On the Notion of Safe Sliding Mode Control

TL;DR

This paper introduces the concept of Safe Sliding Manifold (SSM) in Sliding Mode Control, enabling the design of controllers that ensure system safety and robustness against uncertainties by avoiding unsafe states.

Contribution

It proposes a novel Safe Sliding Manifold (SSM) based on Lyapunov-like functions, facilitating safe control design for uncertain nonlinear systems.

Findings

Construction of SSM from Lyapunov functions

Robust safe controller design for uncertain systems

Ensures system trajectories avoid unsafe regions

Abstract

Within the framework of Sliding Mode Control, safety critical control looks at two problems of theoretical significance: construct a sliding manifold that does not intersect a given unsafe set of the state space, and design a robust controller that safely takes the system trajectory to the manifold during the reaching phase and enforces the sliding motion. In this technical note, we address both problems. We introduce the notion of Safe Sliding Manifold (SSM) of relative degree one, and show that it is possible to construct it from the gradient of a class of Lyapunov-like energy functions, previously reported in the literature, used to asses stability and safety of a nominal system. The constructed SSM allows us providing a robust safe controller for a fair general class of uncertain nonlinear systems.