A sampling-based approach to scalable constraint satisfaction in linear sampled-data systems---Part I: Computation

TL;DR

This paper introduces a novel sampling-based algorithm for accurately approximating the viability kernel in high-dimensional sampled-data linear systems, ensuring safety constraints are met in cyberphysical systems.

Contribution

The paper presents a new algorithm that handles both discrete and continuous aspects of SD systems, with proven correctness and convergence, improving safety analysis in high-dimensional systems.

Findings

Algorithm accurately approximates viability kernel in 12D systems

Handles both discrete and continuous system characteristics

Proven convergence and correctness of the method

Abstract

Sampled-data (SD) systems, which are composed of both discrete- and continuous-time components, are arguably one of the most common classes of cyberphysical systems in practice; most modern controllers are implemented on digital platforms while the plant dynamics that are being controlled evolve continuously in time. As with all cyberphysical systems, ensuring hard constraint satisfaction is key in the safe operation of SD systems. A powerful analytical tool for guaranteeing such constraint satisfaction is the viability kernel: the set of all initial conditions for which a safety-preserving control law (that is, a control law that satisfies all input and state constraints) exists. In this paper we present a novel sampling-based algorithm that tightly approximates the viability kernel for high-dimensional sampled-data linear time-invariant (LTI) systems. Unlike prior work in this area, our algorithm formally handles both the discrete and continuous characteristics of SD systems. We prove the correctness and convergence of our approximation technique, provide discussions on heuristic methods to optimally bias the sampling process, and demonstrate the results on a twelve-dimensional flight envelope protection problem.