Nonlinear Control for Infinite-Dimensional Systems

• Published in: Reference Module in Materials Science and Materials Engineering
• Main Authors: Lhachemi, Hugo, Prieur, Christophe
• Format: Book Chapter
• Language: English
• Published: Elsevier Inc 2015
• Subjects: Distributed parameter system; Heat equation; Hyperbolic system; Lyapunov function; Nonlinear control; Parabolic equation; Partial differential equation; Saturated input; Stability; Wave equation; Wave equation; Hyperbolic system; Parabolic equation; Stability; Heat equation; Saturated input; Distributed parameter system; Nonlinear control; Partial differential equation; Lyapunov function
• ISBN: 9780128035818; 0128035811
• DOI: 10.1016/B978-0-443-14081-5.00150-1

This chapter addresses the problem of control design for infinite-dimensional systems in the presence of an input saturation. The investigated systems are modeled by partial differential equations (PDEs) under either in-domain or boundary control. We cover classes of parabolic and hyperbolic PDEs such as reaction-diffusion equations (typically heat equations), wave equations, and also the Korteweg-de-Vries equation (used in the modeling of fluid dynamics). The considered control inputs act in a nonlinear fashion on the system dynamics due to saturation effects (that is a limitation of the amplitude of the input). The reported control design procedures directly address these nonlinearities for solving the associated stabilization problems. Depending on the particularly studied class of PDEs, different stability results are reported such as local exponential stabilization with estimation of the basin of attraction or global asymptotic stability properties.