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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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