On ANN-enhanced positive invariance for nonlinear flat systems

TL;DR

This paper proposes a neural network-based method to derive positively invariant sets for a class of nonlinear flat systems, facilitating stability verification and control synthesis.

Contribution

It introduces a novel approach using neural network approximation of linearizing transformations for positively invariant set computation in flat systems.

Findings

Neural network approximation effectively captures distorted constraint sets.

The method enables offline invariant set computation for nonlinear flat systems.

Numerical simulations validate the proposed framework.

Abstract

The concept of positively invariant (PI) sets has proven effective in the formal verification of stability and safety properties for autonomous systems. However, the characterization of such sets is challenging for nonlinear systems in general, especially in the presence of constraints. In this work, we show that, for a class of feedback linearizable systems, called differentially flat systems, a PI set can be derived by leveraging a neural network approximation of the linearizing mapping. More specifically, for the class of flat systems, there exists a linearizing variable transformation that converts the nonlinear system into linear controllable dynamics, albeit at the cost of distorting the constraint set. We show that by approximating the distorted set using a rectified linear unit neural network, we can derive a PI set inside the admissible domain through its set-theoretic description. This offline characterization enables the synthesis of various efficient online control strategies, with different complexities and performances. Numerical simulations are provided to demonstrate the validity of the proposed framework.