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Introduction to Hybrid Systems and Control
Course Description
Hybrid systems are pervasive in engineered and biological
systems, including systems which involve multiple
agents, hierarchical structure, or mode-logic, for example.
They are characterized by the interaction of
both continuous and discrete dynamics, and require new methods
and tools which draw upon continuous control and finite
automata theory.
This is a combined upper-level undergraduate and first-year
graduate course in hybrid control systems.
The course will cover fundamental results in hybrid control
theory, and introduce students to current areas of research.
The main emphasis will be on methods and computational tools for
the analysis and control of hybrid systems with linear
continuous dynamics.
Topics will include modeling, stability, optimality, reachability, and observability, and will be introduced through
engineering and biological system examples.
Course Project
Students will work independently or in small groups of two to three
to model, analyze, and design a controller for a hybrid system.
Students can select from
a range of projects provided by the instructor, or
can create their own project, in consultation with the instructor.
The project will require the application (and possible
extension) of hybrid system methods
and tools to a specific problem.
Students must justify a hybrid modeling framework, analyze the
system's behavior and performance, synthesize
a controller, discuss computed or analytical results,
and demonstrate an understanding of
potential problems in actual implementation (in
measurement errors, computational complexity, or
actuation).
Written and potentially oral presentations of the project will be evaluated.
Course Outline and Syllabus
Course syllabus, 2008
- Introduction
- Modeling of continuous, discrete, and hybrid systems
- Linear system review
- Phase-plane analysis; linearization
- Linear system stability; Lypaunov equation
- Hybrid system stability: Multiple Lyapunov functions, Common Lyapunov functions
- Linear hybrid system stability: LQ Lypaunov functions, piecewise quadratic Lyapunov functions
- Switched control, gain scheduling
- Linear hybrid observability and controllability
- Some results in hybrid optimality, estimation
- Student course projects
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