ECE 553 - Optimum Control Systems

Semesters Offered

TitleRubricSectionCRNTypeTimesDaysLocationInstructor
Optimum Control SystemsECE553N33998DIS1400 - 1520 T R  4070 ECE Building Daniel Liberzon

Official Description

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.

Prerequisites

Credit in ECE 313 or STAT 410
Credit in ECE 515

Subject Area

Control Systems

Course Directors

Description

Theoretical and algorithmic foundations of optimal control theory; deterministic dynamical systems described in the continuous time; the Linear-Quadratic-Gaussian design; differential games, H∞-optimal control design.

Topics

  • 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

Detailed Description and Outline

Topics:

  • 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

Texts

Main:
D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton Univ Press, December 2011.

Recommended:
T. Basar and P. Bernhard, H∞-Optimal Control and Related Minimax Design Problems, Birkhäuser, 1995.

Last updated

2/13/2013