MAE 284 - Robust and Multivariable Control (Spring 2004)

Department of MAE, UCSD

Instructor: Prof. Miroslav Krstic, 1808 EBUI, 822-1374, krstic@ucsd.edu

Green and Limebeer, Linear Robust Control, Prentice Hall, 1995 (main text, out of print).

Kemin Zhou, Essentials of Robust Control, Prentice Hall, 1997 (supplemental text).

Prerequisites: Linear Systems (MAE 280B) or consent of instructor

Time and Place: TuThu, 2-3:20, HSS CENTR 205

Office Hours:

M 2:30-3:30 or by appointment (e-mail, phone)

Grading: (click on highlighted items for problem sets)

Homework 35%
Final 65%

Course Objective: To introduce the students to methods for robust control of linear dynamical systems, where a priori known bounds of uncertainties are used to design a single linear controller. The focus is on state space methods for multivariable robust control, input-output properties and norms of systems, and optimal model reduction.

Topics:

• Introduction - Control Objectives: model matching, disturbance attenuation, robust stability.
• Multivariable Frequency Response Design. Singular values. Robust stability. Performance.
• Signals and Systems. Linear spaces, norms, inner products, operators, induced norms. Small gain theorem. Passivity. Bounded real lemma.
• Linear Fractional Transformations.
• LQG Control. Full information + Kalman filter = Measurement feedback.
• Full Information H-infinity Controller. Differential games. Riccati equation. Necessity and sufficiency.
• H-infinity Filter.
• H-infinity Generalized Regulator.
• Model Reduction (time permitting). Balanced realization. Truncation. Hankel norm approximations. Nehari's theorem.