Reduced spatial order model reference adaptive control of spatially varying distributed parameter systems of parabolic and hyperbolic types

Abstract

This paper presents control laws for distributed parameter systems of parabolic and hyperbolic types with unknown spatially varying parameters. These laws, based on the model reference adaptive control approach, guarantee asymptotic tracking of the output of the reference model by the output of the plant for arbitrary time invariant, but spatially varying reference input. The novel capabilities of the algorithms proposed are providing reduced sensitivity to measurement noise due to the reduced order of the spatial di!erentiation of the output data and permitting on-line estimation of the spatially varying plant parameters, constructively enforceable through the reference input and/or boundary conditions. The parameter estimation is carried out by means of an auxiliary system with the time-varying parameters that simultaneously converge in¸ to plant parameters when appropriate input signals in the reference model are used. The orthogonal expansions of these time-varying parameters, which can be computed by passing the auxiliary system parameters through the integrator block, converge to the plant parameters pointwise if the latter are su$ciently smooth. The parameter convergence is obtained by combining the adaptation laws with su$ciently rich input signals, referred to as generators of persistent excitation, which guarantee the existence of a unique steady state for the parameter errors.

On Identifiability of Linear Infinite-Dimensional Systems

“…Then the system has the same Markov parameters CAnB, n = 1,2, Thus, in analogy to the finite-dimensional case, the identifiability of the infinite-dimensional system is guaranteed if it is in a canonical form such that if confined to this form the operators A, B, C are uniquely determined by the Markov parameters. The major challenge will be an explicit definition of the canonical form of a linear Hilbert space-valued system (I), (2).…”

“…Similar to linear finite-dimensional systems, the parameter identifiability in a Hilbert space requires the system with unknown parameters to be specified in a form such that if confined to this form all the unknown parameters are uniquely determined by the transfer function. In contrast to [2], [3], and [lo] where the parameter identifiability is established for linear distributed parameter systems with sensing and actuation distributed over the entire state space, the present development deals with a practical situation where finite-dimensional sensing and actuation are only available.…”

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

“…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. The first difficulty, which also exists in ordinary differential equations (ODEs), is that even for linear plants, adaptive schemes are nonlinear.…”

Adaptive output feedback control for complex-valued reaction-advection-diffusion systems

“…The existing results on adaptive control for distributed parameter systems [3], [4], [5], [8], [11], besides dealing with real-valued plants, typically rely on full-state measurements. In this paper we deal with complex-valued plants with only boundary measurements.…”