CMPE246: Hybrid Dynamical Systems
Lectures: Tuesday and Thursday 6pm to 7:45pm (03/28/16 - 06/03/16), J. Baskin Engr 169
Office hours: Tuesday noon to 1:00 pm and Thursday 5:00pm to 6:00 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
CLASS MATERIAL: Class notes and questions are posted at our Google group
Lecture 1 (03/29/16): Introduction to hybrid dynamical systems.
Lecture 2 (03/31/16): Simulation of hybrid dynamical systems.
Lecture 3 (04/05/16): Modeling hybrid dynamical systems.
Lecture 4 (04/07/16): Definition of solutions and types.
Lecture 5 (04/19/16): Solution concept and examples.
Lecture 6 (04/20/16): Conditions for existence of solutions.
Lecture 7 (04/21/16): Asymptotic stability.
Lecture 8 (04/26/16): Globality and uniformity of asymptotic stability.
Lecture 9 (04/28/16): Sufficient conditions for stability.