研究生視頻公開課——《Model Predictive Control》
Course Abstract
This short course introduces audience to a recently developed Tube Model Predictive Control (MPC). In the presence of uncertainty, the actual state and control trajectories of a system typically deviate from the predicted ones. Therefore, it is necessary to replace the predicted state and control sequences with the sequences of the sets of possible states and controls. These sequences of possible states and controls have become commonly known as the state and control tubes. In tube MPC, the parameterization of the state and control tubes is closely related with the parameterization of the associated control policy. The control policy replaces usual control sequences in conventional setting. The control policy is a sequence of control laws, and, therefore, it enables adequate counteraction to the propagation of the uncertainty. Effectively, different control actions are allowed at different states in the predictions under uncertainty. From the theoretical point of view, tube MPC under suitable parameterization can replicate dynamic programming solution when the latter is numerically plausible. From the computational practicability point of view, the actual implementation demands the use of parameterized state and control tubes as well as related control policy. The parameterizations are sought that yield strong structural properties of the controlled uncertain system, and yet that are computationally efficient.
The course covers background topics as well as concrete topics on tube MPC. The topics covered in the course include:
- Control Synthesis Under Constraints: Basics.
- Control Synthesis Under Constraints and Uncertainty: Basics.
- Model Predictive Control: Basics.
- Tube Model Predictive Control.
Course Content
《Model Predictive Control》 Lecture 1 Reachability, Positive Invariance and Stability-1
《Model Predictive Control》 Lecture 1 Reachability, Positive Invariance and Stability-2
《Model Predictive Control》 Lecture 2 Controllability, Control Invariance and Controlled Stability
《Model Predictive Control》 Lecture 5 Optimal and Model Predictive Control
《Model Predictive Control》 Exercise 6 Optimal and Model Predictive Control
《Model Predictive Control》 Lecture 9 Rigid Tube Model Predictive Control – Coupled Set-Dynamics
《Model Predictive Control》 Lecture 10 Homothetic Tube Model Predictive Control
《Model Predictive Control》 Lecture 11 Elastic Tube Model Predictive Control
《Model Predictive Control》 Lecture 12 Tube Model Predictive Control with Time-Varying Cross-Sections
《Model Predictive Control》 Lecture 13 Tube Model Predictive Control with Optimized Cross Sections
Biographical Information
Dr. Saša V. Raković received the Ph.D. degree in Control Theory from Imperial College London. Dr. Saša V. Raković has been affiliated with a number of the leading international universities, including Imperial College London, ETH Zürich, Oxford University, UMD at College Park, UT at Austin and Texas A&M University at College Station. He is currently a full Professor at Beijing Institute of Technology, Beijing.
His research spans broad areas of artificial intelligence, autonomy, controls, dynamics, systems, applied mathematics, optimization and set-valued analysis. His research focus on problems which belong to the intersection of artificial intelligence, controls, dynamics, systems and optimization.
Dr. Saša V. Raković and Professor William S. Levine have edited a recent Springer’s Handbook of Model Predictive Control. Dr. Saša V. Raković authored 97 publications, most of which are highly cited (i.e., more than 4500 citations according to Google Scholar) and are published in leading international journals and proceedings of key conferences in the fields of control theory and engineering. Dr. Saša V. Raković is best known for his research in model predictive control and has made significant contributions to theory, computation and implementation of conventional, robust and stochastic model predictive control. He is one of the key pioneers of the tube model predictive control framework.
