Linear regulator design for stochastic systems by a multiple time scale method

Teneketzis,; Sandell,

doi:10.1109/cdc.1976.267735

Cited by 2 publications

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“…The gain determination problem for a Kalman filter in a singularly perturbed system has been considered using the numerical power series expansion The approximate solution for the Kalman filter gain is obtained in terms of an outer series and a correction series. 6, 7 The outer series takes advantage of the order reduction associated with degeneration (the degenerate equations obtained from the suppression of a small parameter violate some of the given initial conditions) and the correction series takes care of the violated initial conditions. The steady state Kalman filter gain is obtained by solving the reduced-order linear algebraic equations instead of the non-linear coupled algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

Decomposition method for solving kalman filter gains in singularly perturbed systems

Shen¹,

Rao²,

Ying³

1993

Optim Control Appl Methods

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SUMMARYIn this paper a decomposition method is introduced for the solution of the optimal Kalman filter gains in singularly perturbed systems by solving two reduced-order linear equations. The decomposition is achieved via the use of the Chang transformation, which is applied to the Hamiltonian matrix of the singularity perturbed Kalman filter. Since the decoupling transformation can be obtained up to an arbitrary degree of accuracy at very low cost, this approach produces an efficient numerical method for obtaining the Kalman filter gains. A numerical example is given to demonstrate the efficiency of the method.

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Section: Introductionmentioning

confidence: 99%

Decomposition method for solving kalman filter gains in singularly perturbed systems

Shen¹,

Rao²,

Ying³

1993

Optim Control Appl Methods

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“…it was demonstrated by Teneketzis and Sandell (1977) and Haddad and Kokotovic (1977) that the optimal solution may be approximated by the solutions of two reduced order stochastic control problems in the slow and fast time scale.…”

Section: Stochastic Filtering and Controlmentioning

confidence: 99%

Applications of Singular Perturbation Techniques to Control Problems

Kokotović¹

1984

SIAM Rev.

387

126

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This paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years. The first three sections are devoted to the standard model and its time-scale, stability and controllability properties. The next two sections deal with linear-quadratic optimal control and one with cheap (near-singular) control. Then the composite control and trajectory optimization are considered in two sections, and stochastic control in one section. The last section returns to the problem of modeling, this time in the context of large scale systems. The bibliography contains more then 250 titles. D IS T R I B U T I O N / A V A I L A B I L I T Y O F A B S T R A C T U N C L A S S I F I E D / U N L I M I T E D S S A M E A S R PT. □ O T I C U S E R S □ 21. A B S T R A C T S E C U R I T Y C L A S S I F I C A T I O NUnclassified S E C U R I T Y C L A S S I F I C A T I O N O F T H IS P A G E S E C U R IT Y C L A S S IF IC A T IO N O F TH IS P A G E S E C U R I T Y C L A S S I F I C A T I O N O F T H I S P A G E APPLICATIONS OF SINGULAR PERTURBATION TECHNIQUES

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Linear regulator design for stochastic systems by a multiple time scale method

Cited by 2 publications

References 0 publications

Decomposition method for solving kalman filter gains in singularly perturbed systems

Decomposition method for solving kalman filter gains in singularly perturbed systems

Applications of Singular Perturbation Techniques to Control Problems

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