Class Information
Meeting Times: Tu & Th 9:30 - 11:00
Meeting Location: Cory Hall, Room 540AB
Lectures by Dr. S. Shankar Sastry, with guest lectures by Dr. Claire Tomlin, Dr. Jaime Fisac, and Dr. Dexter Scobee
Lectures are recorded and
available 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 time, continuous variable 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.
The two behaviors influence each other. 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 simulation of hybrid dynamical systems, and shows the application of the theory to the design of the control
architecture for complex, large scale systems.
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, switched systems, and other recent advances.
For hybrid verification we treat decidability of timed automata, rectangular automata,
general nonlinear systems with some approximation properties and some software verification tools.
We present emerging approaches for hybrid system simulation. 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.
Materials
Students are encouraged to read the lecture notes for key definitions before Shankar's corresponding lecture.
For synthesis, refer to the three textbooks for the corresponding weeks
Weeks 0 - 5 and 11
Lygeros, Sastry, and Tomlin
"Hybrid Systems: Foundations, Advanced Topics, and Applications"
Weeks 12 - 14
Fisac
"Game Theoretic Safety Assurance for Human-Centered Robotic Systems"
These drafts are provided copyright of their respective authors
and must not be reproduced without their consent.
