Prescribed-Time Extremum Seeking for Delays and PDEs Using Chirpy Probing

• 成果类型: Article
• 署名作者: Yilmaz, Cemal Tugrul; Krstic, Miroslav
• 署名单位: 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.2024.3397162
• 发表日期: 2024
• 页码: 7710-7725
• 关键词: Chirp; CONVERGENCE; DELAYS; PLANNING; Perturbation methods; stability analysis; Heating systems; extremum seeking; Partial differential equations; prescribed-time optimization

摘要

Extremum seeking, an online model-free optimization algorithm with traditionally exponential convergence, was recently advanced by Poveda and coauthors to fixed-time convergence, using nonsmooth time-invariant feedback. In this article, we introduce an alternative time-varying prescribed-time extremum seeking (PT-ES) approach to reaching the optimum in a user-assignable prescribed time (PT), independent of the initial condition of the estimator. Instead of conventional sinusoidal probing signals, we employ chirpy perturbations, i.e., sinusoids with growing frequencies. In addition to providing a result for a static input-output map, we provide algorithms for a map in cascade with a delay, a wave partial differential equation (PDE), and a heat/diffusion PDE. The designs are based on the time-varying PT backstepping approach, which transforms the PDE-ordinary-differential-equation cascade into a suitable PT-stabilized target system, and on averaging-based estimates of the gradient and Hessian of the map. Classical averaging does not apply for the analysis of PT-ES algorithms for four reasons: neither is probing periodic, nor is the average system exponentially stable, nor is the original system finite-dimensional, nor is the interval of operation infinite. We develop an averaging technique needed for this non-periodic finite-time infinite-dimensional problem. Along with PDE Lyapunov analysis, we show that the input converges to the optimizer in PT. We present three numerical examples to illustrate the effectiveness of the proposed technique for delay-free case as well as for compensation of time-delay and diffusion PDE dynamics.