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Title: $H_2$ optimal decoupling of previewed signals in the discrete-time case (English)
Author: Marro, Giovanni
Author: Prattichizzo, Domenico
Author: Zattoni, Elena
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 38
Issue: 4
Year: 2002
Pages: [479]-492
Summary lang: English
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Category: math
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Summary: The synthesis of a feedforward unit for $H_2$ optimal decoupling of measurable or previewed signals in discrete-time linear time-invariant systems is considered. It is shown that an $H_2$ optimal compensator can be achieved by connecting a finite impulse response (FIR) system and a stable dynamic unit. To derive the FIR system convolution profiles an easily implementable computational scheme based on pseudoinversion (possibly nested to avoid computational constraints) is proposed, while the dynamic unit is derived by solving a standard LQR problem, in general cheap or singular. (English)
Keyword: optimal decoupling of signal
Keyword: discrete-time system
MSC: 93B36
MSC: 93C55
MSC: 93C62
MSC: 93E12
idZBL: Zbl 1265.93177
idMR: MR1937142
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Date available: 2009-09-24T19:47:57Z
Last updated: 2015-03-25
Stable URL: http://hdl.handle.net/10338.dmlcz/135479
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Reference: [1] Barbagli F., Marro, G., Prattichizzo D.: Solving signal decoupling problems through self-bounded controlled invariants.In: Proc. 39th IEEE Conference on Decision and Control (CDC 2000), Sydney 2000
Reference: [2] Basile G., Marro G.: L’invarianza rispetto ai disturbi studiata nello spazio degli stati.In: Rendiconti della LXX Riunione Annuale AEI, paper no. 1-4-01, Rimini 1969
Reference: [3] Basile G., Marro G.: Controlled and conditioned invariant subspaces in linear system theory.J. Optim. Theory Appl. 3 (1969), 5, 306–315 Zbl 0172.12501, MR 0246661, 10.1007/BF00931370
Reference: [4] Basile G., Marro G.: A new characterization of some structural properties of linear systems: unknown-input observability, invertibility and functional controllability.Internat. J. Control 17 (1973), 5, 931–943 Zbl 0255.93009, MR 0325195, 10.1080/00207177308932438
Reference: [5] Basile G., Hamano, F., Marro G.: Some new results on unknown input observability.In: Proc. Eighth Triennial World Congress of the International Federation of Automatic Control, Kyoto, Japan 1981, pp. 21–25
Reference: [6] Basile G., Marro G.: Controlled and Conditioned Invariants in Linear System Theory.Prentice Hall, Englewood Cliffs, NJ 1992 Zbl 0758.93002, MR 1149379
Reference: [7] Bhattacharyya S. P.: Disturbance rejection in linear systems.Internat. J. Systems Science 5 (1974), 7, 931–943 Zbl 0295.93003, MR 0363580
Reference: [8] Bitmead R. R., Gevers, M., Wertz V.: Adaptive Optimal Control-The Thinking Man’s GPC.Prentice Hall, Englewood Cliffs, NJ, 1990 Zbl 0751.93052
Reference: [9] Estrada M. Bonilla, Malabre M.: Necessary and sufficient conditions for disturbance decoupling with stability using PID control laws.IEEE Trans. Automat. Control AC-44 (1999), 6, 1311–1315 MR 1689159, 10.1109/9.769398
Reference: [10] Estrada M. Bonilla, Malabre M.: Structural conditions for disturbance decoupling with stability using proportional and derivative control laws.IEEE Trans. Automat. Control AC-46 (2001), 1, 160–165 MR 1809481, 10.1109/9.898711
Reference: [11] Chen B. M.: $H_\infty $ control and its applications.(Lecture Notes in Control and Inform. Sciences 235.), Springer–Verlag, New York 1999 Zbl 0912.93003, MR 1636909
Reference: [12] Chen B. M.: Robust and $H_\infty $ Control.(Communications and Control Engineering Series.) Springer, New York 2000 Zbl 0996.93002, MR 1761689
Reference: [13] Davison E. J., Scherzinger B. M.: Perfect control of the robust servomechanism problem.IEEE Trans. Automat. Control AC-32 (1987), 8, 689–701 Zbl 0625.93051
Reference: [14] Nicolao G. De, Strada S.: On the stability of receding-horizon LQ control with zero-state terminal constraint.IEEE Trans. Automat. Control 42 (1997), 2, 257–260 Zbl 0880.93042, MR 1438456, 10.1109/9.554406
Reference: [15] Devasia S., Chen, D., Paden B.: Nonlinear inversion-based output tracking.IEEE Trans. Automat. Control 41 (1996), 7, 930–942 Zbl 0859.93006, MR 1398777, 10.1109/9.508898
Reference: [16] Dorato P.: On the inverse of linear dynamical systems.IEEE. Trans. System Sci. and Cybernetics SSC-5 (1969), 1, 43–48 Zbl 0184.18402, 10.1109/TSSC.1969.300243
Reference: [17] Francis B. A.: The optimal linear quadratic time invariant regulator with cheap control.IEEE Trans. Automat. Control AC-24 (1979), 616–621 Zbl 0424.49022, MR 0538820, 10.1109/TAC.1979.1102097
