CMPE246: Hybrid Dynamical Systems
Lectures: Tuesday and Thursday 4pm to 5:45pm (01/05/15 - 03/16/15), J. Baskin Engr 169
Office hours: T 6:00pm to 7:00 pm and Th 3:00pm to 4:00 pm (both at E2-321)
Driven by recent technological advances and user specifications, most systems of today combine digital and analog devices, humans interacting with embedded computers, software distributed through networks, etc. As a result, they have state variables evolving both continuously and dis- continuously due to features such as events, logic transitions, and impacts; they rely on algorithms implemented in embedded computers, which are interfaced with the plants through analog/digital and digital/analog devices; and they involve sensing and actuation through networks using com- munication protocols. Due to the presence of two types of dynamics, continuous and discrete, these systems are called hybrid dynamical systems.
This course provides an introduction to hybrid dynamical systems and presents advances tools for their analysis. After a short review of several mathematical concepts, a general modeling framework is introduced and exercised in several applications. A definition of solutions (or trajectories) to these systems is introduced next and their structural properties are investigated. A phenomenon unique to hybrid systems, called Zeno behavior, is introduced and discussed. Definitions of stability and convergence are presented next. Sufficient conditions for convergence to and asymptotic stability of equilibrium sets are given first for the linear case, which consist of invariance and eigenvalue conditions, respectively, and then for the nonlinear case, which are Lyapunov based. A characterization of the robustness properties induced by asymptotic stability follow and is illustrated with several applications. Throughout the course, the students will be guided on methods for simulation of hybrid systems and encouraged to apply them to several applications.
TOPICS: Modeling; Definition of solutions; Zeno behavior; Equilibrium sets; Stability and convergence; Nominal robustness; Numerical simulation. The content will be mainly theoretical. Applications will be on modeling and analysis of hybrid systems in the context of unmanned aerial vehicles, robotic manipulators, hard-disk drive, mechanical systems with impacts, impulse-coupled oscillators, cellular networks, and others.
SYLLABUS: The class syllabus is available here (last update: 01/06/15)
CLASS MATERIAL: Class notes and questions are posted at our Google group
Lecture 1 (01/06/15): Introduction to hybrid dynamical systems.
Lecture 2 (01/08/15): Engineering examples of hybrid dynamical systems.
Lecture 3 (01/13/15): Control examples of hybrid dynamical systems.
Lecture 4 (01/15/15): Modeling framework.
Lecture 5 (01/20/15): Hybrid time.
Lecture 6 (01/22/15): Definition of solutions and types.
Lecture 7 (01/27/15): Existence of solutions.
Lecture 8 (01/29/15): Basic conditions for existence.
Lecture 9 (02/03/15): Asymptotic stability.
Lecture 10 (02/05/15): Globality and uniformity of asymptotic stability.
Lecture 11 (02/10/15): Sufficient conditions for stability.
Lecture 12 (02/12/15): Relaxed sufficient conditions for stability.
Lecture 13 (02/17/15): Applications.
Lecture 14 (02/19/15): Applications.
Lecture 15 (02/24/15): Effect of small perturbations.
Midterm is on 02/26/15 (no class)
Lecture 16 (03/03/15): Hybrid basic conditions.
Lecture 17 (03/05/15): Consequences of hybrid basic conditions.
Lecture 18 (03/10/15): Revisiting asymptotic stability and robustness.
Lecture 19 (03/12/15): Robust asymptotic stability.
Project presentations will be on the second week of March (TBD)