Backstepping Reach-avoid Controller Synthesis for Multi-input Multi-output Systems with Mixed Relative Degrees

TL;DR

This paper introduces a new control synthesis framework for multi-input multi-output systems that guarantees safety and reachability using backstepping and feedback linearization, addressing scalability and conflicting constraints.

Contribution

It presents a novel systematic approach for synthesizing reach-avoid controllers with formal guarantees for complex systems, overcoming limitations of existing methods.

Findings

Successfully demonstrated through simulations

Ensures system outputs reach target set safely

Addresses scalability in high-dimensional systems

Abstract

Designing controllers with provable formal guarantees has become an urgent requirement for cyber-physical systems in safety-critical scenarios. Beyond addressing scalability in high-dimensional implementations, controller synthesis methodologies separating safety and reachability objectives may risk optimization infeasibility due to conflicting constraints, thereby significantly undermining their applicability in practical applications. In this paper, by leveraging feedback linearization and backstepping techniques, we present a novel framework for constructing provable reach-avoid formal certificates tailored to multi-input multi-output systems. Based on this, we developed a systematic synthesis approach for controllers with reach-avoid guarantees, which ensures that the outputs of the system eventually enter the predefined target set while staying within the required safe set. Finally, we demonstrate the effectiveness of our method through simulations.