Date of Award
Doctor of Philosophy (PhD)
D. Brett Ridgely, PhD
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.
DTIC Accession Number
Walker, David E., "H2 Optimal Control with H∞, µ, and L1 Constraints" (1994). Theses and Dissertations. 6591.