Abstract
This paper deals with the stabilization of a class of uncertain nonlinear ordinary differential equations (ODEs) with a dynamic controller governed by a linear 1−d heat partial differential equation (PDE). The control operates at one boundary of the domain of the heat controller, while at the other end of the boundary, a Neumann term is injected into the ODE plant. We achieve the desired global exponential stabilization goal by using a recent infinite-dimensional backstepping design for coupled PDE-ODE systems combined with a high-gain state feedback and domination approach. The stabilization result of the coupled system is established under two main restrictions: the first restriction concerns the particular classical form of our ODE, which contains, in addition to a controllable linear part, a second uncertain nonlinear part verifying a lower triangular linear growth condition. The second restriction concerns the length of the domain of the PDE which is restricted.
Highlights
We deal with the stabilization problem of a chemical reaction by control via heat diffusion equation, where the interaction occurs at the boundary of the heat domain and the control input is located at the second boundary [1,2,3,4]
The closed-loop system of such models is expressed as a nonlinear ordinary differential equations (ODEs) coupled with 1 − d heat diffusion systems
We design a global stabilizing dynamic feedback control governed by the 1 − d heat equation to stabilize a class of nonlinear ODE systems
Summary
We deal with the stabilization problem of a chemical reaction by control via heat diffusion equation, where the interaction occurs at the boundary of the heat domain and the control input is located at the second boundary [1,2,3,4]. In the case where the nonlinear term is dominated by an upper triangular linear system, the observer-based output feedback of the same coupled ODE and 1 − d heat is designed in [28]. We design a global stabilizing dynamic feedback control governed by the 1 − d heat equation to stabilize a class of nonlinear ODE systems. We are focused on the design of global stabilizing state feedback for the following class of nonlinear finite-dimensional systems. To solve the stabilization problem, we apply backstepping transformation for coupled ODE-PDE system introduced recently by [10,12] combined with high gain feedback and domination methods for finite dimensional systems [31]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
