
332:505 Control Theory I
Syllabus
Chapter and section numbers correspond to the text, Systems
and Controls by S. Zak, Oxford University Press, 2003.
 Analysis of Modeling Equations (one to two lectures)
 StatePlane (PhasePlane) Analysis
 Examples of PhasePortraits
 The Method of Isoclines
 Numerical Techniques
 The Method of Taylor Series
 Euler's Methods
 PredictorCorrector Method
 Runge's Method
 RungeKutta Method
 Principles of Linearization
 Linearizing Differential Equations
 Describing Function Method
 Scalar Product of Functions
 Fourier Series
 Describing Function in the Analysis of Nonlinear Systems
 Linear Systems (one to two lectures)
 Reachability and Controllability
 Observability and Constructibility
 Companion Forms
 Controller Form
 Observer Form
 Linear StateFeedback Control
 State Estimators
 FullOrder Estimator
 ReducedOrder Estimator
 Combined ControllerEstimator Compensator
 Stability (two to three lectures)
 Informal Introduction to Stability
 Basic Definitions of Stability
 Stability of Linear Systems
 Evaluating Quadratic Indices
 DiscreteTime Lyapunov Equation
 Constructing Robust Linear Controllers
 Hurwitz and Routh Stability Criteria
 Stability of Nonlinear Systems
 Lyapunov's Indirect Method
 Discontinuous Robust Controllers
 Uniform Ultimate Boundedness
 LyapunovLike Analysis
 LaSalle's Invariance Principle
Midterm Exam, Lecture 7, March 5, 2003,
will cover lectures 1 through 6.
 Optimal Control (four lectures)
 Performance Indices
 A Glimpse at the Calculus of Variations
 Variation and Its Properties
 EulerLagrange Equation
 Linear Quadratic Regulator
 Algebraic Riccati Equation (ARE)
 Solving the ARE Using the Eigenvector Method
 Optimal Systems with Prescribed Poles
 Optimal Saturating Controllers
 Linear Quadratic Regulator for Discrete Systems on an Infinite
Time Interval
 Dynamic Programming
 DiscreteTime Systems
 Discrete Linear Quadratic Regulator Problem
 Continuous Minimum Time Regulator Problem
 The HamiltonJacobiBellman Equation
 Pontryagin's Minimum Principle
 Optimal Control with Constraints on Inputs
 A TwoPoint BoundaryValue Problem
 Sliding Modes (one to three lectures if time permits)
 Simple Variable Structure Systems
 Sliding Mode Definition
 A Simple Sliding Mode Controller
 Sliding in MultiInput Systems
 Sliding Modes and System Zeros
 Nonideal Sliding Mode
 Sliding Surface Design
 State Estimation of Uncertain Systems
 Discontinuous Estimators
 Boundary Layer Estimators
 Sliding Modes in Solving Optimization Problems
 Optimization Problem Statement
 Penalty Function Method
 Dynamical Gradient Circuit Analysis
Final Exam will cover lectures 8 through 14.
Printable copy of syllabus
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Page last modified 07/18/07. 
