Discrete-time trailing horizon direct adaptive disturbance rejection.

Abstract

Discrete-time adaptive disturbance rejection is an important area of research however, its theoretical foundation is incomplete. Evidence of this fact is the lack of an overarching theory as exemplified by the proliferation of patents and algorithms. The state of the art depends heavily on heuristic algorithms. In this dissertation a novel discrete-time direct adaptive disturbance rejection algorithm is developed. We provide a complete proof of stability and clarify the assumptions under which the proof of stability is valid. This method is valid for minimum phase and non-minimum phase plants. In the case of minimum phase plants we are able to achieve simultaneous adaptive stabilization and disturbance rejection. For the non-minimum phase case, however, we require the plant to be asymptotically stable. Distinguishing features of this method are the use of nonminimal plant models and the computation of control over a finite horizon in the <italic>past</italic>, and thus the name trailing horizon control. This research also revealed the absence of a suitable Lyapunov function framework for establishing stability in adaptive systems, except for a narrow class of continuous-time Lyapunov based adaptive control algorithms in which the controller is specifically designed to render the derivative of the Lyapunov function negative definite. So part of this research is also concerned with Lyapunov Stability of discrete-time adaptive control systems. The main contribution of this research was to establish the link between logarithmic Lyapunov functions and adaptive control laws with normalized estimators. Logarithmic Lyapunov functions are then used to prove Lyapunov stability of full state feedback and output feedback adaptive control algorithms.