Funnel-Based Online Recovery Control for Nonlinear Systems With Unknown Dynamics

TL;DR

This paper introduces a funnel-based control approach utilizing Recurrent Equilibrium Networks to recover nonlinear systems from attacks or failures, with formal guarantees on learning unknown dynamics and ensuring state deviations stay within invariant sets.

Contribution

It presents a novel combination of RENs and funnel-based control for nonlinear system recovery with formal guarantees, addressing unknown dynamics and invariant set computation.

Findings

Effective learning of unknown dynamics with formal guarantees.

Successful stabilization of nominal trajectories using invariant funnels.

Simulation demonstrates practical applicability in a DC microgrid.

Abstract

In this paper, we focus on recovery control of nonlinear systems from attacks or failures. The main challenges of this problem lie in (1) learning the unknown dynamics caused by attacks or failures with formal guarantees, and (2) finding the invariant set of states to formally ensure the state deviations allowed from the nominal trajectory. To solve this problem, we propose to apply the Recurrent Equilibrium Networks (RENs) to learn the unknown dynamics using the data from the real-time system states. The input-output property of this REN model is guaranteed by incremental integral quadratic constraints (IQCs). Then, we propose a funnel-based control method to achieve system recovery from the deviated states. In particular, a sufficient condition for nominal trajectory stabilization is derived together with the invariant funnels along the nominal trajectory. Eventually, the effectiveness of our proposed control method is illustrated by a simulation example of a DC microgrid control application.