The package NLControl, developed in the Institute of Cybernetics at Tallinn University of Technology within the Mathematica environment, has been made partially available over the internet using webMathematica tools. The package consists of functions that assist the solution of different modelling, analysis, and synthesis problems for nonlinear control systems, described either by state or by input-output equations. This paper focuses on describing the webMathematica-based tools for discrete-time nonlinear control systems.
Aranda-Bricaire, E. and Kotta, Ü. A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems. Kybernetika, 2004, 40, 197–206.
Aranda-Bricaire, E., Kotta, Ü, and Moog, C. Linearization of discrete-time systems. SIAM J. Control Optim., 1996, 34, 1999–2023.
doi:10.1137/S0363012994267315
Baheti, R., Mohler, R., and Spang, H. Second-order correlation method for bilinear system identification. IEEE Trans. Autom. Control, 1980, 25, 1141–1146.
doi:10.1109/TAC.1980.1102516
Conte, G., Moog, C., and Perdon, A. Algebraic Methods for Nonlinear Control Systems. Springer, London, 2007.
de Jager, B. The use of symbolic computations in nonlinear control. Is it viable? IEEE Trans. Autom. Control, 1995, 40, 84–89.
doi:10.1109/9.362897
Fliess, M. Automatique en temps discret et algèbre aux différences. Forum Math., 1990, 2, 213–232.
Isidori, A. Nonlinear Control Systems (3rd ed.). Springer, Berlin, 1995.
Kaddouri, A., Blais, S., Ghribi, M., and Akhrif, O. NLSOFT: An interactive graphical software for designing nonlinear controllers. Math. Comput. Simulation, 2006, 71, 377–384.
doi:10.1016/j.matcom.2006.02.016
Kazantzis, N. and Kravaris, C. Discrete-time nonlinear observer design using functional equations. Systems Control Lett., 2001, 42, 81–94.
doi:10.1016/S0167-6911(00)00071-2
Kotta, Ü. Comments on “On the discrete-time normal form”. IEEE Trans. Autom. Control, 2000, 45, 2197.
doi:10.1109/9.887696
Kotta, Ü. Decomposition of discrete-time nonlinear control systems. Proc. Estonian Acad. Sci. Phys. Math., 2005, 54, 154–161.
Kotta, Ü. and Nurges, Ü. Identification of input-output bilinear systems. In A Bridge Between Control Science and Technology: Proceedings of the Ninth Triennial World Congress of IFAC, Budapest, Hungary, 2–6 July 1984, Vol. 2 (Gertler, J. and Keviczky, L., eds). Pergamon, Oxford, 1985, 723–727 (IFAC Proceedings series, 1985, 1).
Kotta, Ü. and Tõnso, M. Transfer equivalence and realization of nonlinear higher order input/output difference equations using Mathematica. J. Circuits Systems Comput., 1999, 9, 23–25.
doi:10.1142/S0218126699000049
Kotta, Ü. and Tõnso, M. Linear algebraic tools for discrete-time nonlinear control systems with Mathematica. In Nonlinear and Adaptive Control, NCN4 2001 (Zinober, A. and Owens, D., eds), Lecture Notes in Control and Inform. Sci., 2003, 281, 195–205, Springer, Berlin.
Kotta, Ü. and Tõnso, M. Irreducibility conditions for discrete-time nonlinear multi-input multi-output systems. In 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS) (Allgöwer, F., ed.). Stuttgart, Germany, 2004, 269–274.
Kotta, Ü. and Tõnso, M. Realization of discrete-time nonlinear input-output equations: polynomial approach. In 7th World Congress on Intelligent Control and Automation, Chongqing, China. IEEE, 2008, 529–534.
Kotta, Ü., Zinober, A., and Liu, P. Transfer equivalence and realization of nonlinear higher order input-output difference equations. Automatica, 2001, 37, 1771–1778.
doi:10.1016/S0005-1098(01)00144-3
Kujan, P., Hromčik, M., and Šebek, M. Web-based Mathematica platform for systems and control education. In Proceedings of the 13th Mediterranean Conference on Control and Automation, Limassol, Cyprus. IEEE, Limassol, 2005, 376–381.
Nijmeijer, H. and van der Schaft, A. Nonlinear Dynamical Control Systems. Springer, New York, 1990.
Ondera, M. and Huba, M. Web-based tools for exact linearization control design. In Proceedings of the 14th IEEE Mediterranean Conference on Control and Automation, Ancona, Italy, 28–30 June 2006. IEEE (CD ROM).
Ore, O. Theory of non-commutative polynomials. Annals Math., 1933, 34, 480–508.
doi:10.2307/1968173
Rodrigues-Millan, J. Integrated symbolic-graphic-numeric analysis and design in nonlinear control through notebooks in Mathematica. Lecture Notes in Comput. Sci., 2001, 2178, 405–420. Springer-Verlag, Berlin.
doi:10.1007/3-540-45654-6_32
Rothfuβ, R. and Zeitz, M. A toolbox for symbolic nonlinear feedback design. In Proceedings of the 13th World Congress, International Federation of Automatic Control. Vol. F. Nonlinear Systems II (Gertler, J. J., Cruz, J. B., Jr., Peshkin, M., Bitmead, R., and Isidori, A., eds). Pergamon, Oxford, 1997, 283–288.
