2024/06/03 by Pedro Henrique Silva Coutinho, Coutinho, Pedro Henrique Silva, Tiago Roux Oliveira +3 · 1 citation
Engineering · #35B37 #93B52 #93C20 #93C40 #Advanced Control Systems Optimization #Extremum Seeking Control Systems #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2406.01564
openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with the gradient extremum seeking control for static scalar maps with actuators governed by distributed diffusion partial differential equations (PDEs). To achieve the real-time optimization objective, we design a compensation controller for the distributed diffusion PDE via backstepping transformation in infinite dimensions. A further contribution of this paper is the appropriate motion planning design of the so-called probing (or perturbation) signal, which is more involved than in the non-distributed counterpart. Hence, with these two design ingredients, we provide an averaging-based methodology that can be implemented using the gradient and Hessian estimates. Local exponential stability for the closed-loop equilibrium of the average error dynamics is guaranteed through a Lyapunov-based analysis. By employing the averaging theory for infinite-dimensional systems, we prove that the trajectory converges to a small neighborhood surrounding the optimal point. The effectiveness of the proposed extremum seeking controller for distributed diffusion PDEs in cascade of nonlinear maps to be optimized is illustrated by means of numerical simulations.