Course on Robust Nonlinear Model Predictive Control: Recent Advances in Design and Computation
James B. Rawlings and Moritz Diehl
UC Santa Barbara and University of Freiburg
Monday, March 25, 2024, 10:00 - Thursday, March 28, 2024, 17:00
University of California Santa Barbara
All course material can be found on the course page at UCSB:
https://sites.chemengr.ucsb.edu/~jbraw/ucsb2024/
Contents.
This 4-day graduate course is designed to teach the fundamentals of advanced nonlinear model predictive control (NMPC) design, computation, and implementation, with a focus on robust MPC.
The course starts with a compact summary of nominal design of nonlinear MPC (MPC using nonlinear dynamic models). The theoretical properties achieved by nominal MPC are presented, including its closed-loop stability and robustness to model errors and disturbances. Novel features include discrete as well as continuous decision variables and economic as well as tracking objective functions. In parallel with this nominal theory, the computational methods used to solve many forms of nominal NMPC problems are presented. Starting from differential equation models, we transition to discrete time models via direct multiple shooting, and discuss Newton-type methods for nonlinear programming. Computational examples are solved in CasADi and acados, using either python or matlab as APIs.
After this brief 1 1/2-day introduction, the main topic of robust MPC design is presented over the next 2 1/2 days. Both linear and nonlinear models are considered. A main technique discussed is robust minmax MPC, where we consider optimizing over parameterized feedback policies. Here, the robust MPC controller solves online a noncooperative, sequential game with the disturbance. The excellent closed-loop stability and robustness properties of the resulting minmax MPC controller are then presented. For linear dynamic models with state feedback, connections are made to both H-infinity control and the linear quadratic regulator.
In parallel with the robust MPC theory, favorable and often approximate minmax problem formulations and tailored computational methods for their solution are presented. Among many alternatives, we cover scenario-tree and affine disturbance feedback formulations. As both the design and computation of the robust minmax MPC approach are subject to active research, open problems in the design and the computation are highlighted.
Exercises.
All of the lecture material will be followed up with hands-on exercise sessions led by the instructors and graduate students in their research groups. Solving computational examples will be an essential part of the course.
Prerequisites.
First graduate level linear systems and feedback control course. Familiarity with nominal model predictive control using linear models at the level of Chapter 1 of Rawlings, Mayne, and Diehl (2020), available online here:
https://sites.engineering.ucsb.edu/~jbraw/mpc/
Familiarity with basic optimization theory and algorithms and some experience using linear, quadratic, and nonlinear programming packages.
Basic programming experience with either python or matlab.
Venue.
The class will be held on the beautiful UCSB campus in Santa Barbara, California. The class will start at 10:00 a.m. on Monday, March 25 and end at 5:00 p.m. on Thursday, March 28.
Pre-Registration.
About the instructors.
James B. Rawlings received the B.S. from the University of Texas and the Ph.D. from the University of Wisconsin, both in Chemical Engineering. He spent one year at the University of Stuttgart as a NATO postdoctoral fellow and then joined the faculty at the University of Texas. He moved to the University of Wisconsin in 1995, and then to the University of California, Santa Barbara in 2018, and is currently the Mellichamp Process Control Chair in the Department of Chemical Engineering, and the co-director of the Texas-Wisconsin-California Control Consortium (TWCCC).
Professor Rawlings's research interests are in the areas of chemical process modeling, monitoring and control, nonlinear model predictive control, moving horizon state estimation, and molecular-scale chemical reaction engineering. He has written numerous research articles and coauthored three textbooks: "Modeling and Analysis Principles for Chemical and Biological Engineers," 2nd ed. (2022), with Mike Graham, "Model Predictive Control: Theory Computation, and Design," 2nd ed. (2020), with David Mayne and Moritz Diehl, and "Chemical Reactor Analysis and Design Fundamentals," 2nd ed. (2020), with John Ekerdt. He is a fellow of IFAC, IEEE, and AIChE.
Moritz Diehl studied physics and mathematics at Heidelberg, Germany, and Cambridge, UK, from 1993-1999, and received his Ph.D. degree in Scientific Computing from Heidelberg University in 2001. From 2006 to 2013, he was a professor at KU Leuven University, Belgium, and served as the Principal Investigator of KU Leuven's Optimization in Engineering Center OPTEC. Since 2013, he is full professor at the University of Freiburg, Germany, where he heads the Systems Control and Optimization Laboratory, in the Department of Microsystems Engineering (IMTEK), and is also affiliated to the Department of Mathematics. His research interests are in optimization and control, spanning from numerical method development to applications in different branches of engineering, with a focus on embedded and on renewable energy systems.
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