W. H. Kwon and D. G. Byun. Receding horizon tracking control as a predictive control and its stability properties. Int. J. Control, 50(5):1807--1824, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the more classical problems of finite horizon and infinite horizon. It combines the stability requirement that is intrinsic to infinite horizon problems, with the numerical simplicity of finite horizon methods, providing the grounds to deal with adaptiveness in various settings, e.g. see [6] [9], 10] and [5] In parallel, the interest on receding horizon strategies for filtering problems has increased. In this context, receding horizon usually appears in limited memory filters (FIR filters) that preclude divergence due to modeling errors. Michalska and Mayne in [14] presented receding ....

W. H. Kwon and D. G. Byun. Receding horizon tracking control as a predictive control and its stability properties. Int. J. Control, 50(5):1807--1824, 1989.

....but this reduces to an end constraint for unstable systems. Various other stability guaranteeing formulations have been developed, but stability analysis of the standard finite horizon policy without an end constraint has remained a challenging task. While the subject has previously been addressed [4, 12], it has not resulted in a completely satisfactory theory. Recently, a potentially more encompassing approach to stability and performance analysis was used in [9] for unconstrained non quadratic RHC. In [6] some of these ideas were exploited to present a more unified framework for the analysis ....

W.H. Kwon and D.G. Byun, "Receding horizon tracking control as a predictive control and its stability properties", In Int. J. Control, Vol. 50, No. 5, pp.18071824, 1989.

....inner feedback loop, and then applies GPC. All these strategies are in fact equivalent but have different numerical properties due to different implementation (Rossiter and Kouvaritakis, 1994) As another approach to the stability issue, finite terminal weighting may be added to the GPC cost (Kwon and Byun, 1989; Demircioglu and Clarke, 1993; Jolly and Bentsman, 1993) in order that the receding horizon cost is monotonic, thereby leading to stability. This monotonicity can also be obtained by employing time varying weighting, which places more emphasis on tracking errors and control increments further ....

....Theorem 1 Given N 2 Gamma N u 0, there exists a finite N o such that the closed loop is stable if N u N o with N 1 = 1 and ae 0. In other words, if N u 1; N 1 = 1; N 2 N u ; ae 0; 19) the closed loop predictive control system is stable (Clarke et al. 1987; Clarke and Mohtadi, 1989; Kwon and Byun, 1989). Outline of proof: This theorem is proved by observing that the predictive scheme in question tends to the steady state LQ controller for which there is a stability guarantee. Moreover, given any 0, an integer N( can be found such that a norm between the closed loop state transition ....

Kwon, W. H. and Byun, D. G. (1989). Receding horizon tracking control as a predictive control and its stability properties. Int. J. Control, 50(5), 1807--1824.

.... function (7) is general in that it can lead to a wide range of predictive methods including GPC (fl = 1) and CRHPC (fl = 0) The use of a nonzero number ( 1) for fl is expected to have effects similar to those observed in receding horizon control with finite end point weighting as discussed in Kwon and Byun (1989) and Demircioglu and Clarke (1993) In order to rewrite the cost (7) in a simple vector form, we define: DeltaU = Deltau(t) T Deltau(t 1) T Delta Delta Delta Deltau(t N u Gamma 1) T ] T ; w i 1 = w i (t N 1 ) w i (t N 1 1) Delta Delta Delta w i (t N y Gamma ....

Kwon, W. H. and Byun, D. G. (1989). Receding horizon tracking control as a predictive control and its stability properties. Int. J. Control, 50(5), 1807--1824.

....the desired trajectory is known only over a finite future interval of time. For example, Lee, et al. 10] describe the use of an instantaneous optimal controller producing a terrain tracking design for an aircraft, without requiring the solution of a two point boundary value problem. Kwon, et al. [8,9] have examined the use of an optimal receding horizon control design for tracking and disturbance rejection. However, the design requires the solution of a Ricatti type equation online. The adaptation of the sliding horizon was first discussed in [13,14] In [15] the technique of sliding horizon ....

W.H. Kwon and D.G. Byun. Receding horizon tracking control as a predictive control and it's stability properties, Int. J. Control, 50(5) (1989), 1807--1824.

....in which the optimal solutions are implemented, the intervalwise strategy is optimal, while the pointwise one is suboptimal. Hence the tracking performance of the intervalwise strategy is superior to the other one. The pointwise strategy has been developed for general timevarying systems [8] [10], 11] while the intervalwise strategy only for periodic and time invariant systems [2] 3] 9] There has been a few studies on the receding horizon tracking problems and its stability property in the H1 problem [4] 5] 11] But the intervalwise receding horizon strategy has not been ....

....control Deltau in (22) is stabilizing from Theorem 3 in the previous section. Now we will show that the stabilizing IHTC with integral action provides the zero offset. Corollary 2 The stabilizing IHTC with integral action provides the zero offset. proof: g e (t) is derived similarly to [10]: g e (t) GammaOE T e (T 1; t 1)C T e Fy r Gamma T X j=t 1 [OE T e (j; t 1)B ce (j Gamma 1)C T e y r ] t 2 [1; T Gamma 1] where OE e (t; t 0 ) A ce (t Gamma 1)A ce (t Gamma 1) Delta Delta Delta A ce (t 0 ) A ce (t) I B 2e B T 2e P e (t) Gamma1 A e [I B fle ....

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W. H. Kwon and D. G. Byun, "Receding horizon tracking control as a predictive control and its stability properties," Int.J.Control., vol. 50, no. 5, pp. 18071824, 1989.

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Kwon, W. H. and Byun, D. G., "Receding horizon tracking control as a predictive control and its stability properties," International Journal of Control, Vol.50, No.5, 1989, pp. 1807-1824.

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