M18 PARIS-SACLAY

Supervisory control theory of discrete-event systems (DES) provides a rigorous framework for the analysis and control of complex, event-driven systems such as automated manufacturing, warehouse, traffic, and more recently AI-driven systems. Unlike continuous-time systems governed by differential equations, DES evolve through discrete states and event-driven transitions. This course introduces the fundamentals of DES and their supervisory control, from automaton models to closed-loop control synthesis, with a strong emphasis on hands on learning. Students will explore automaton creation, system properties, synchronous product, controllability, and optimal supervisory control. A key feature of the course is the integration of PyTCT, a Python-based software tool developed for teaching, simulation, and design of supervisory controllers. Through guided exercises, students will not only understand theoretical concepts but also acquire hands-on skills to design correct, nonblocking, and optimal controllers for DES. Outline 1. Introduction and Modeling of DES • Discrete-event dynamics: states, events, transitions • Automaton representation and modeling principles • Software tool: PyTCT 2. Properties of Automata • Reachability, coreachability, trimness, nonblocking • Behavioral analysis and structural properties • Implementation and verification with PyTCT 3. Composition of Systems • Synchronous product of automata • Modeling multi-component and multi-agent systems • Conflict detection and resolution 4. Supervisory Control Loop • Control requirements and specifications • Supervisor synthesis for closed-loop systems • Case studies: safety enforcement, resource allocation 5. Controllability and Optimality • Controllability: definition and characterization • Supremal controllable sublanguages • Optimal supervisory control design using PyTCT 6. Advanced Topics • Observability • Distributed control of multi-agent systems • Data-driven approaches