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Optimal stochastic adaptive control with quadratic index. (English) Zbl 0582.93066
The discrete-time stochastic control system with complete observation is considered with quadratic loss function when the constant coefficients of the system are unknown. The parameter estimates given by the recursive least-squares method are used to define the feedback gain, and the adaptive control is taken to be either a linear-state feedback disturbed by a sequence of random vectors with variances tending to zero or only the disturbance without the feedback term in accordance with stopping times defined on the trajectory of the system. It is proved that the parameter estimates are strongly consistent and the loss function reaches its minimum, i.e. the adaptive control is optimal.

MSC:
93E20 Optimal stochastic control
93C40 Adaptive control/observation systems
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
93E10 Estimation and detection in stochastic control theory
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[1] CAINES , P. E. ,CHEN, H. F, 1985 , Proc. of Conf. on Decision and Control , Las Vegas , Nevada December , 1984 , I.E.E.E. Trans, autom. Control , 30 , 185 .
[2] DOI: 10.1109/TAC.1984.1103520 · Zbl 0538.93071
[3] CHEN , H. F. , 1984 a ,SIAM J. Control and Optim., 22 , 758 ; 1984 b , Acta Math. Sci. , 4 , 51 ; 1985 , Recursive Estimation and Control for Stochastic Systems ( New York John Wiley ).
[4] CHEN , H. F. , and CAINES , P. E. , 1984 , Preprints oflFAC 9th World Congress, Vol. XII , Budapest , 150; 1985 , Proc. ofConf. on Decision and Control , Las Vegas , Nevada , December , 1984 , I.E.E.E. Trans, autom. Control , 30 , 189 .
[5] CHEN H. F., Advances in Control and Dynamic Systems 24 (1985)
[6] DOI: 10.1214/aoms/1177700166 · Zbl 0134.34003
[7] DOI: 10.1137/0319052 · Zbl 0473.93075
[8] DOI: 10.1109/TAC.1983.1103212 · Zbl 0504.93072
[9] DOI: 10.1137/0321009 · Zbl 0508.93066
[10] DOI: 10.1214/aos/1176345697
[11] LIPTSER R. S., Statistics of Random Processes (1977) · Zbl 0364.60004
[12] DOI: 10.1016/0005-1098(82)90091-7 · Zbl 0489.93055
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