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 ScheduleReading assignments should be completedbefore
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 |