FEL3230 PhD Course on Hybrid Systems, HT24

Credits: The course is worth 7.5 credits. Grading is based on P/F system.

 

Course responsible: Dimos Dimarogonas, dimos@kth.se.

 

Lecturers: Dimos Dimarogonas, Siyuan Liu, Maria Charitidou, Mani Hemanth Dhullipalla

 

Abstract

 

Hybrid systems are dynamical systems that exhibit both continuous and discrete behavior and as such, they allow to model complex dynamic phenomena in real-world systems, such as cyber-physical systems, with application examples varying from automotive industry, to consumer electronics, power systems, smart buildings, and transportation systems. For all of these examples, properties such as stability or correctness with respect to design specifications are crucial. However, the rich expressiveness of hybrid systems requires special techniques to analyze and derive these properties.  This course will focus on selected related topics in hybrid systems, with a special focus on their stability, stabilization, abstraction and formal verification.

 

Keywords

 

Learning outcomes

 

After the course, the student should be able to:

·       know the essential theoretical tools to model hybrid control systems and cope with related verification problems

·       know the established problems and results in the area

·       apply the theoretical tools to problems in the area

·       contribute to the research frontier in the area

 

Course main content

 

A preliminary structure and exact dates are given below. Reading material for each lecture will be updated as the course evolves. All lectures will be given at room Harry Nyquist, Malvinas Väg 10, 7th floor.

 

Lecture 1:  Course outline. Introduction to hybrid systems. Motivating examples. Modelling and hybrid Automata. Zeno behavior (October 29, 1-3 pm)

Reading material for lecture 1:

1.     J. Lygeros, K. H. Johansson, S. Simic, J. Zhang, and S. Sastry, Dynamical properties of hybrid automata, IEEE Transactions on Automatic Control, 48:1, 2-17, 2003.

 

Lecture 2: Stability of hybrid systems. Multiple Lyapunov Functions. (October 31, 1-3 pm)

Reading material for lecture 2:

  1. D. Liberzon, Switching in Systems and Control, Birkhauser, 2003, Part II.
  2. M. S. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems (Links to an external site.), IEEE Transactions on Automatic Control, Vol. 43, No. 4, pp. 475-482, April 1998.

 

Lecture 3: Stabilization of hybrid systems. Quantized and event-based control. (November 5, 1-3 pm)

Reading material for lecture 3:

  1. D. Liberzon, Switching in Systems and Control, Birkhauser, 2003, Part III.
  2. P. Tabuada, Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks, IEEE Transactions on Automatic Control, Vol. 52, No. 9, pp. 1680-1685, Sept. 2007.

 

Lecture 4: Transitions systems, simulation and bisimulation relations, reachability and safety, temporal logic specifications (November 8, 1-3 pm)

Reading material for lecture 4:

  1. C. Belta, B. Yordanov and E.A. Gol, Formal Methods for Discrete-Time Dynamical Systems, Springer, 2017, Chapters 1-3.

 

Lecture 5: Timed automata, bisimilar linear systems. (November 12, 1-3 pm)

 

Reading material for lecture 5:

1.      G. Pappas, Bisimilar linear systems, Automatica, 39(12):2035-2047, 2003.

2.      R. Alur, Timed Automata, Conference on Computer Aided Verification (CAV), pp. 379-395, 1999.

 

Lecture 6: Signal Temporal Logic Control. (November 19, 1-3 pm)

Reading material for lecture 6:

1.     Lars Lindemann and Dimos V. Dimarogonas, Control Barrier Functions for Signal Temporal Logic Tasks, IEEE Control Systems Letters (L-CSS), Vol. 3, No. 1, pp. 96-101, January 2019.

 

Lecture 7: Control of systems under STL tasks using Model Predictive Control. (November 22, 1-3 pm)

Reading material for lecture 7:

M. Charitidou and D. V. Dimarogonas, "Barrier Function-based Model Predictive Control under Signal Temporal Logic Specifications," 2021 European Control Conference (ECC), Delft, Netherlands, 2021, pp. 734-739, doi: 10.23919/ECC54610.2021.9655231

 

M. Charitidou and D. V. Dimarogonas, "Receding Horizon Control With Online Barrier Function Design Under Signal Temporal Logic Specifications," in IEEE Transactions on Automatic Control, vol. 68, no. 6, pp. 3545-3556, June 2023, doi: 10.1109/TAC.2022.3195470.

 

Lecture 8: Multi-agent systems. (November 26, 1-3 pm)

Reading material for lecture 8:

 

Project presentations:    (TBA)

 

Course disposition

 

Lectures, course literature.

 

Prerequisites

 

Basic courses on Automatic Control, Linear Algebra. At least one advance course in automatic control will be of help, but not compulsory.

 

Requirements for final grade

 

Passing Grade based on homework and final project/take-home exam.