1. Optimization related to Mu -synthesis
2. Computer assistance with non commuting algebra problems

Bill Helton, Mathematics, US San Diego

Two topics will be treated briefly:

The talk will specialize the more general theory in Thursdays talk to the Mu -synthesis problem. Also the speaker will say those things on Friday he forgot to say on Thursday.

Most formulas in linear control theory (and some in nonlinear control) involve matrices and so deriving these formulas involves noncommuting algebra. We are currently the main providers of general noncommutative capability under Mathematica.

Our research focuses on an algorithm for putting systems of equations into "canonical form". The talk will first illustrate how this is useful for automatically simplifying complicated expressions. Then we turn to a bold undertaking. The objective is:

Given a (complicated) set of algebra equations we want to "solve", reduce it to a small set of equations (eg. Riccati equations) which are numerically solvable by Matlab.

Many theorems in control (eg. the famous DGKF two Riccati equation theorem) can be thought of this way. Our idea is to run the algorithm, sort the output, a human looks and makes a decision, run the algorithm again, etc. The goal is to isolate and minimize the amount of human intervention required. We are testing our method on various classic theorems of control to get an idea of how much the algorithm can do and how much a human must do.