University of California at Berkeley
Department of Electrical Engineering and Computer Sciences

EE C291E/ME C290S
Hybrid Systems---Computation and Control

Spring Semester 2021

Course information: UCB On-Line Course Catalog and Schedule of Classes

Lecture Information: TTh 9.30-11, online.

Course Description

Advances in networked embedded computing and communication devices have fueled the need for design techniques that can guarantee safety and performance specifications of embedded systems, or systems that involve the integration of discrete logic with the analog physical environment. Hybrid dynamical systems are continuous state systems with a phased operation. The phases of operation capture the system's discrete event or linguistic behavior, while the continuous variable dynamics capture the system's detailed or ``lower-level'' behavior. Hierarchical organization is implicit in hybrid systems, since the discrete event dynamics represent planning which is based on an abstraction of the continuous dynamics. Hybrid systems are important in applications in real-time software, robotics and automation, mechatronics, aeronautics, air and ground transportation systems, systems biology, process control, and have recently been at the center of intense research activity in the control theory, computer-aided verification, and artificial intelligence communities. In the past several years, methodologies have been developed to model hybrid systems, to analyze their behavior, and to synthesize controllers that guarantee closed-loop safety and performance specifications. This class presents recent advances in the theory for analysis, control, verification, and learning of hybrid dynamical systems, and shows the application of the theory to a variety of examples.

We will present hybrid automaton models and related modeling approaches. In hybrid controller synthesis, we will treat different control system setups such as game theoretic and optimal control, and we will present recent advances in integrating learning-based approaches into such methods. Finally, we apply the theory in case studies to complex problems such as automated highway systems, air traffic management systems, networks of unmanned vehicles, closing the loop around sensor networks, and systems biology.


Background in systems and control, such as EECS 221A or ME 232 is desirable. EECS 222 is offered concurrently and is a useful class to take with this one.

Notes and Textbook

There is no required textbook. We will provide lecture notes throughout the term. Additionally, the draft of a monograph by Lygeros, Tomlin and Sastry is available here:


Discussion Links

Recorded Lectures and Board Notes

Grading and Evaluation

This is a project-based course, and the project is worth 50% of the grade. There will be homework assignments, worth 40% of the grade. 10% of the grade is for participation.

Class Project

The projects can either be in the form of a review of a part of the literature or, preferably, involve the exploration of original research ideas. If the project is a review of the literature, it needs to be thoroughly digested and homogenized. The project should be chosen in consultation with the instructors. The schedule is as follows:
  • Project Proposal (two page summary) (due before term break)
  • Project Report (10-12 pages) and presentation (due final week of classes) Joint project proposals (with groups of 2 or 3 per group) are encouraged.

    An initial suggestion of areas for projects is:
  • Investigation of a subclass of hybrid systems: linear hybrid systems (ellipsoidal calculus, switched Lyapunov functions); discrete-time hybrid systems; stochastic hybrid systems.
  • Multiple objective systems; topics from game theory (n-player pursuit evasion games, cooperative games); safety-based control; optimization of hybrid systems.
  • Observability of hybrid systems; hybrid state estimation; model identification.
  • Topics in safe learning: integrating learning into safety-based control.
  • Topics in human-machine systems: modeling, analysis, and control.
  • Applications: groups of coordinating vehicles; multi-modal robotic systems; perception-based robotics; identification of modes in ATC observed data; gait modeling, stability and control; engine control; guidance of a UAV; biological modeling and control; embedded control and real time scheduling.

  • Links Updated 01/04/21