Formal Synthesis of Safety Controllers via k-Inductive Control Barrier Certificates

• Published in: IEEE transactions on reliability Vol. 74; no. 2; pp. 2668 - 2677
• Main Authors: Ren, Tianxiang, Lin, Wang, Ding, Zuohua
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> k</tex-math> </inline-formula> </named-content>-inductive control barrier certificates (<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> k</tex-math> </inline-formula>-ICBCs); Certificates; Control systems; Controllers; Cyber-physical systems; Discrete time systems; discrete-time dynamical systems; formal verification; Integer programming; Linear programming; Mixed integer; mixed integer linear programs; Neural networks; Polynomials; Safety; safety controllers; Supervised learning; Synthesis; Training
• ISSN: 0018-9529; 1558-1721
• DOI: 10.1109/TR.2024.3399739

Control barrier certificate is an ingenious and practical approach of safety controller synthesis for cyber-physical systems. In this article, we present an approach for synthesizing safety controllers for controlled discrete-time systems subject to safety constraints. We first introduce a new type of <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-inductive control barrier certificates (<inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-ICBCs), which relaxes the strict nonincreasing condition of general control barrier certificates. Apart from this, we propose a certificate synthesis framework that includes a learner and a verifier. They collaborate continuously to search for safety controllers and their corresponding <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-ICBCs simultaneously. The learner obtains neural controllers and candidate <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-ICBCs through supervised learning, while the verifier addresses a series of mixed integer linear programming problems to validate the candidate <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-ICBCs or provide counterexamples to guide the learner further. Thanks to the less conservatism of <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-inductive conditions, safety neural controllers, and <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-ICBCs can be easily and quickly obtained. We showcase through benchmark examples that our method is efficient, and <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-inductive conditions can improve the effectiveness of control barrier certificate synthesis methods by successfully verifying systems that are challenging to handle with general control barrier certificate conditions.