Safety-Critical Control Synthesis for Unknown Sampled-Data Systems via Control Barrier Functions

TL;DR

This paper develops a control synthesis method for safety-critical sampled-data systems with unknown dynamics, using control barrier functions to ensure safety at each sampling time despite the system's complexity.

Contribution

It introduces a novel approach combining control barrier functions with a non-convex program decomposition for safety guarantees in unknown sampled-data systems.

Findings

Guarantees safety for unknown sampled-data systems at all times.

Decomposes a non-convex control problem into convex sub-problems for practical implementation.

Validated approach with a numerical case study.

Abstract

As the complexity of control systems increases, safety becomes an increasingly important property since safety violations can damage the plant and put the system operator in danger. When the system dynamics are unknown, safety-critical synthesis becomes more challenging. Additionally, modern systems are controlled digitally and hence behave as sampled-data systems, i.e., the system dynamics evolve continuously while the control input is applied at discrete time steps. In this paper, we study the problem of control synthesis for safety-critical sampled-data systems with unknown dynamics. We overcome the challenges introduced by sampled-data implementation and unknown dynamics by constructing a set of control barrier function (CBF)-based constraints. By satisfying the constructed CBF constraint at each sampling time, we guarantee the unknown sampled-data system is safe for all time. We formulate a non-convex program to solve for the control signal at each sampling time. We decompose the non-convex program into two convex sub-problems. We illustrate the proposed approach using a numerical case study.