# 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

https://www.eventbrite.com/e/robust-nonlinear-model-predictive-control-course-registration-810502774617?aff=oddtdtcreator

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.

Please respond to this registration page at your earliest convenience to help us plan the instructional facilities.