# Minimum variance control of discrete — time linear stochastic system, using instantaneous output feedback

Optimal Control Stochastic

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## Abstract

This paper considers the problem of determining the linear output feedback control which minimizes a quadratic performance index, for a linear, discrete — time stochastic system. Both the finite and infinite — time versions of this problem are solved. For the finite terminal time case, the two-point boundary value problem that specifies the optimal feedback gain matrices is derived, and an algorithm is proposed for solving it. For the infinite-time case, two coupled non linear matrix equations must be solved to realize the optimal control; an algorithm is also proposed for solving those equations. A numerical example is treated comparing this control policy to the optimal Kalman — type control policy.

## Keywords

Output Feedback Linear Stochastic System Optimal Feedback Gain Minimum Variance Control Feedback Gain Matrice
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## References

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1976