Optimum Control Systems
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Displaying course information from Spring 2014.
||1400 - 1520
|| T R
||1304 Siebel Center for Comp Sci
||Theoretical and algorithmic foundations of deterministic optimal control theory, including calculus of variations, maximum principle, and principle of optimality; the Linear-Quadratic-Gaussian design; differential games and H-infinity optimal control design. Course Information: Prerequisite: ECE 313 and ECE 515.
||Credit in ECE 313 or STAT 410
Credit in ECE 515
|Detailed Description and Outline
- Introduction: formulation of optimal control problems; parameter optimization versus path optimization; local and global optima; general conditions on existence and uniqueness; some useful results finite-dimensional optimization
- Calculus of variations: Euler-Lagrange equation and the associated transversality conditions; path optimization subject to equality and inequality constraints; differences between weak and strong extrema; second-order conditions for extrema
- Minimum principle and Hamilton-Jacobi theory: Pontryagin's minimum principle; optimal control with state and control constraints; time-optimal control; singular solutions; Hamilton-Jacobi-Bellman equation, and relationship with dynamic programming
- Linear quadratic problems: basic finite-time and infinite-time state regulator (review of material covered in ECE 415); spectral factorization, robustness, frequency weightings; tracking and disturbance rejection; the Kalman filter and duality; the linear-quadratic-Gaussian (LQG) design
- Perturbational and computational methods: near-optimal designs; gradient methods; numerical methods based on the second variation
- Differential games: solution concepts for zero-sum and nonzero-sum games; general theorems on existence and uniqueness; explicit solutions to linear-quadratic games
- H[infinity]-optimal control design: relationships with zero-sum differential games; optimum or near-optimum designs under different information patterns
D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton Univ Press, December 2011.
T. Basar and P. Bernhard, H∞-Optimal Control and Related Minimax Design Problems, Birkhäuser, 1995.
Last updated: 2/13/2013