2018 Hybrid Systems Control

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Graduate major in Systems and Control Engineering
Imura Jun-Ichi 
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Course description and aims

 Hybrid system is a dynamical system composed of discrete-valued variables and continuous-valued variables. It is also defined as a dynamical system composed of logical variables and physical variables. This includes control systems with logic operations and ON-OFF switches, discontinuous physical phenomena such as jump behavior. This course focuses on such systems, and covers the fundamentals on hybrid system representation and control design methods.
 The aim of this course is that students who have already learned classical control theory and modern control theory will learn, as an advanced control theory, how to represent logical systems such as an automaton, and how to combine the logical system model and physical system model as a hybrid system model, and then how to design a model predictive control of the hybrid system model.

Student learning outcomes

 At the end of this course, students will be able to:
1) Explain the concept of hybrid systems composed of discrete-valued variables and continuous-valued variables.
2) Derive a hybrid system model expressing complex system behavior in a form being suitable to control design.
3) Design a model predictive controller based on hybrid system models.


Hybrid system, Discrete event system, Event triggered system, Proposition logic, Automaton, Mixed logical dynamical system, Piecewise affine system, Jump phenomena, Model predictive control, Mixed integer programming problem.

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

The first 60 min. of each class includes the lecture on topics, and the other 30 min. includes exercise problems related to the lecture given that day.
To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 An introduction to hybrid systems Understand the notion of a hybrid system.
Class 2 Hybrid system model and basic representation of mixed logical dynamical model Understand the notion of hybrid system models and the representation of mixed logical dynamical model.
Class 3 Mixed logical dynamical model representation and propositional logic Derive a model of a hybrid system including logical operation.
Class 4 Examples of mixed logical dynamical model representation Derive a mixed logical dynamical model expressing e.g., multi-modal piecewise affine systems and hybrid automata.
Class 5 Advanced mixed logical dynamical model representation Derive a mixed logical dynamical model expressing complex behavior such as jump phenomena.
Class 6 Exercise on hybrid system modeling Review hybrid system modeling throughout exercises.
Class 7 Control of hybrid systems and model predictive control Understand a summary of control of hybrid systems, and basis of model predictive control.
Class 8 Model predictive control and mixed logical programing problem Derive the relation between model predictive control problem of mixed logical dynamical model and mixed logical programing problem.


Text books are unspecified, but handouts are available at each class.

Reference books, course materials, etc.

・Jun-ichi Imura, Shun-ichi Azuma, Izumi Masubuchi, Control of Hybrid dynamical Systems, CORONA PUBLISHING, CO., LTD. ISBN 978-4-339-03320-5 (in Japanese)
・A.J. van der Schaft, M.J. Schumacher, An introduction to hybrid dynamical systems, Lecture Notes in Control and Information Sciences 251, Springer 2000
・A. Bemporad and M. Morari, Control of systems integrating logic, dynamics, and constraints, Automatica, Vol.35, pp.407-427, 1999

Assessment criteria and methods

1) Students will be assessed on their basic understanding of modeling of hybrid systems and control design based on model predictive control.
2) Students’ course scores are based on final exam (90%) and exercise problems (10%).

Related courses

  • SCE.C301 : Linear System Theory

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed SCE.C301:Linear System Theory or have equivalent knowledge.

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