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2012 | 22 | 3 | 507-522
Tytuł artykułu

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g., Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.
Rocznik
Tom
22
Numer
3
Strony
507-522
Opis fizyczny
Daty
wydano
2012
otrzymano
2012-01-24
poprawiono
2012-04-02
poprawiono
2012-04-16
Twórcy
  • Department of Automation and Control, Far Eastern Federal University, Sukhanova street, 8, Vladivostok, 690990, Russia
  • Department of Automation and Control, Far Eastern Federal University, Sukhanova street, 8, Vladivostok, 690990, Russia
Bibliografia
  • Albertini, F. and D'Alessandro, D. (2002). Observability and forwardbackward observability of discrete-time nonlinear systems, Mathematics of Control, Signal and Systems 15(3): 275-290.
  • Guermah, S., Djennoune, S. and Bettayeb, M. (2008). Controllability and observability of linear discrete-time fractionalorder systems, International Journal of Applied Mathematics and Computer Science 18(2): 213-222, DOI: 10.2478/v10006-008-0019-6.
  • Herman, R. and Krener, A. (1977). Nonlinear controllability and observability, IEEE Transactions on Automatic Control AC-22(5): 728-740.
  • Isidori, A. (1989). Nonlinear Control Systems, Springer, London.
  • Jakubczyk, B. and Sontag, E. (1990). Controllability of nonlinear discrete-time systems: A lie-algebraic approach, SIAM Journal Control and Optimization 28(1): 1-33.
  • Jank, G. (2002). Controllability, observability and optimal control of continuous-time 2-D systems, International Journal of Applied Mathematic and Computer Science 12(2): 181-195.
  • Kalman, R., Falb, P. and Arbib, M. (1969). Topics in Mathematical System Theory, Mc Graw-Hill Company, New York, NY.
  • Kang, W. (2010). Analyzing control systems by using dynamic optimization, 8th IFAC Symposium on Nonlinear Control Systems, Bologna, Italy.
  • Kang, W. and Xu, L. (2009). A quantitative measure of observability and controllability, 48th IEEE Conference on Decision and Control, Shanghai, China, pp. 6413-6418.
  • Kawano, Y. and Ohtsuka, T. (2010). Global observability of discrete-time polynomial systems, 8th IFAC Symposium on Nonlinear Control Systems, Bologna, Italy, pp. 646-651.
  • Klamka, J. (1973). Uncontrollability and unobservability of composite systems, IEEE Transactions on Automatic Control AC-18(5): 539-540.
  • Klamka, J. (1975). On the global controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(1): 170-172.
  • Klamka, J. (2002). Controllability of nonlinear discrete systems, American Control Conference, Anchorage, AK, USA, pp. 4670-4671.
  • Koplon, R. and Sontag, E. (1993). Linear systems with signobservations, SIAM Journal Control and Optimization 31(12): 1245-1266.
  • Kotta, U. and Schlacher, K. (2008). Possible non-integrability of observable space for discrete-time nonlinear control systems, 17th IFAC World Congress, Seoul, Korea, pp. 9852-9856.
  • Krener, A. and Ide, K. (2009). Measures of unobservability, 48th IEEE Conference on Decision and Control, Shanghai, China, pp. 6401-6406.
  • Kwakernaak, H. and Sivan, R. (1972). Linear Optimal Control Systems, A Division of John Sons, Inc., New York, NY.
  • Mincheko, L. and Sirotko, S. (2002). Controllability of non-smooth discrete systems with delay, Optimization 51(1): 161-174.
  • Murphey, T. and Burdick, J. (2002). Nonsmooth controllability theory and an example, 41st IEEE Conference on Decision and Control, Shanghai, China, pp. 370-376.
  • Nijmeijer, H. (1982). Observability of autonomous discrete-time nonlinear systems: A geometric approach, International Journal of Control 36(6): 867-874.
  • Sontag, E. (1979). On the observability of polynomial systems, I: Finite-time problems, SIAM Journal of Control and Optimization 17(1): 139-151.
  • Sussmann, H. (1979). Single-input observability of continuoustime systems, Mathematical Systems Theory 12(3): 371-393.
  • van der Schaft, A.J. (1982). Observability and controllability for smooth nonlinear systems, SIAM Journal of Control and Optimization 20(3): 338-354.
  • Wohnam, M. (1985). Linear Multivariable Control, Springer-Verlag, New York, NY.
  • Zhirabok, A. (1998a). Controllability of nonlinear discrete dynamic systems, NOLCOS'98 Symposium, Enschede, The Netherlands, pp. 281-283.
  • Zhirabok, A. (1998b). Observability and controllability properties of nonlinear dynamic systems, International Journal of Computer and Systems Sciences 37(1): 1-4.
  • Zhirabok, A. (2010). Analysis of observability and controllability of nonlinear dynamic systems by linear methods, International Journal of Computer and Systems Sciences 49(1): 8-15.
  • Zhirabok, A. and Shumsky, A. (2008). The Algebraic Methods for Analysis of Nonlinear Dynamic Systems, Dalnauka, Vladivostok, (in Russian).
  • Zhirabok, A. and Shumsky, A. (2010). Linear methods in observability and controllability of nonlinear systems, 8th IFAC Symposium on Nonlinear Systems, Bologna, Italy, pp. 308-313.
  • Zhirabok, A. and Usoltsev, S. (2002). Fault diagnosis for nonlinear dynamic systems via linear methods, 15th IFAC World Congress, Barcelona, Spain.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv22z3p507bwm
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