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Sub-Optimal Nonlinear Predictive and Adaptive Control Based on the Parametric Volterra Model
International Journal of Applied Mathematics and Computer Science, Tome 9 (1999) no. 1, pp. 161-173.

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Predictive control algorithms have been worked out mainly to control linear plants. There is a great demand to apply different control ideas to nonlinear systems. Using predictive control algorithms for nonlinear systems is a promising technique. Extended horizon one-step-ahead and long-range optimal predictive control algorithms are given here for the parametric Volterra model (which includes also the generalized Hammerstein model). A quadratic cost function is minimized which considers the quadratic deviations of the reference signal and the output signal at a future point (or points) beyond the dead time and also penalizes large control signal increments. For prediction of the output signal, a predictive model is applied which uses information about the input and output signals up to the current time. A predictive transformation of the nonlinear dynamic model is given. The incremental model is advantageous since the cost function contains the control increment and not the control signal itself. An incremental transformation of the predictive forms is also described. Sub-optimal solutions to the optimal control algorithms are discussed with different assumptions for the control signal during the control horizon. The effect of the different strategies and the effect of the tuning parameters is investigated through simulation examples.
Keywords: predictive control, nonlinear control, optimal control, nonlinear systems, adaptive control
Mots-clés : sterowanie predykcyjne, sterowanie nieliniowe, sterowanie optymalne, układ nieliniowy, adaptacyjny układ sterowania 
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     author = {Haber, R. and Bars, R. and Lengyel, O.},
     title = {Sub-Optimal {Nonlinear} {Predictive} and {Adaptive} {Control} {Based} on the {Parametric} {Volterra} {Model}},
     journal = {International Journal of Applied Mathematics and Computer Science},
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Haber, R.; Bars, R.; Lengyel, O. Sub-Optimal Nonlinear Predictive and Adaptive Control Based on the Parametric Volterra Model. International Journal of Applied Mathematics and Computer Science, Tome 9 (1999) no. 1, pp. 161-173. http://geodesic.mathdoc.fr/item/IJAMCS_1999_9_1_a6/