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/infinity 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. We may also invite speakers from various industries to talk about a wide range of applications where MPC was used with great benefit.
While the basics in linear systems and convex optimization will be reviewed in first few lectures, it is recommended that students take these courses before taking the MPC course. There will be exercise sessions throughout the course, where the students can test their understanding of the material. We will make use of the Multi-Parametric Toolbox for MATLAB which was developed by the automatic control group at ETH and other universities.
Mon, Wed 1:30-3:00 pm in Towne 315
Linear Systems (ESE 500), Optimization (ESE 504/605), MATLAB. Note, the main concepts on Linear Systems and Optimization will be reviewed in the course as needed.
New book by F. Borrelli, A. Bemporad and M. Morari on “Predictive Control for Linear and Hybrid Systems” to be published by Cambridge University Press in Spring 2017. Please note that this material is not to be distributed outside the University of Pennsylvania.
Actual schedule may vary depending on student interest and preparation
|Jan 11||Chapter 1: Introduction and Overview|
|Jan 16||No classes - Martin Luther King Jr. Day|
|Jan 18, 23||Chapter 2: System Theory Basics|
|Jan 18, 23||Chapter 3: Model Uncertainty and State Estimation|
|Jan 23 - Feb 1||Chapter 4: Convex Optimization|
|Feb 6, 8||Chapter 5: Unconstrained Linear Quadratic Optimal Control|
|Feb 13, 15||Chapter 6: Constrained Finite Time Optimal Control|
|Feb 20, 22||Chapter 7: Feasibility and Stability; Chapter 8: Invariance|
|Feb 27||Chapter 9: Reachability and Invariant Sets|
|Mar 6, 8||No classes - Spring Break|
|Mar 13, 15||Chapter 10: Practical Issues|
|Mar 20, 22||Chapter 11: Explicit MPC|
|Mar 27, 29||Chapter 12: Hybrid MPC|
|Apr 3, 5||Chapter 13: Robust MPC|
|Apr 10, 12||Chapter 14: Numerical Methods|
|Apr 17, 19||Chapter 14/15: Numerical Methods / Operator Splitting Methods|
|Apr 24, 26||To be determined|
Please check Canvas