ECE 68000 - Modern Automatic Control
Course Details
Credits: 3
Areas of Specialization:
- Automatic Control
Counts as:
Normally Offered:
Fall - odd years
Campus/Online:
On-campus and online
Requisites:
MA 51100 (required); ECE 60200 or equivalent (recommended).
Requisites by Topic:
Linear algebra, ordinary differential equations, and calculus of several variables, including matrix manipulation, linear spaces, quadratic forms, differentiation of real-valued functions of many variables, gradients, and the chain rule. Working knowledge of linear systems.
Catalog Description:
Theoretical methods in optimal control theory. Topics include the calculus of variations and the Pontryagin minimum principle with applications to minimum fuel and minimum energy problems. Geometric methods will be applied to the solution of minimum time problems. Computational methods, singular problems, observer theory and sufficient conditions for existence of solutions are also discussed.
Required Text(s):
- Systems and Control , Stanislaw Zak , Oxford , ISBN No. 019-515-0112
Recommended Text(s):
- Optimal Control , F. Lewis , John Wiley & Sons , 1986 , ISBN No. 0471812404
Learning Outcomes
A student who successfully fulfills the course requirements will have demonstrated an ability to:
- Describe the meaning of control as it relates to dynamical systems
- Construct models of dynamical systems arising in various applications, such as: mechanical, electrical, pneumatic, hydraulic, economic, and biological systems
- Apply different properties of dynamical systems, such as: stability, controllability, observability, stabilizability, detectability to physical, or real-life, systems
- Design advanced controllers for different real-life systems, using modern control engineer tools, such as: linear matrix inequalities, fuzzy logic, and different system behavior animation methods/techniques
- Validate controller designs using simulation tools, such as MATLAB and Simulink
Lecture Outline:
| Topic | |
|---|---|
| 1. Static Optimization A. Optimization without Constraints B. Optimization with Equality Constraints C. Numerical Solution Methods Problems | |
| 2. Optimal Control of Discrete-Time Systems A. Solution of the General Discrete Optimization Problem B. Discrete-Time Linear Quadratic Regulator C. Digital Control of Continuous-time Systems D. Steady-State Closed-Loop Control and Suboptimal Feedback E. Frequency-Domain Results F. The Tracking Problem G. Regulator with Function of Final State Fixed H. Second-Order Variations in the Performance Index Problems Problems | |
| 3. Optimal Control of Continuous-Time Systems A. The Calculus of Variations B. Solution of the General Continuous Optimization Problem C. Continuous-Time Linear Quadratic Regulator D. Steady-State Closed-Loop Control and Suboptimal Feedback E. Frequency-Domain Results F. The Tracking Problem G. Regulator with Function of Final State Fixed H. Second-Order Variations in the Performance Index I. Final-Time-Free Problems J. Constrained Input Problems Problems | |
| 4. Dynamic Programming A. Bellman's Principle of Optimality B. Discrete-Time Systems C. Continuous-Time Systems Problems | |
| 5. Optimal Control for Polynomial Systems A. Discrete Linear Quadratic Regulator B. Digital Control of Continuous-Time Systems Problems |
Assessment Method:
Homework, exams. (9/2025)