Modeling and analysis of dynamical systems with aerospace applications.
1. Basic mathematical tools
Complex variables and functions.
Linear, time-invariant, differential equations.
Frequency domain analysis
Frequency domain methods
Jointly offered by
Jianghai Hu, School of Electrical and Computer Engineering
Term offered: Spring, 2006
Prerequisite: Linear system theory and linear algebra.
Hybrid systems are
dynamical systems with both continuous and discrete
dynamics. Developed jointly by the computer science and control
communities, they are finding increasing applications in a variety of
fields, even in scientific fields such as biological systems. This
cover some basic aspects of hybrid systems, including their modeling,
reachability and stability analysis, controller synthesis,
optimization, and simulation
tools, that are important in applying hybrid systems to engineering
The revolution in digital technology has fueled a need for design techniques that can guarantee safety and performance specifications of embedded systems, or systems that couple discrete logics with analog physical environment. Such systems can be modeled by hybrid systems, which are dynamical systems that combine continuous-time dynamics modeled by differential equations and discrete-event dynamics modeled by finite automata. Important applications of hybrid systems include CAD, real-time software, robotics and automation, mechatronics, aeronautics, air and ground transportation systems, process control, as well as biological systems. Recently, hybrid systems have been at the center of intense research activity in the control theory, computer-aided verification, and artificial intelligence communities, and methodologies have been developed to model hybrid systems, to analyze their behaviors, and to synthesize controllers that guarantee closed-loop safety and performance specifications. These advances have also been complemented by computational tools for the automatic verification and simulation of hybrid systems. This course will present the recent advances in modeling, analysis, control, and verification of hybrid systems. Topics covered in this course include the following aspects of hybrid systems: continuous-time and discrete-event models; reachability analysis; safety specifications and model checking; optimal control and differential games; (Lyapunov) stability analysis and verification tools; stochastic hybrid systems; numerical simulations; and a range of engineering applications.
Term offerd: Spring 2007
Prerequisite: Linear System Theory
main objective of this course is to study analysis and synthesis
optimal controllers and estimators for stochastic dynamical systems.
control is a time-domain method that computes the control input to a
system which minimizes a cost function. The dual problem is optimal
which computes the estimated states of the system with stochastic
by minimizing the errors between the true states and the estimated
Combination of the two leads to optimal stochastic control.
optimal stochastic control are to be found in science, economics, and
engineering. The course presents a review of mathematical background,
control and estimation, duality, and optimal stochastic control.