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A note on model matching for nonrealizable nonlinear systems

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EN
In this technical note the model matching problem for nonlinear systems not admitting the state space realization is discussed. Both continuous- and discrete-time cases are addressed. It is demonstrated, by using a transfer function formalism, that even in case of nonrealizable systems it is sometimes still possible to find realizable compensators.
Rocznik
Strony
451--461
Opis fizyczny
Bibliogr. 25 poz., rys.
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autor
Bibliografia
  • [1] M. D. DI BENEDETTO: Nonlinear strong model matching. IEEE Transactions on Automatic Control, 35 (1990), 1351 -1355.
  • [2] M. D. DI BENEDETTO and A. ISIDORl: The matching of nonlinear models via dynamie state feedback. In 23rd IEEE Conf. on Decision and Control, Las Vegas, USA, (1984).
  • [3] G. CONTE, C.H. MOOG and A.M. Perdon: Algebraic methods for nonlinear control systems. Theory and applications. Communications and Control Engineer-ing. Springer-Verlag, London, 2nd edition, 2007.
  • [4] P. E. Crouch, F. Lamnabhi-Lagarrigue and D. Pinchon: A realization algorithm for input-output systems. Int. J. of Control, 62(4), (1995), 941-960.
  • [5] M. FLIESS: Une interpretation algebriąue de la transformation de laplace et des matrices de transfert. Linear Algebra and its Applications, 203 (1994), 429-442.
  • [6] M. Fliess, C. Join and H. Sira-Ramirez: Non-linear estimation is easy. Int. J. Modelling, Identification and Control, 4 (2008), 12-27.
  • [7] M. Fliess, J. Levine, P. Martin and P. Rouchon: Flatness and defect of non-linear systems: introductory theory and examples. Int. J. Control, 61 (1995), 1327-1361.
  • [8] M. HAŁAS: An algebraic framework generalizing the concept of transfer functions to nonlinear systems. Automatica, 44 (2008), 1181-1190.
  • [9] M. Halas: Nonlinear time-delay systems: a polynomial approach using ore alge-bras. In J.J. Loiseau, W. Michiels, S. Niculescu and R. Sipahi: Topics in Time-Delay Systems: Analysis, Algorithms and Control, Lecture Notes in Control and Information Sciences, Springer, 2009.
  • [10] M. Halas and U. KOTTA: Transfer functions of discrete-time nonlinear control systems. Proc. Estonian Acad. Sci. Phys. Math., 56 (2007), 322-335.
  • [11] M. Halas and U. KOTTA: A polynomial approach to the synthesis of observers for nonlinear systems. In 47th Conf. on Decision and Control, Cancun, Mexico, (2008).
  • [12] M. Halas and U. KOTTA: Realization problem of SISO nonlinear systems: a transfer function approach. In 7th IEEE Int. Conf. on Control & Automation, Christchurch, New Zealand, (2009).
  • [13] M. Halas, U. KOTTA and C.H. MOOG: Transfer function approach to the model matching problem of nonlinear systems. In 17th IFAC World Congress, Seoul, Korea, (2008).
  • [14] H. J. C. HUIJBERTS: A nonregular solution of the nonlinear dynamie disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem. SIAM J. of Control Optimization, 30 (1992), 350-366.
  • [15] J. JOHNSON: Kahler differentials and differential algebra. Annals ofMathematics, 89(1969), 92-98.
  • [16] U. Kotta: Inversion method in the discrete-time nonlinear control systems syn-thesis problems. Springer, Berlin, 1995.
  • [17] U. KOTTA: Irreducibility conditions for nonlinear input-output difference equa-tions. In 39th IEEE Conf. on Decision and Control, Sydney, Australia, (2000).
  • [18] U. Kotta, A.S.I. Zinober and P. Liu: Transfer equivalence and realization of nonlinear higher order input-output difference eąuations. Automatica, 37 (2001), 1771-1778.
  • [19] Z. Li, M. Ondera and H. Wang: Simplifying skew fractions modulo differential and difference relations. In Int. Symp. on Symbolic and Algebraic Computation, Linz, Austria, (2008).
  • [20] O. Ore: Linear eąuations in non-commutative fields. Annals of Mathematics, 32 (1931),463-477.
  • [21] O. ORE: Theory of non-commutative polynomials. Annals of Mathematics, 34 (1933), 480-508.
  • [22] A. M. Perdon, C.H. MoOGandG. Conte: The pole-zero structure of nonlinear control systems. In 7th IFAC Symposium NOLCOS, Pretoria, South Africa, (2007).
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  • [24] Y. ZHENG and L. Cao: Transfer function description for nonlinear systems. J. of East China Normal University (Natural Science), 2 (1995), 15-26.
  • [25] Y. ZHENG, J. WILLEMS and C. ZHANG: A polynomial approach to nonlinear system controllability. IEEE Trans, on Automatic Control, 46 (2001), 1782-1788.
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Bibliografia
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bwmeta1.element.baztech-article-BSW3-0061-0024
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