Optimal Safety for Constrained Differential Inclusions using Nonsmooth Control Barrier Functions

TL;DR

This paper develops a method to ensure safety and optimality for nonlinear systems with constraints by using nonsmooth control barrier functions to design continuous state-feedback laws.

Contribution

It introduces a novel approach combining nonsmooth analysis and control barrier functions to guarantee safety and optimality for differential inclusions with constraints.

Findings

Guarantees safety and optimality with continuous control laws.

Uses nonsmooth analysis tools for control design.

Demonstrates effectiveness through obstacle avoidance example.

Abstract

For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs. Through the use of nonsmooth analysis tools, we show that a continuous optimal control law can be selected from a set-valued constraint capturing the system constraints and conditions guaranteeing safety using control barrier functions. Our results guarantee optimality and safety via a continuous state-feedback law designed using nonsmooth control barrier functions. An example pertaining to obstacle avoidance with a target illustrates our results and the associated benefits of using nonsmooth control barrier functions.