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.
The authors are with the "Laboratoire d'Automatique et d'Analyse des Systèmes", Centre National de la Recherche Scientifique, 7 Avenue du Colonel Roche, 314OO TOULOUSE, France.
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Keywords
- Output Feedback
- Linear Stochastic System
- Optimal Feedback Gain
- Minimum Variance Control
- Feedback Gain Matrice
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References
P. DORATO, A. H. LEVIS "Optimal Linear Regulators: the discrete-time case" — IEEE Trans. Aut. Contr. 1971 pp. 613–620.
E. TSE "The optimal Control of Stochastic Linear Systems" — IEEE Trans. Aut. Contr. 1971 pp. 776–785.
W. M. WONHAM "On the separation theorem of Stochastic Control" SIAM J. Control, 1968 pp. 312–326
W. S. LEVINE, T. L. JOHNSON, M. ATHANS "Optimal Limited State Variable Feedback Controllers for Linear Systems" — IEEE Trans. Aut. Contr. 1971 pp. 785–793.
R. L. KOSUT "Suboptimal Control of Linear Time — invariant Systems subject to control Structure constraints" — IEEE Trans. Aut. Contr. 1970 pp. 557–563.
P. J. Mc LANE "Linear Optimal Stochastic Control using instantaneous output feedback" Int. J. Control 1971 pp. 383–396.
S. AXASTER "Suboptimal time-variable feedback control of linear dynamic systems with random inputs" — Int. J. Control, 1966 — pp. 549–566.
B. Z. KURTARAN and M. SIDAR " Optimal Instantaneous output feedback controllers for linear stochastic Systems" Int. J. Contr., 1974, pp. 797–816.
M. ATHANS " The Matrix Minimum Principle" — Information and Control, 1967, pp. 592–606.
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© 1976 Springer-Verlag Berlin Heidelberg
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Blanvillain, P., Favier, G. (1976). Minimum variance control of discrete — time linear stochastic system, using instantaneous output feedback. In: Cea, J. (eds) Optimization Techniques Modeling and Optimization in the Service of Man Part 2. Optimization Techniques 1975. Lecture Notes in Computer Science, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07623-9_317
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DOI: https://doi.org/10.1007/3-540-07623-9_317
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