo symmetric Matrices’ are used as the class of desirable closed loop system matrices. Based on these matrices, which capture the maximum achievable robustness index, robust control design is carried out such that the eventual closed loop system possesses a stability robustness index as close to the maximum achievable index as possible. Two separate robust control design algorithms are presented, which are relatively simple to implement. The algorithms are illustrated with several examples. It is hoped that the proposed robust control design algorithms aid in the revival of the field of robust control with new insights provided by ecological principles.