Extremum Seeking Control for Scalar Maps With Distributed Diffusion PDEs

• 成果类型: Article
• 署名作者: Coutinho, Pedro Henrique Silva; Oliveira, Tiago Roux; Krstic, Miroslav
• 署名单位: Universidade do Estado do Rio de Janeiro; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3545584
• 发表日期: 2025
• 页码: 4865-4872
• 关键词: Perturbation methods; trajectory; Vehicle dynamics; Real-time systems; optimization; mathematical models; Heating systems; nonlinear dynamical systems; DELAYS; aerodynamics; Adaptive control; backstepping in infinite-dimensional systems; distributed-diffusion compensation; extremum seeking; partial differential equations (PDEs); real-time optimization

摘要

This article 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 article is the appropriate motion planning design of the so-called probing (or perturbation) signal, which is more involved than in the nondistributed 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.