Aperiodic-sampled neural network controllers with closed-loop stability verifications (extended version)

TL;DR

This paper develops aperiodic-sampled deep neural network control schemes with formal stability guarantees, using integral quadratic constraints and convex relaxations, demonstrated on an inverted pendulum example.

Contribution

It introduces novel aperiodic-sampled DNN control methods with closed-loop stability verification based on advanced mathematical tools.

Findings

Successful stability guarantees for the control schemes.

Effective control of an inverted pendulum example.

Framework for designing event- and self-triggered control logic.

Abstract

In this paper, we synthesize two aperiodic-sampled deep neural network (DNN) control schemes, based on the closed-loop tracking stability guarantees. By means of the integral quadratic constraint coping with the input-output behaviour of system uncertainties/nonlinearities and the convex relaxations of nonlinear DNN activations leveraging their local sector-bounded attributes, we establish conditions to design the event- and self-triggered logics and to compute the ellipsoidal inner approximations of region of attraction, respectively. Finally, we perform a numerical example of an inverted pendulum to illustrate the effectiveness of the proposed aperiodic-sampled DNN control schemes.