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

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.