Optimization and Systems Theory Seminar
Friday, Nov. 12, 1999, 11.00-12.00, Room 3721, Lindstedtsv. 25

Andrey Ghulchak
Department of Automatic Control
Lund Institute of Technology
Lund, Sweden
E-mail: ghulchak@control.lth.se

Robust controller design via linear programming

The result concerns the particular case of a linear dependence of the closed-loop characteristic polynomial on an uncertain parameter. In this case the convex parameterization of all robustly stabilizing controllers is obtained. The algorithm proposed is a sequence of the standard linear programming problems of growing dimension which approximate the original problem. Then the standard free software (e.g. PCX package) can be used to solve the problem.

The finite dimensional approximation gives us only the lower bound of the uncertainty radius. However, using the convex duality arguments the dual problem to the uncertainty radius optimization is derived. It has mainly the form of H_1 optimization. It is shown that the dual problem can be solved in the same linear programming framework as the primal one. It gives the upper bound of the uncertainty radius. So running both the primal and dual algorithms one can maximize the bound with a prespecified accuracy.

Calendar of seminars
Last update: Ocotber 13, 1999 by Anders Forsgren, anders.forsgren@math.kth.se.