Abstract
An unconstrained stochastic optimization problem involving a discrete-time linear process with a normally distributed initial condition and subject to additive gaussian state and measurement noise is formulated in terms of a quite general finite horizon, discrete-time quadratic cost criterion and solved when there is either complete or incomplete state information. It is shown that both the stochastic sampled-data optimal tracker and the stochastic sampled-data optimal regulator are special cases of this problem. A breakdown of the minimum cost for both sampled-data controllers is given.
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References
Davis, M. H. A., and Vinter, R. B. (1985) Stochastic Modelling and Control. Chapman and Hall, London.
Haddad, W. M., and Bernstein, D. S. (1988) Optimal nonzero setpoint regulation via fixed-order dynamic compensation. IEEE Trans. Automat. Control, 33:848–852.
Halyo, N., and Caglayan, A. K. (1976) A separation theorem for the stochastic sampled-data LQG problem. Internat. J. Control, 23(2):237–244.
Johnson, A. (1985) Process Dynamics, Estimation and Control. Peregrinus, London.
Johnson, A. (1990) The discrete and sampled-data deterministic control problems. PDR Research Group Technical Report No 64, TU Delft.
Levis, A. H., Schlueter, R. A., and Athans, M. (1971) On the behaviour of optimal sampled-data regulators. Internat. J. Control, 13(2):343–361.
Lewis, F. L. (1986) Optimal Estimation. Wiley, New York.
Nour Eldin, H. A. (1971) Optimierung linearer regelsysteme mit quadratischer zielfunction. Lecture Notes in Economics and Mathematical Systems, Vol. 47. Springer-Verlag, Berlin.
Van Willigenburg, L. G. (1991) Digital optimal control of rigid manipulators. Ph.D. Thesis, Faculty of Applied Physics, TU Delft.
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Johnson, A. Discrete and sampled-data stochastic control problems with complete and incomplete state information. Appl Math Optim 24, 289–316 (1991). https://doi.org/10.1007/BF01447747
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DOI: https://doi.org/10.1007/BF01447747