D. c. optimization approach to robust control: Feasibility problems. (English) Zbl 0998.93012

Tuan, H. D.; Apkarian, P.; Hosoe, S.; Tuy, H.

Int. J. Control 73, No. 2, 89-104 (2000).

Global optimization algorithms are designed to solve numerically some difficult non-convex problems arising in robust control of linear systems, namely \(H_\infty\) output feedback control with constant scalings and more general bilinear matrix inequality problems. It is shown how the particular problem structure can be exploited in a branch and bound scheme: branching is performed on a reduced number of variables, whereas bounding is done on d.c. (difference of convex functions) inequalities relaxed to linear or linear matrix constraints. Very preliminary numerical results are described.

Reviewer: Didier Henrion (Toulouse)

MSC:

93B40	Computational methods in systems theory (MSC2010)
90C26	Nonconvex programming, global optimization
93B36	\(H^\infty\)-control
90C22	Semidefinite programming
93D09	Robust stability
93B51	Design techniques (robust design, computer-aided design, etc.)

Keywords:

robust control; global optimization; nonconvex programming; semidefinite programming; \(H_\infty\) control; constant scalings; bilinear matrix inequality; branch and bound scheme; difference of convex functions