Online Optimization of Dynamical Systems with Deep Learning Perception

TL;DR

This paper develops a data-driven control method for dynamical systems using neural networks to estimate states and unknown costs, ensuring stability and robustness in the control loop.

Contribution

It introduces a neural network-based feedback controller for constrained optimization in dynamical systems, with stability guarantees under unknown and high-dimensional data.

Findings

Controller achieves exponential input-to-state stability.

Neural networks effectively estimate unknown functions.

Method demonstrated on robotics and epidemic control scenarios.

Abstract

This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or partially known. In particular, we focus on the design of data-driven controllers to regulate a dynamical system to the solution of a constrained convex optimization problem where: i) the state must be estimated from nonlinear and possibly high-dimensional data; and, ii) the cost of the optimization problem -- which models control objectives associated with inputs and states of the system -- is not available and must be learned from data. We propose a data-driven feedback controller that is based on adaptations of a projected gradient-flow method; the controller includes neural networks as integral components for the estimation of the unknown functions. Leveraging stability theory for perturbed systems, we derive sufficient conditions to guarantee exponential input-to-state stability (ISS) of the control loop. In particular, we show that the interconnected system is ISS with respect to the approximation errors of the neural network and unknown disturbances affecting the system. The transient bounds combine the universal approximation property of deep neural networks with the ISS characterization. Illustrative numerical results are presented in the context of control of robotics and epidemics.