A Search Algorithm for a Class of Optimal Finite-Precision Controller Realization Problems with Saddle Points

Abstract

With game theory, we review the optimal digital controller realization problems that maximize a finite word length (FWL) closed-loop stability measure. For a large class of these optimal FWL controller realization problems which have saddle points, a minimax-based search algorithm is derived for finding a global optimal solution. The algorithm consists of two stages. In the first stage, the closed form of a transformation set is constructed which contains global optimal solutions. In the second stage, a subgradient approach searches this transformation set to obtain a global optimal solution. This algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these FWL realization problems. Furthermore, for a small class of optimal FWL controller realization problems which have no saddle point, the proposed algorithm also provides useful information to help solve them.

DOI: 10.1137/S0363012903435084

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Cite this paper

@article{Wu2005ASA, title={A Search Algorithm for a Class of Optimal Finite-Precision Controller Realization Problems with Saddle Points}, author={Jun Wu and Sheng Chen and Gang Li and Jian Chu}, journal={SIAM J. Control and Optimization}, year={2005}, volume={44}, pages={1787-1810} }