Input-to-State Stabilizing Neural Controllers for Unknown Switched Nonlinear Systems within Compact Sets

TL;DR

This paper presents a neural network control framework that guarantees safety and input-to-state stability for unknown switched nonlinear systems within compact sets, using Lyapunov functions and data-driven training.

Contribution

It introduces a novel neural network-based control design with formal stability guarantees for unknown switched nonlinear systems, incorporating dwell time and Lipschitz conditions.

Findings

Successfully guarantees safety and ISS in simulations

Provides a data-driven training method with formal stability proofs

Recovers ISS and safety under arbitrary switching with common Lyapunov functions

Abstract

This paper develops a neural network based control framework that ensures system safety and input-to-state stability (ISS) for general nonlinear switched systems with unknown dynamics. Leveraging the concept of dwell time, we derive Lyapunov based sufficient conditions under which both safety and ISS of the closed-loop switched system are guaranteed. The feedback controllers and the associated Lyapunov functions are parameterized using neural networks and trained from data collected over a compact state space via deterministic sampling. To provide formal stability guarantees under the learned controllers, we introduce a validity condition based on Lipschitz continuity assumptions, which is embedded directly into the training framework. This ensures that the resulting neural network controllers satisfy provable correctness and stability guarantees beyond the sampled data. As a special case, the proposed framework recovers ISS and safety under arbitrary switching when a common Lyapunov function exists. Simulation results on a representative switched nonlinear system demonstrate the effectiveness of the proposed approach.