ECE465 Modern Control Theory

• Brief review of state-space systems, controllability, observability and state feedback
• Lyapunov theory: stability, direct method, Lyapunov equation and physical interpretation, extensions, global stability, invariant sets, region of attraction, input-to-state stability (ISS)
• Optimal control: problem formulation, Bellman’s principle of optimality and dynamic programming, Linear Quadratic Regulator (LQR): design, Riccati equation and interpretation
• Constrained systems: physical constraints and the need for Model Predictive Control, basic algorithm, feasibility, stability and performance-computational cost trade-offs, numerical solution and applications
• Set-based methods: invariant sets and safety concepts, reachability and safety verification under constraints
• Data-driven control methods, elements of reinforcement learning, hybrid systems, selected topics

The course deepens students’ understanding of advanced methods for the analysis and design of cyber-physical control systems. After successful completion of the course, students will be able to:
• analyse dynamic systems in state space in continuous and discrete time.
• use Lyapunov methods for stability and robustness analysis, including input-to-state stability.
• formulate and solve optimal control problems using dynamic programming, design LQR optimal controllers, and interpret their behaviour.
• apply Model Predictive Control.
• analyse constrained systems using set-based methods and safety concepts.
• be introduced to concepts of reinforcement learning and data-driven methods.
• apply advanced control techniques to real systems.