ECE 515: Control System Theory and Design - Spring 2014

Department of Electrical and Computer Engineering
The University of Illinois at Urbana-Champaign

The main web page for this course is maintained by the ECE Department. You'll find it here. This page includes all information about grading, homeworks, exams, TA's, etc.

Daily Schedule

Reading assignments should be completed before the lecture for which they are assigned.
Topics for lectures in the future are subject to change.
Lecture Date Topic Reading Assignments  
1 Jan. 21 Course Overview Read Chapter 1 of the course notes
2 Jan. 23 Fields, vector spaces, subspaces, linear operators, range space, null space Read Chapter 2 of the course notes
3 Jan. 28 Linear operators as matrices, coordinate transformations, similarity transformations, eigenvalues and eigenvectors, diagonalization  
4 Jan. 30 Jordan form, Cayley-Hamilton Theorem, matrix exponential, solutions to linear systems differential equations Read Chapter 3 of the course notes  
5 Feb. 4 Computing the matrix exponential for (i) diagonal matrices, (ii) diagonalizable matrices, (iii) nilpotent matrices (iv) matrices in Jordan form  
6 Feb. 6 Solutions to linear time-varying (LTV) systems: Peano-Baker Series, solutions form an n-dimensional vector space, fundamental matrices, the state transition matrix and its properties, solutions for forced systems (with a slight digression to the Leibniz rule for differentiating integrals), time varying coordinate transformations and equivalence transformations  
7 Feb. 11 Inner products, norms, symmetric matrices, symmetric and antisymmetric parts of a matrix, quadratic forms, quadratic forms under change of coordinates, induced norms, sub-multiplicative property of the induced matrix norm, positive definite matrices Review Chapter 2 of the course notes  
8 Feb. 13 Introduction to stability concepts: BIBO stability, stability in the sense of Lyapunov, Asymptotic Stability (A.S.), Global Asymptotic Stability (G.A.S.), for LTI systems the origin is the only possible A.S. equilibrium, and A.S. implies G.A.S Read Chapter 4 of the course notes  
9 Feb. 18 Stability of LTI systems: boundedness and stability, boundedness of solutions, boundedness for solutions in Jordan form. Lyapunov functions and Lyapunov's direct method.  
10 Feb. 20 Lyapunov's 2nd method applied to LTI systems, the Lyapunov equation  
11 Feb. 25 Stability subspaces, Lyapunov's first method, BIBO stability, examples  
12 Feb. 27 Controllability: definition, controllability grammian, controllability for LTV systems, controllability for LTI systems Read Chapter 5 of the course notes  
13 Mar. 4 Controllability: invariance w.r.t. similarity transformations, Kalman contollability canonical form  
14 Mar. 6 Hautus-Rosenbrock and eigenvector tests for controllability, Observability: distinguishable initial conditions, unobservable subspace, the observability grammian, observability grammian rank test, recovering initial state from output, duality Read Chapter 6 of the course notes
15 Mar. 11 Various applications of duality to LTI systems; transfer functions and realizations, uniqueness, minimal realizations, Markov parameters, equivalent realizations have the same Markov parameters  
16 Mar. 13 Minimality, controllability and observability; Feedback control: controllable canonical form (CCF), pole placement for CCF case Read Chapter 7 of the course notes
17 Mar. 18 Transformation to CCF, pole placement for general controllable systems, stabilization of systems that are not controllable  
18 Mar. 20 No Class (to compensate for evening exam)  
--- Mar. 25 SPRING BREAK  
--- Mar. 27 SPING BREAK  
19 Apr. 1 Intro. to Observers, Luenberger observers, observable canonical form, observer feedback Read Chapter 8 of the course notes
20 Apr. 3 Reduced order observers, tracking and disturbance rejection  
21 Apr. 8 Broad recap of the course until now; overview of optimal control (HJB vs. PMP); discrete dynamic programming: cost, value function, principle of optimality, finite and infinite horizon problems, value iteration algorithm, computational complexity and the curse of dimensionality Read Sections 10.1 and 10.2 of the course notes  
22 Apr. 10 Formulation of the optimal control problem for continuous time systems, derivation of the HJB Equations  
23 Apr. 15 Finding the optimal control by minimizing the Hamiltonian, sufficiency of HJB Equation, a simple scalar, linear system with quadratic cost  
24 Apr. 17 Finite horizon LQR, the Riccati Differential Equation, HJB vs. the minimum priciple Read Section 10.3 of the course notes
25 Apr. 22 A first introduction to the minimum principle, including a derviation that relies on the HJB equation, LQR via the minimum principle Read Section 11.1 and of the course notes
-- Apr. 24 No Class  
26 Apr. 29 The Hamiltonian matrix, Infinite horizon LQR, the Algebraic Riccati Equation Read Sections 11.4, 10.4 nd 10.5 of the course notes
27 May 1 Infinite horizon LQR: value function, and the optimal control; Review of optimization and Lagrange multipliers  
28 May. 6 Derivation of the minimum principle using Lagrange multiplier theory