Nonsmooth H∞ synthesis

Authors:
Pierre Apkarian;Dominikus Noll
Affiliations:
ONERA, Control Dept., Maths. Dept., Paul Sabatier University, Toulouse, France;ONERA, Control Dept., Maths. Dept., Paul Sabatier University, Toulouse, France
Venue:
ACMOS'05 Proceedings of the 7th WSEAS international conference on Automatic control, modeling and simulation
Year:
2005

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Abstract

We develop nonsmooth optimization techniques to solve H∞ synthesis problems under additional structural constraints on the controller. Our approach avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems. The proposed framework is very versatile and can accommodate a number of challenging design problems including static, fixed-order, fixed-structure, decentralized control, design of PID controllers and simultaneous design and stabilization problems. Our algorithmic strategy uses generalized gradients and bundling techniques suited for the H∞-norm and other nonsmooth performance criteria. Convergence to a critical point from an arbitrary starting point is proved (full version) and numerical tests are included to validate our methods.