Reference: [18] Gross E., Tomizuka M.: Experimental flexible beam tip tracking control with a truncated series approximation to uncancelable inverse dynamics.IEEE Trans. Control Syst. Techn. 3 (1994), 4, 382–391 10.1109/87.338659
Reference: [19] Hunt L. R., Meyer, G., Su R.: Noncausal inverses for linear systems.IEEE Trans. Automat. Control 41 (1996), 4, 608–611 Zbl 0864.93055, MR 1385335, 10.1109/9.489285
Reference: [20] Imai H., Shinozuka M., Yamaki T., Li, D., Kuwana M.: Disturbance decoupling by feedforward and preview control.Trans. ASME J. Dynamic Systems, Measurement Control 105 (1983), 3, 11–17 Zbl 0512.93029, 10.1115/1.3139721
Reference: [21] Kwon W. H., Pearson A. E.: On feedback stabilization of time-varying discrete linear systems.IEEE Trans. Automat. Control AC-23 (1978), 3, 479–481 Zbl 0378.93038, MR 0496918, 10.1109/TAC.1978.1101749
Reference: [22] Malabre M., Kučera V.: Infinite structure and exact model matching problem: a geometric approach.IEEE Trans. Automat. Control AC-29 (1982), 3, 266–268 10.1109/TAC.1984.1103502
Reference: [23] Marro G., Fantoni M.: Using preaction with infinite or finite preview for perfect or almost perfect digital tracking.In: Proceedings of the Melecon’96 – 8th Mediterranean Electrotechnical Conference, Bari 1996, Vol. 1, pp. 246–249
Reference: [24] Marro G., Prattichizzo, D., Zattoni E.: Geometric insight into discrete-time cheap and singular linear quadratic Riccati (LQR) problems.IEEE Trans. Automat. Control 47 (2002), 1 MR 1879695, 10.1109/9.981727
Reference: [25] Marro G., Prattichizzo, D., Zattoni E.: ${H}_2$ optimal decoupling of previewed signals with FIR systems.In: Proc. 1st IFAC Symposium on System Structure and Control (SSSC 2001), (P. Horáček, ed.), Prague 2001
Reference: [26] Marro G., Prattichizzo, D., Zattoni E.: A unified algorithmic setting for signal–decoupling compensators and unknown–input observers.In: Proc. 39th Conference on Decision and Control (CDC 2000), Sydney 2000
Reference: [27] Marro G., Prattichizzo, D., Zattoni E.: A nested computational scheme for discrete-time cheap and singular LQ control.In: Proc. 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation (IMACS 2000), Lausanne 2000
Reference: [28] Marro G., Prattichizzo, D., Zattoni E.: Convolution profiles for noncausal inversion of multivariable discrete-time systems.In: Proc. 8th IEEE Mediterranean Conference on Control & Automation (MED 2000), (P. P. Groumpos, N. T. Koussoulas, and P. J. Antsaklis, eds.), University of Patras, Rio 2000
Reference: [29] Marro G., Prattichizzo, D., Zattoni E.: An algorithmic solution to the discrete-time cheap and singular LQR problems.In: Proc. 14th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2000), Perpignan 2000
Reference: [30] Morse A. S.: Structural invariants of linear multivariable systems.SIAM J. Control 11 (1973), 3, 446–465 Zbl 0259.93011, MR 0386762, 10.1137/0311037
Reference: [31] Park S. H., Kim P. S., Kwon O.-K., Kwon W. H.: Estimation and detection of unknown inputs using optimal FIR filter.Automatica 36 (2000), 1481–1488 Zbl 0959.93517, MR 1829760, 10.1016/S0005-1098(00)00063-7
Reference: [32] Qiu L., Davison E. J.: Performance limitations of non-minimum phase systems in the servomechanism problem.IEEE Trans. Automat. Control 29 (1993), 2, 337–349 Zbl 0778.93053, MR 1211291
Reference: [33] Saberi A., Sannuti, P., Chen B. M.: $H_2$ Optimal Control.(System and Control Engineering.) Prentice Hall International, London 1995
Reference: [34] Saberi A., Stoorvogel A. A., Sannuti P.: Control of linear systems with regulation and input constraints.(Communications and Control Engineering Series.) Springer, New York 2000 Zbl 0977.93001, MR 1756793
Reference: [35] Sain M. K., Massey J. L.: Invertibility of linear time-invariant dynamical systems.IEEE Trans. Automat. Control AC-14 (1969), 2, 141–149 MR 0246664, 10.1109/TAC.1969.1099133
Reference: [36] Silverman L.: Inversion of multivariable linear systems.IEEE Trans. Automat. Control AC-14 (1969), 3, 270–276 MR 0267927, 10.1109/TAC.1969.1099169
Reference: [37] Trentelman H. L., Stoorvogel A. A., Hautus M.: Control theory for linear systems.(Communications and Control Engineering Series.) Springer, New York 2001 Zbl 0963.93004, MR 1851149
Reference: [38] Willems J. C.: Feedforward control, PID control laws, and almost invariant subspaces.Systems Control Lett. 1 (1982), 4, 277–282 Zbl 0473.93032, MR 0670212, 10.1016/S0167-6911(82)80012-1
Reference: [39] Wonham W. M.: Linear Multivariable Control: A Geometric Approach.Third edition. Springer, New York 1985 Zbl 0609.93001, MR 0770574
Reference: [40] Wonham W. M., Morse A. S.: Decoupling and pole assignment in linear multivariable systems: a geometric approach.SIAM J. Control 8 (1970), 1, 1–18 Zbl 0206.16404, MR 0270771, 10.1137/0308001
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