Composite optimal control for interconnected singularly perturbed systems

Abstract

This dissertation deals with the design of a decentralized control and estimators for large scale interconnected singularly perturbed stochastic systems for system stabilization and cost minimization. Singular perturbation theory is used to decompose the full-order systems into two, reduced-order slow and fast subsystems. It is shown that a near optimal composite control, which is obtained as a combination of a slow control and a fast control computed in separate time scales, can approximate the optimal control. The Kalman-Bucy, or simply Kalman filtering approach is utilized to derive decentralized estimators at each subsystem level when the states of the systems are not available for measurement and/or corrupted by external noise. Because of modeling inaccuracy resulting from the simplified model of a real physical plant, certain features of systems might not actually be what they are assumed to be. Hence, a robustness analysis to guarantee stability and performance is then necessary to validate the design in the face of system uncertainties. The problem of robust control for the above system is subject to two types of uncertainties: norm-bounded nonlinear uncertainties and unknown disturbance inputs are investigated. The problem of ??? control in which a robust stability and robust disturbance attenuation is addressed using the Hamiltonian approach. The state feedback (SFB) gain matrices can be constructed from the positive definite (PD) solutions to a couple of linear matrix inequalities (LMIs).