Minimum output variance control for FSN models: Continuous-time case
<p>In this paper we consider the Finite Signal-to-Noise ratio model for linear stochastic systems. It is assumed that the intensity of noise corrupting a signal is proportional to the variance of the signal. Hence, the signal-to-noise ratio of each sensor and actuator is finite – as...
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2000-01-01
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Online Access: | http://www.hindawi.net/access/get.aspx?journal=mpe&volume=6&pii=S1024123X00001319 |
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doaj-66c6630fa47d443280c69bfaaca451e12020-11-24T22:49:05ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472000-01-0162-3171188Minimum output variance control for FSN models: Continuous-time caseShi GuojunSkelton Robert E.Grigoriadis Karolos M.<p>In this paper we consider the Finite Signal-to-Noise ratio model for linear stochastic systems. It is assumed that the intensity of noise corrupting a signal is proportional to the variance of the signal. Hence, the signal-to-noise ratio of each sensor and actuator is finite – as opposed to the infinite signal-to-noise ratio assumed in LQG theory. Computational errors in the controller implementation are treated similarly. The objective is to design a state feedback control law such that the closed loop system is mean square asymptotically stable and the output variance is minimized. The main result is a controller which achieves its maximal accuracy with finite control gains – as opposed to the infinite controls required to achieve maximal accuracy in LQG controllers. Necessary and sufficient conditions for optimality are derived. An optimal control law which involves the positive definite solution of a Riccati-like equation is derived. An algorithm for solving the Riccati-like equation is given and its convergence is guaranteed if a solution exists.</p> http://www.hindawi.net/access/get.aspx?journal=mpe&volume=6&pii=S1024123X00001319Linear systems; Optimal control |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shi Guojun Skelton Robert E. Grigoriadis Karolos M. |
spellingShingle |
Shi Guojun Skelton Robert E. Grigoriadis Karolos M. Minimum output variance control for FSN models: Continuous-time case Mathematical Problems in Engineering Linear systems; Optimal control |
author_facet |
Shi Guojun Skelton Robert E. Grigoriadis Karolos M. |
author_sort |
Shi Guojun |
title |
Minimum output variance control for FSN models: Continuous-time case |
title_short |
Minimum output variance control for FSN models: Continuous-time case |
title_full |
Minimum output variance control for FSN models: Continuous-time case |
title_fullStr |
Minimum output variance control for FSN models: Continuous-time case |
title_full_unstemmed |
Minimum output variance control for FSN models: Continuous-time case |
title_sort |
minimum output variance control for fsn models: continuous-time case |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2000-01-01 |
description |
<p>In this paper we consider the Finite Signal-to-Noise ratio model for linear stochastic systems. It is assumed that the intensity of noise corrupting a signal is proportional to the variance of the signal. Hence, the signal-to-noise ratio of each sensor and actuator is finite – as opposed to the infinite signal-to-noise ratio assumed in LQG theory. Computational errors in the controller implementation are treated similarly. The objective is to design a state feedback control law such that the closed loop system is mean square asymptotically stable and the output variance is minimized. The main result is a controller which achieves its maximal accuracy with finite control gains – as opposed to the infinite controls required to achieve maximal accuracy in LQG controllers. Necessary and sufficient conditions for optimality are derived. An optimal control law which involves the positive definite solution of a Riccati-like equation is derived. An algorithm for solving the Riccati-like equation is given and its convergence is guaranteed if a solution exists.</p> |
topic |
Linear systems; Optimal control |
url |
http://www.hindawi.net/access/get.aspx?journal=mpe&volume=6&pii=S1024123X00001319 |
work_keys_str_mv |
AT shiguojun minimumoutputvariancecontrolforfsnmodelscontinuoustimecase AT skeltonroberte minimumoutputvariancecontrolforfsnmodelscontinuoustimecase AT grigoriadiskarolosm minimumoutputvariancecontrolforfsnmodelscontinuoustimecase |
_version_ |
1725677373110616064 |