Perception-Based Sampled-Data Optimization of Dynamical Systems

TL;DR

This paper introduces a perception-based sampled-data control framework for dynamical systems, integrating neural networks for state estimation from high-dimensional sensory data, ensuring stability and tracking optimal solutions in real-time autonomous driving scenarios.

Contribution

It proposes a novel sampled-data feedback control method combining neural networks and projected gradient descent for perception-based dynamical system regulation.

Findings

Ensures local input-to-state stability of the control loop.

Achieves tracking of the optimization problem's solution trajectory with bounded error.

Demonstrates effectiveness through vision-based autonomous driving simulations.

Abstract

Motivated by perception-based control problems in autonomous systems, this paper addresses the problem of developing feedback controllers to regulate the inputs and the states of a dynamical system to optimal solutions of an optimization problem when one has no access to exact measurements of the system states. In particular, we consider the case where the states need to be estimated from high-dimensional sensory data received only at discrete time intervals. We develop a sampled-data feedback controller that is based on adaptations of a projected gradient descent method, and that includes neural networks as integral components to estimate the state of the system from perceptual information. We derive sufficient conditions to guarantee (local) input-to-state stability of the control loop. Moreover, we show that the interconnected system tracks the solution trajectory of the underlying optimization problem up to an error that depends on the approximation errors of the neural network and on the time-variability of the optimization problem; the latter originates from time-varying safety and performance objectives, input constraints, and unknown disturbances. As a representative application, we illustrate our results with numerical simulations for vision-based autonomous driving.