Model-Free Nonlinear Feedback Optimization

Abstract

Feedback optimization is a control paradigm that enables physical systems to autonomously reach efficient operating points. Its central idea is to interconnect optimization iterations in closed-loop with the physical plant. Since iterative gradient-based methods are extensively used to achieve optimality, feedback optimization controllers typically require the knowledge of the steady-state sensitivity of the plant, which may not be easily accessible in some applications. In contrast, in this paper we develop a model-free feedback controller for efficient steady-state operation of general dynamical systems. The proposed design consists in updating control inputs via gradient estimates constructed from evaluations of the nonconvex objective at the current input and at the measured output. We study the dynamic interconnection of the proposed iterative controller with a stable nonlinear discrete-time plant. For this setup, we characterize the optimality and the stability of the closed-loop behavior as functions of the problem dimension, the number of iterations, and the rate of convergence of the physical plant. To handle general constraints that affect multiple inputs, we enhance the controller with Frank-Wolfe type updates.

Deployment of an Online Feedback Optimization Controller for Reactive Power Flow Optimization in a Distribution Grid

“…Also, temporary constraint violations [22] and the suboptimality are bounded [25]. Last but not least, the sensitivity can be learned online from measurements [26] and OFO controllers exist that rely on zeroth order optimization algorithms and therefore do not need any sensitivity [27].…”

I Can Read Your Mind: Control Mechanism Secrecy of Networked Dynamical Systems under Inference Attacks

“…In recent years, plenty of works have displayed increasing interests in designing optimal, stable and safe controllers from data [114]- [116]. These methods remove the design dependency on the model knowledge (e.g., specific model forms), where state-of-the-art reinforcement learning and model-free optimization techniques are used as main tools [117]- [120]. We point out that, when there exist interactions between the NDSs and the environment, it is possible that the online learning strategy for the system itself can also be leveraged by external attackers to infer the control mechanism.…”

Nonconvex Distributed Feedback Optimization for Aggregative Cooperative Robotics

“…In [11], a feedback optimization law has been designed and applied to a power system setup. In [12]- [14] feedback optimization has been used to implement model-free optimization algorithms with constraint handling. In [15], algebraic systems are controlled by relying on gradient information affected by random errors modelled as Sub-Weibull distributions.…”