Guaranteed Cost Boundary Control for Reaction–Diffusion Systems

This paper investigates the problem of guaranteed-cost boundary control for reaction–diffusion systems (RDSs). The boundary controller proposed herein can comprehensively take into account both the system stability and energy consumption cost. Meanwhile, it is also capable of eliminating the impacts of system parameters and time delays on the system, which constitutes the advantage of guaranteed-cost control over other control methods that are highly dependent on the accuracy of the system model. In addition, compared with distributed control, the boundary control adopted in this paper is easier to implement and has a broader scope of application. The structure of this paper is organized as follows: First, by combining the Lyapunov method with inequality techniques, the study derives the boundary control law, thereby realizing the guaranteed-cost boundary control for uncertain reaction–diffusion systems (URDSs). This control law can also ensure that the given quadratic cost function has an upper bound. Second, for uncertain reaction–diffusion systems with time delays (DURDSs), this paper further provides sufficient conditions for achieving guaranteed-cost boundary control. Finally, numerical simulations are present to verify the effectiveness of the proposed theoretical results.