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Last Updated: 2026-02-05 15:10:10
Abstract
System complexity and demanding performance render traditional control inadequate. Applications from the process industry to the communications sector increasingly use MPC. The last years saw tremendous progress in this interdisciplinary area. The course first gives an overview of basic concepts and then uses them to derive MPC algorithms. There are exercises and invited speakers from industry.
Objective
Increased system complexity and more demanding performance requirements have rendered traditional control laws inadequate regardless if simple PID loops are considered or robust feedback controllers designed according to some H2/infty criterion. Applications ranging from the process industries to the automotive and the communications sector are making increased use of Model Predictive Control (MPC) where a fixed control law is replaced by on-line optimization performed over a receding horizon. The advantage is that MPC can deal with almost any time-varying process and specifications, limited only by the availability of real-time computer power. In the last few years we have seen tremendous progress in this interdisciplinary area where fundamentals of systems theory, computation and optimization interact. For example, methods have emerged to handle hybrid systems, i.e. systems comprising both continuous and discrete components. Also, it is now possible to perform most of the computations off-line thus reducing the control law to a simple look-up table. The first part of the course is an overview of basic concepts of system theory and optimization, including hybrid systems and multi-parametric programming. In the second part we will show how these concepts are utilized to derive MPC algorithms and to establish their properties. On the last day, speakers from various industries will talk about a wide range of applications where MPC was used with great benefit. There will be exercise sessions throughout the course, where the students can test their understanding of the material. We will make use of the MPC Toolbox for Matlab that is distributed by the MathWorks.
Content
Tentative Programme Day 1 Fundamentals of linear system theory – Review (system representations, poles, zeroes, stability, controllability & observability, stochastic system descriptions, modelling of noise). Day 2 Optimal Control and Filtering for Linear Systems (Liner Quadratic Regulator, Linear Observer, Kalman Filter, Separation Principle, Riccati Difference Equation). Days 3 & 4 Fundamentals of Optimization (linear programming, quadratic programming, mixed integer linear/quadratic programming, Duality Theory, KKT conditions, constrained optimization solvers). Exercises Day 5 MPC – formulation, finite horizon optimal control, receding horizon control, stability & feasibility, computation. Exercises Day 6 MPC Toolbox for Matlab: Graphical User Interface and Simulink Library, Classroom Matlab exercises. Introduction to Multi Parametric Toolbox. Day 7 Explicit formulation of MPC. Quadratic norm, Multiparametric Quadratic Programming. Infinity norm, multiparametric linear programming. Exercises Day 8 MPC for Hybrid Systems (i.e. systems with mixed continuous/discrete dynamics). Modeling of Hybrid Systems. MPC algorithm and stability, mixed-integer programming. Explicit formulation of hybrid MPC. Moving horizon state estimation. Reachability analysis. PWA models and dynamic programming, MLD description. Day 9 Applications / Case Studies
General Information
- Language
- English
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Model Predicitive Control
Belegung: Voraussichtlich Mo 3.4. bis Do 13.4., 10.00 - 17.00 Uhr, ETL K25
|
No time listed | 4 h weekly |