**Optimal** Control

**Optimal**Control

**Optimal Control ****– ***UNIVERSITY OF MARYLAND*, College Park,Electrical & Computer Engineering & Institute for Systems Research

**Lecture Notes by P. S. Krishnaprasad**

**Survey Lecture on Linear Systems and link to ENEE 660 System Theory Notes **

**Lecture 1****Lecture 2****Lecture 3****Lecture 4 and an addendum****Lecture 4 Page 12 fix****Lecture 5(a), updated; Lecture 5(b); Lecture 5(c) Lecture 5(c) Update****Lecture 6****Lecture 7 and solution to Queen Dido’s problem****Lecture 7 addendum (on transversality condition)****Lecture 8 on fixed point problems****Lecture 9(a) on Newton’s method and additional material (lecture 9(b)) on****mean value theorem****Lecture 10(a) on Newton’s method and rate of convergence and****Lecture 10(b) on iterative minimization****Lecture 11(a) on second order necessary conditions****Lecture 11(b) on Taylor’s theorem****Lecture 11(c) on second order necessary conditions in the calculus of variations (Legendre)****Lecture 12 on maximum principle****Lecture 13 on Hamilton Jacobi Bellman Equation**

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**Lecture Notes by Professor Andre L. Tits **

Homework Assignments

*Optimal Control – **University of Illinois at Urbana-Champaign*

**Texts Book:**

- Dimitri P. Bertsekas, Dynamic Programming and Optimal Control, Volume I, 3rd edition, Athena Scientific, 2005.
- M. Athans and P.L. Falb, Optimal Control, McGraw Hill, 2007 (paper back).
- I. M. Gel’fand and S. V. Fomin, Calculus of Variations, Dover Publications, 2000.

# Homework | Lectures Notes

**Course Outline:**

- Formulation of optimal control problems
- Parameter optimization versus path optimization
- Local and global optima; general conditions on existence and uniquenes.
- Some basic facts from finite-dimensional optimization.

II. **The Calculus of Variations **

- The Euler-Lagrange equation
- Path optimization subject to constraints
- Weak and strong extrema

III. **The Minimum (Maximum) Principle and the Hamilton-Jacobi Theory **

- Pontryagin’s minimum principle
- Optimal control with state and control constraints
- Time-optimal control
- Singular solutions
- Hamilton-Jacobi-Bellman (HJB) equation, and dynamical programming
- Viscosity solutions to HJB

IV. **Linear Quadratic Gaussian (LQG) Problems **

- Finite-time and infinite-time state (or output) regulators
- Riccati equation and its properties
- Tracking and disturbance rejection
- Kalman filter and duality
- The LQG design

V. **Nonholonomic System Optimal Control **

VI. **Game Theoretic Optimal Control Design**