Knowledge and Understanding -Understand the key differences between classical and optimization-based control approaches. -Recognize the benefits and trade-offs of LQR techniques and their role in modern systems. - Grasp the principles and applications of Kalman filtering for state estimation in linear and nonlinear systems. - Understand MPC’s versatility for constrained control of linear, nonlinear, and hybrid systems. - Learn how MHE formulates state estimation as an optimization problem, highlighting its advantages. Applying Knowledge and Understanding - Apply optimal control to unconstrained linear systems. - Implement controllers and estimation algorithms in Matlab or Python, ensuring real-time feasibility. - Design and deploy Kalman filters integrated with sensor data and system models. - Develop MPC and MHE strategies for constrained systems, addressing practical tuning and robustness. Making Judgments - Critically evaluate control and estimation strategies in Cyber-Physical Systems. - Assess trade-offs among performance, robustness, and computational cost. Communication Skills - Present and justify modeling, control, and estimation solutions using appropriate technical language. Learning Skills - Develop the ability to autonomously explore advanced control and estimation methods. - Strengthen independent learning skills for lifelong professional development in automation and control.

Basic knowledge of mathematics, including calculus and linear algebra. Familiarity with control systems and dynamical systems.

This course equips students with theoretical and computational tools for designing control and state estimation algorithms in dynamical systems, with applications in robotics, industrial automation, embedded systems, and cyber-physical systems. It integrates system modeling, numerical optimization, and real-time implementation. Optimal Control General formulation for nonlinear systems; analytical solutions for linear-quadratic cases (LQR/LQG); discrete-time implementation; robustness analysis. State Estimation and Kalman Filtering Real-time state inference via Kalman filtering; nonlinear extensions (EKF, linearized predictors). Model Predictive Control (MPC) Constrained optimal control in discrete time; stability and performance guarantees; real-time Linear MPC; tracking and constrained regulation; Explicit MPC for efficient deployment. Moving Horizon Estimation (MHE) Constrained optimization for state estimation over a moving horizon; comparison with recursive filters; advantages for complex models and constraints. MPC for Hybrid Systems Control of systems with continuous/discrete dynamics; modeling via automata and logic rules; handling logical constraints and discontinuities.

Advanced and Multivariable Control by Lalo Magni and Riccardo Scattolini, Società Editrice Esculapio, 2023 - Predictive Control for Linear and Hybrid Systems by Francesco Borrelli, Alberto Bemporad, and Manfred Morari, Cambridge University Press, 2017 - Model Predictive Control: Theory, Computation, and Design by James Blake Rawlings, David Q. Mayne, and Moritz Diehl, Nob Hill Publishing Madison, WI, 2017 Note: The recommended books are optional, as the course material, slides, and notes provided are sufficient to prepare for the exam. Additional research papers and online resources may be recommended by the instructor throughout the course.

This course provides theoretical and computational tools for the design of control and state estimation algorithms in dynamical systems. Emphasis is placed on advanced techniques widely used in robotics, industrial automation, embedded systems, and cyber-physical systems. The course bridges system modeling, numerical optimization, and real-time implementation. 1. Optimal Control of Dynamical Systems General formulation of the optimal control problem for nonlinear systems. Analytical solutions for linear-quadratic cases (LQR/LQG) and implementation in discrete time. Analysis of robustness properties with respect to uncertainty and disturbances. 2. State Estimation and Kalman Filtering Fundamentals of the Kalman filter and its use for real-time state inference. Extensions to nonlinear systems: Extended Kalman Filter (EKF) and linearized predictors. 3. Model Predictive Control (MPC) Formulation of constrained optimal control problems in discrete time. Stability analysis and performance guarantees. Design and real-time implementation of Linear MPC. Techniques for trajectory tracking and constrained regulation (Tracking MPC). Explicit MPC: offline solution of the control problem via state-space partitioning for efficient deployment on resource-limited hardware. 4. Advanced State Estimation via Moving Horizon Estimation (MHE) State estimation formulated as a constrained optimization problem over a moving time horizon. Comparison with recursive filters and benefits in the presence of complex models and constraints. 5. MPC for Hybrid Systems Extension of MPC strategies to systems with mixed (continuous/discrete) dynamics. Modeling approaches for hybrid systems (e.g., finite-state automata, logic rules) and control design. Handling logical constraints and discontinuities in the optimization problem.

The course combines instructor-led lectures, hands-on exercises, and interactive lab sessions, with approximately 35% of the time dedicated to laboratory work. The lectures will provide the theoretical foundations and core concepts needed to approach modern control and estimation problems. Practical exercises will guide students through the design of optimal controllers and observers tailored for Cyber-Physical Systems (CPSs), promoting an active learning experience. In the lab sessions, students will implement and test these methods using programming environments such as Matlab or Python. This practical component reinforces the material covered in class and helps bridge the gap between theory and real-world applications through coding, simulation, and experimentation.

Student learning will be assessed through a project-based evaluation. The project will require the design, implementation, and critical analysis of optimal control and state estimation algorithms for Cyber-Physical Systems (CPS), using tools such as Matlab or Python. The evaluation will consider: - Technical correctness of the implemented algorithms and results; - Ability to apply theoretical concepts to realistic and constrained scenarios; - Clarity and rigor in presenting methods, assumptions, and outcomes; - Critical thinking and autonomy in analyzing performance and limitations. Students will submit a project report and may be asked to deliver an oral presentation or demonstration. Detailed guidelines—regarding structure, scope, and expectations—will be provided in advance. No fixed grade breakdown between components is defined a priori; the final grade will reflect the overall quality of the work based on the above criteria and alignment with the course learning outcomes, including communication and analytical skills.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)