ECEN865-Theory of Linear Systems

Spring 2015
Course Title: ECEN-865 Theory of Linear Systems
Instructor: Dr. Ali Karimoddini, Dept. of Electrical and Computer Engineering, NC A&T University, 336-285-3313, akarimod at
Prerequisite: ECEN-668 or equivalent or consent of instructor
Class Time: Monday, Wednesday, Friday, 11:00AM to 11:50
Office Hours: : Monday and Wednesday, 9:00 – 11:00 AM, 1:00 – 3:00 PM, 5:00 – 6:00 PM , or by appointment

Course Overview

In many practical control problems it is required to find a control technique to optimally improve the dynamical system's performance while satisfying different physical constraints. The system performance can be quantified as a performance index or a cost function. Then, the problem will be reduced to find a control law to optimize a given cost functions. This course explores theory and application of optimal control for linear and nonlinear systems. The course uses optimal control theory and computational optimal control algorithms to improve the system's performance, reduce the control energy, and stabilize the system.


Topics will include most of the following:

  • Formulation of optimal control problems

  • Static Optimization

    • Optimization without Constraints

    • Optimization with Equality Constraints

    • Numerical Solution Methods

  • Optimal Control of Continuous-Time Systems

    • The Calculus of Variations

    • Variational Approach to Optimal Control

    • Solution of the General Continuous Optimization Problem

    • Continuous-Time Linear Quadratic Regulator

    • Steady-State Closed-Loop Control and Suboptimal Feedback

  • Optimal Tracking Control Problem

  • Optimal Servo Control Problem

  • State Estimation (Kalman-Bucy Filter) for Continuous-Time Systems

  • Linear-Quadratic-Gaussian (LQG) Control

  • Loop-Transfer Recovery

In addition following topics may be covered or the students may be asked to research about:

  • Optimal Control of Discrete-Time Systems

  • Constrained Input Control

  • Stochastic optimal control

  • Robust H_inf control

  • predictive control

  • Dynamic Programming

  • Differential Games

  • Reinforcement Learning and Optimal Adaptive Control

  • Optimal hybrid control systems


Required: F.L. Lewis, D. Vrabie, and V. Syrmos, Optimal Control, third edition, John Wiley and Sons, New York, 2012.
Optional: Anderson, B., and Moore, J., Optimal Control: Linear-Quadratic Methods, Prentice Hall, 1990.

Simulation Tools

MATLAB with SIMULINK toolbox