H₂ Optimal Control with H_∞, µ, and L₁ Constraints

Author

David E. Walker

Date of Award

6-1994

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

D. Brett Ridgely, PhD

Abstract

H₂ optimization with convex constraints is considered. The optimal order-free solution is shown to be unique through convex analysis. H_∞ constraints with feedforward terms and singular constraints are also allowed. The optimal fixed-order solution is shown to have the same characteristics as a mixed problem with regular H_∞ constraints. Furthermore, these results are shown to hold for controller orders as low as the optimal H₂ order. A numerical method is developed based on analytical gradients which results in sub- and super-optimal fixed-order controllers. The problem is extended to include an upper bound on a mu constraint through a modification of the D-K iteration method. Next. multiple H_∞ constraints are developed. Fixed-order solutions to the multiple constraint problem are characterized and the numerical method is extended to include multiple constraints. Next, a continuous Ll constraint is added. A numerical approach is proposed based on bounding the L₁-norm by the 11- norm of an Euler approximating system. Finally. H₂ optimization with a finite set of H_∞, mu, and L₁ constraints is characterized. SISO and MIMO numerical examples demonstrate the application of these methods.

AFIT Designator

AFIT-DS-AA-94-2

DTIC Accession Number

ADA280593

Comments

The author's Vita page is omitted.

Recommended Citation

Walker, David E., "H₂ Optimal Control with H_∞, µ, and L₁ Constraints" (1994). Theses and Dissertations. 6591.
https://scholar.afit.edu/etd/6591