Control of partially-known dynamical systems
This is a specialized book on adaptive control. Roughly, adaptive control refers to any methodology for updating a given feedback configuration as new information becomes available to improve or guarantee performance of the closed loop system in the face of plant uncertainty. The methods are usually necessarily nonlinear. The plant uncertainty might be structured parameter uncertainty, where the form of the dynamical equations is known but the precise values of various parameters in the equations are unknown, or unstructed, for example there may be unmodeled high frequency dynamics. In the analysis of an adaptive system, a first assumption is that the true plant is one member of a specified class of models; the goal is to guarantee stability or some other measure of performance if the true plant is any member of this class of models. Robust stability refers to preservation of the stability notion or performance measure even in the presence of an uncertainty not explicitly accounted for in the adaptive mechanism. The first results in adaptive control ignored the robustness issues. Later refinements guaranteed robustness under various assumptions on the external disturbances or undertainties. After a quick historical summary of much of the work in adaptive control, the present book presents a new adaptive law (a modification of earlier work of Ioannou and Kokotovic and of Narendra and Annaswamy) for the robust adaptive control of plants with unmodeled high frequency dynamics. Also considered explicitly are linear, discrete-time plants having unmodeled high frequency dynamics and/or external bounded disturbances, the stabilization problem for a class of linear time-invariant, discrete-time systems with additive-type uncertainties, a fix to relax the matching conditions (the assumption that the true plant has degree no larger than that of the nominal plant), and decentralized, adaptive control for linear interconnected dynamical systems with additive-type bounded uncertainties.
scientific article; zbMATH DE number 194831