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Control of linear processes with distributed lags using dynamic programming from first principles

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Abstract

A simple dynamic programming argument is presented for the quadratic-cost controller synthesis problem for discrete-time linear processes with delay. Distributed delays are allowed in both state and control. The solution obtained has a discrete-time Riccati difference structure closely analogous to the Riccati differential structure associated with delay problems in continuous time. Extensions are provided for the cases of varying lag-limits, performance criterion dependent on past variables, and the time-invariant regulator problem. A feedback solution is also obtained for a continuous-time problem with distributed delays in the control, by passage to limit from the discrete results.

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References

  1. Alekal, Y., Brunovsky, P., Chyung, D. H., andLee, E. B.,The Quadratic Problem for Systems with Time Delays, IEEE Transactions on Automatic Control, Vol. 16, No. 6, 1971.

  2. Aggarwal, J. K., andEller, D. H.,Optimization of Functional Differential Systems, Journal of Optimization Theory and Applications, Vol. 11, No. 1, 1973.

  3. Kushner, H. J., andBarnea, D. I.,On the Control of a Linear Functional Differential with Quadratic Cost, SIAM Journal on Control, Vol. 8, No. 2, 1970.

  4. Sendaula, H. M.,Optimal Control of Linear Systems with Time-Varying Lags, IEEE Transactions on Automatic Control, Vol. 17, No. 5, 1972.

  5. Koivo, H. N., andLee, E. B.,Controller Synthesis for Linear Systems with Retarded State and Control Variables and Quadratic Cost, Automatica, Vol. 8, No. 2, 1972.

  6. Lee, E. B.,Variational Problems for Systems Having Delay in the Control Action, IEEE Transactions on Automatic Control, Vol. 13, No. 6, 1968.

  7. Banks, H. T.,The Optimization of Trajectories of Linear Functional Differential Equations, SIAM Journal on Control, Vol. 8, No. 4, 1970.

  8. Arthur, W. B.,Optimal Control Theory with Time Delay. Ph.D. Dissertation, University of California, Berkeley, California, Operations Research Center, Report No. ORC 73-27, 1973.

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  9. Dorato, P., andLevis, A. H.,Optimal Linear Regulators: The Discrete-Time Case, IEEE Transactions on Automatic Control, Vol. 16, No. 6, 1971.

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Authors and Affiliations

  1. International Institute of Applied Systems Analysis, Laxenburg, Austria

    W. B. Arthur (Research Scholar)

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  1. W. B. Arthur
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Communicated by S. E. Dreyfus

This work was supported by the Operations Research Center, University of California, Berkeley, California, under NSF Grant No. GP-30961X2. The author would like to thank Professor S. E. Dreyfus for guidance and helpful suggestions.

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Arthur, W.B. Control of linear processes with distributed lags using dynamic programming from first principles. J Optim Theory Appl 23, 429–443 (1977). https://doi.org/10.1007/BF00933451

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  • DOI: https://doi.org/10.1007/BF00933451

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