Model Reference Adaptive Control of Distributed Parameter Systems

Abstract

A model reference adaptive control law is de ned for nonlinear distributed parameter systems. The reference model is assumed to be governed by a strongly coercive linear operator de ned with respect to a Gelfand triple of re exive Banach and Hilbert spaces. The resulting nonlinear closed loop system is shown to be well posed. The tracking error is shown to converge to zero, and regularity results for the control input and the output are established. With an additional richness, or persistence of excitation assumption, the parameter error is shown to converge to zero as well. A nite dimensional approximation theory is developed. Examples involving both rst (parabolic) and second (hyperbolic) order systems and linear and nonlinear systems are discussed, and numerical simulation results are presented.

Control of spatially distributed processes with unknown transport‐reaction parameters via two layer system adaptations

“…This fact shows the importance of using system identification and adaptive strategies in monitoring and control of such processes. 2,3 While adaptive control of finite-dimensional systems is an advanced field that has produced adaptive control methods for a very general class of linear time-invariant systems, [4][5][6] system identification and adaptive control techniques have been developed for only a few classes of PDEs restricted by relative degree, stability, and domain wide actuation assumptions. [7][8][9][10][11][12][13][14] There are two sources of difficulty in dealing with PDEs with parametric uncertainties.…”

An adaptive observer for hyperbolic systems with application to UnderBalanced Drilling

“…One of the most important drawbacks (see Bohm et al [1998]) of most of the existing adaptive schemes for PDEs (see e.g. Bentsman and Orlov [2001], Duncan et al [1992]) is that they require measurement of the full distributed state, which is seldom the case in applications.…”

Robust Adaptive Control of a Cantilevered Flexible Structure with Spatiotemporally Varying Coefficients and Bounded Disturbance

“…Compared to the finite dimensional case, the adaptive control of infinite dimensional systems is not well developed and has only recently been studied (5) - (10) . In this paper, a robust model reference adaptive control (MRAC) of a cantilevered flexible beam with unknown spatiotemporally varying coefficients and disturbance is developed.…”