Evolutionary method in the design of robust control systems

Abstract

In this thesis, we present new systematic methods to synthesize non-decentralized and decentralized robust feedback control systems for classical and quantum dynamical systems. For the decentralized case, we assume that the interconnections between subsystems are known and thus, we do not treat them as uncertainties. We employ a differential evolution (DE) algorithm to solve nonconvex nonlinear constrained optimization problems arising in the feedback control syntheses for those systems. As a class of evolutionary algorithms, the DE algorithm is equipped with variation operators: mutation and recombination, and selection operator. In addition, we also apply a penalty-based fitness test procedure as a link between the DE algorithm and the particular controller design algorithm being considered. Regarding classical systems, we are concerned with robust H-inf control for a class of nonlinear uncertain systems via a stable nonlinear output feedback controller. Structured uncertainties and nonlinearities in the system are required to satisfy integral quadratic constraints and global Lipschitz conditions, respectively. Applying this controller, we aim to achieve closed loop absolute stability with a specified disturbance attenuation level. The controller is constructed using stabilizing solutions to algebraic Riccati equations parameterized by scaling constants associated with the uncertainties and nonlinearities. A decentralized version of this control problem is also considered. For quantum systems, we deal with coherent quantum feedback control for a class of quantum systems represented in terms of linear quantum stochastic differential equations. Synthesis algorithms are provided to construct physically realizable quantum controllers, which are used to solve quantum entanglement and quantum robust H-inf control problems. In particular, we are interested in synthesizing a strict bounded real quantum robust H-inf controller for an uncertain quantum system. This quantum controller is applied to obtain a strict bounded real closed loop quantum system with a specified disturbance attenuation level. The controller matrices are formed using stabilizing solutions to complex algebraic Riccati equations parameterized by scaling constants corresponding to all uncertainties in the quantum system. The same type of quantum controller is used to solve a decentralized quantum robust H-inf control problem.