Observer Design for Lipschitz Nonlinear Parabolic PDE Systems With Unknown Input

Abstract

In this article, a novel method to design the observer for a class of uncertain Lipschitz nonlinear parabolic partial differential equations (PDE) systems is investigated. First, the observer and the dynamic errors with undetermined parameters for the parabolic PDE systems subject to appropriate boundary conditions are presented. The conditions of the designed observer are involved. Then the analysis of asymptotic stability and H ∞ performance conditions for the observer design of uncertain nonlinear parabolic PDE systems are studied and presented in terms of matrix inequalities based on the Lyapunov stability theory. Finally, the effectiveness of the proposed method is validated by a numerical parabolic PDE system. INDEX TERMS Parabolic PDE, H ∞ observer design, Uncertain input, Asymptotic stability.

A sufficient condition to design unknown input observers for nonlinear systems with arbitrary relative degree

“…The following convex optimization problem with LMI constraints enlarges the ellipsoid ℰ within the convex polytope 𝒟 ⊖ ℛ. min P, Lj ,∀j∈B q trace(P) s.t. P > 0, (14), (20).…”

“…Although there are relevant advances on the UIO design for nonlinear systems, the achievements regarding relaxation of the UI decoupling and error stabilization conditions are still incipient, and most of them are applicable for nonlinear systems with specific structures. For example, in References 17,20‐22, UIO design approaches are proposed for systems with Lipschitz nonlinearities. The UIO design for a more general class of nonlinear systems is achieved using quasi‐LPV representations with local error convergence guarantees 9,23 .…”

Hybrid-Triggered H∞ Control for Parabolic PDE Systems Under Deception Attacks

“…In the last few years, stabilization of PDEs has acquired immense attention and several control approaches were developed such as fault-tolerant control [1], non-fragile control, [2] and so forth. PDEs can be classified into three major types, namely (i) parabolic [3], [4], (ii) elliptic [5], [6], and (iii) hyperbolic PDEs [7], [8]. Parabolic PDEs play a crucial role among the above because of its broad practical applications [9], [10].…”

Boundary Control for Cascaded System of Nonlinear ODE/Hyperbolic PDE With Time-Varying Parameter

“…Using the backstepping transformation and boundary feedback the unstable PDE is changed to a transport PDE, which converges to zero in finite time [1]. The hyperbolic PDE (1)-( 3) can be modelled chemical reactors, traffic flows, and heat exchangers [2]- [5]. Further, in [6], predictor control is presented for the following cascaded systeṁ X(t) = f (X(t), v(0, t)),…”