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ECE Course Syllabus

ECE6553 Course Syllabus


Optimal Control and Optimization (3-0-3)

Technical Interest
Systems and Controls

ECE 6550


Catalog Description
Optimal control of dynamic systems, numerical optimization techniques and their applications in solving optimal-trajectory problems.

D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, , Princeton University Press, 2012.(optional) (comment: FREE Internet copy: https://netfiles.uiuc.edu/liberzon/www/teaching/cvoc.pdf 2011)

A.E. Bryson and Y.-C. Ho, Applied Optimal Control, Hemisphere, 1975.(optional)

Indicators (SPIs)
SPIs are a subset of the abilities a student will be able to demonstrate upon successfully completing the course.

Topical Outline
1.	Introductory material
	a.	Review of linear, time-invariant systems
	b.	Linear, time-varying systems	
2.	Parameter Optimization 
	a.	Unconstrained Optimization: gradient-descent algorithms and Newton-Raphson methods
	b.	Optimization with constrains: Lagrange multipliers and the Karush-Kuhn-Tucker method, linear programming and the penalty-function method 
3.	Optimal Control 	
	a.	Unconstrained problems, the calculus of variations, Lagrangian Dynamics
	b.	The Bolza problem with free final time and fixed final time
	c.	Problems with and without constraints on the final state
4.	Optimal control problems with control-inequality constraints
	a.	Pontryagin Maximum Principle
	b.	Bang-Bang Control, Sliding Modes
	c.	Minimum time problems, minimum fuel and minimum energy problems
5.	Optimal Feedback Control 
	a.	Dynamic programming
	b.	The Hamilton-Jacobi-Bellman Equation
6.	Linear systems with quadratic criteria
	a.	LQR control and the Riccati equation
	b.	Square root characteristic equation, spectral factorization
7.	Supplements (to be covered selectively if time permits)
	a.	Model Predictive Control
	b.	Minimum Sensitivity Design and Maximum Accuracy Control 
	c.	Relaxed controls
	d.	Optimal Control of Systems with Delays
	e.	Singular Optimal Control