Adaptive Feedback Control of Generalized Hamiltonian Systems With Unstructured Components

Abstract

This dissertation considers the problem of feedback controller design for systems represented in non-exact generalized Hamiltonian form. The generalized Hamiltonian representation of dynamical systems has some properties that facilitate stability and controller design for nonlinear control systems. Despite extensive studies on generalized or port-Hamiltonian controlled systems, application to chemical engineering processes is limited as mass and energy balances are difficult to re-write exactly in potential-driven forms. We represent dynamics as a combination of a structured generalized Hamiltonian component and an unstructured component. We explore the stability of the unforced system after introducing the non-exact generalized Hamiltonian form and show that the non-exact generalized Hamiltonian system is stable in open-loop given mild assumptions on the unstructured component. Then, we exploit the properties of the structured part of the dynamic to design a state and observer-based feedback controller to stabilize the system at a desired set-point. In the next stage, we demonstrate the robustness of the proposed algorithms by modifying the obtained controller so that it can handle uncertain parameters and ensure stability even if exact parameter estimation is not available. In the last phase of the research, we aim to develop adaptive state and observer-based stabilizing feedback controllers guaranteeing exact parameter estimation. Different cases and applications are discussed.