A search algorithm for a class of optimal finite-precision controller realization problems with saddle points
A search algorithm for a class of optimal finite-precision controller realization problems with saddle points
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.
1787-1810
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Chen, S.
9310a111-f79a-48b8-98c7-383ca93cbb80
Li, G.
f0f77e84-2dca-4e91-854e-156d36434431
Chu, J.
08744087-3532-4f12-9d8a-5c8e5d79be0e
October 2005
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Chen, S.
9310a111-f79a-48b8-98c7-383ca93cbb80
Li, G.
f0f77e84-2dca-4e91-854e-156d36434431
Chu, J.
08744087-3532-4f12-9d8a-5c8e5d79be0e
Wu, J., Chen, S., Li, G. and Chu, J.
(2005)
A search algorithm for a class of optimal finite-precision controller realization problems with saddle points.
SIAM Journal on Control and Optimization, 44 (5), .
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.
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SIAM-43508.pdf
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Published date: October 2005
Organisations:
Southampton Wireless Group
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Local EPrints ID: 261581
URI: http://eprints.soton.ac.uk/id/eprint/261581
PURE UUID: aee32396-e58c-460c-82a0-2c6f6e00e8c1
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Date deposited: 24 Nov 2005
Last modified: 14 Mar 2024 06:55
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Author:
J. Wu
Author:
S. Chen
Author:
G. Li
Author:
J. Chu
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