메뉴 건너뛰기




Volumn 42, Issue 4-6, 1996, Pages 641-657

Iterated derivatives of the output of a nonlinear dynamic system and Faà di Bruno formula

Author keywords

Algebraic identification; Combinatorics; Generating series; Nonlinear systems; Syntactic methods

Indexed keywords

ALGEBRA; COMBINATORIAL MATHEMATICS; COMPUTATIONAL GRAMMARS; ENCODING (SYMBOLS); IDENTIFICATION (CONTROL SYSTEMS); ITERATIVE METHODS; PROBLEM SOLVING;

EID: 0030284693     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(96)00040-7     Document Type: Article
Times cited : (4)

References (20)
  • 1
    • 0348188291 scopus 로고
    • Graphic simulation of nonlinear control systems behaviour
    • SCRATCHPAD, Lille
    • F. Boussemart, V. Hoang Ngoc Minh, Graphic simulation of nonlinear control systems behaviour, in: SCRATCHPAD, IMACS Symp. MCTS (Lille, 1991).
    • (1991) IMACS Symp. MCTS
    • Boussemart, F.1    Hoang Ngoc Minh, V.2
  • 2
    • 0346088661 scopus 로고
    • Context-free grammars, differential operators and formal power series
    • Bordeaux, 2-4 May
    • W.Y. Chen, Context-free grammars, differential operators and formal power series, Séries formelles et combinatoire algébrique (Bordeaux, 2-4 May 1991) 145-159.
    • (1991) Séries Formelles et Combinatoire Algébrique , pp. 145-159
    • Chen, W.Y.1
  • 3
    • 84963078899 scopus 로고
    • Iterated integrals and exponential homomorphisms
    • K.T. Chen, Iterated integrals and exponential homomorphisms, Proc. London Math. Soc. 4 (1954) 502-512.
    • (1954) Proc. London Math. Soc. , vol.4 , pp. 502-512
    • Chen, K.T.1
  • 4
    • 84967713725 scopus 로고
    • Integration of paths, a faithful representation of paths by noncommutative formal power series
    • K.T. Chen, Integration of paths, a faithful representation of paths by noncommutative formal power series, Trans. Amer. Math. Soc. 89 (1958) 395-407.
    • (1958) Trans. Amer. Math. Soc. , vol.89 , pp. 395-407
    • Chen, K.T.1
  • 5
    • 84966202575 scopus 로고
    • Iterated path integrals
    • K.T. Chen, Iterated path integrals, Bull. Amer. Math. Soc. 83 (1977) 831-879.
    • (1977) Bull. Amer. Math. Soc. , vol.83 , pp. 831-879
    • Chen, K.T.1
  • 6
    • 0003870282 scopus 로고
    • State realizations of nonlinear systems defined by input - Output differential equations
    • Springer, New York
    • P. Crouch and F. Lamnabhi-Lagarrigue, State realizations of nonlinear systems defined by input - output differential equations, Lecture Notes in Control and Information Sciences, Vol. 11 (Springer, New York, 1988) 138-149.
    • (1988) Lecture Notes in Control and Information Sciences , vol.11 , pp. 138-149
    • Crouch, P.1    Lamnabhi-Lagarrigue, F.2
  • 7
    • 84891347644 scopus 로고
    • Successive derivatives of a function of several functions
    • L.S. Dederick, Successive derivatives of a function of several functions, Ann. of Math. 27 (1925) 385-394.
    • (1925) Ann. of Math. , vol.27 , pp. 385-394
    • Dederick, L.S.1
  • 8
    • 0347994376 scopus 로고
    • Un outil algébrique: Les séries formelles non commutatives
    • G. Marchesini and S.K. Mitter, eds., Mathematical System Theory, Springer, Berlin
    • M. Fliess, Un outil algébrique: les séries formelles non commutatives, in: G. Marchesini and S.K. Mitter, eds., Mathematical System Theory, Lecture Notes in Economics and Mathematical Systems, vol. 131 (Springer, Berlin, 1976) 122-148.
    • (1976) Lecture Notes in Economics and Mathematical Systems , vol.131 , pp. 122-148
    • Fliess, M.1
  • 9
    • 0001843817 scopus 로고
    • Fonctionnelles causales non linéaires et indéterminées non commutatives
    • M. Fliess, Fonctionnelles causales non linéaires et indéterminées non commutatives, Bull. Soc. Math. France 109 (1981) 3-40.
    • (1981) Bull. Soc. Math. France , vol.109 , pp. 3-40
    • Fliess, M.1
  • 11
    • 0042558162 scopus 로고
    • Calcul des approximations locales bilinéaires de systèmes analytiques
    • C. Hespel and G. Jacob, Calcul des approximations locales bilinéaires de systèmes analytiques, RAIRO APII 23 (1989) 331-349.
    • (1989) RAIRO APII , vol.23 , pp. 331-349
    • Hespel, C.1    Jacob, G.2
  • 12
    • 0026102962 scopus 로고
    • Approximation of nonlinear dynamic systems by rational series
    • C. Hespel and G. Jacob, Approximation of nonlinear dynamic systems by rational series, Theoret. Comput. Sci. 79 (1991) 151-162.
    • (1991) Theoret. Comput. Sci. , vol.79 , pp. 151-162
    • Hespel, C.1    Jacob, G.2
  • 13
    • 0042057282 scopus 로고
    • Truncated bilinear approximants: Carleman, finite Volterra, Padé-type, geometrical and structural automata
    • Paris, 13-15 March
    • C. Hespel, Truncated bilinear approximants: Carleman, finite Volterra, Padé-type, geometrical and structural automata, Proc. 1st European Conf. on Algebraic Computing in Control (Paris, 13-15 March 1991).
    • (1991) Proc. 1st European Conf. on Algebraic Computing in Control
    • Hespel, C.1
  • 15
    • 0347558646 scopus 로고
    • Input/output behaviour of nonlinear control systems: About exact and approximated computations
    • Lille
    • V. Hoang Ngoc Minh, Input/output behaviour of nonlinear control systems: About exact and approximated computations, Proc. IMACS Symp. MCTS (Lille, 1991).
    • (1991) Proc. IMACS Symp. MCTS
    • Hoang Ngoc Minh, V.1
  • 16
    • 0042715194 scopus 로고
    • Algebraic methods and computer algebra for nonlinear systems' study
    • G. Jacob, Algebraic methods and computer algebra for nonlinear systems' study, Proc. IMACS Symp. MCTS (1991).
    • (1991) Proc. IMACS Symp. MCTS
    • Jacob, G.1
  • 17
    • 0024048515 scopus 로고
    • A formula for iterated derivatives along trajectories of nonlinear systems
    • F. Lamnabhi-Lagarrigue and P.E. Crouch, A formula for iterated derivatives along trajectories of nonlinear systems, Systems and Control letters 11 (1988) 1-7.
    • (1988) Systems and Control Letters , vol.11 , pp. 1-7
    • Lamnabhi-Lagarrigue, F.1    Crouch, P.E.2
  • 19
    • 0346297500 scopus 로고
    • Implantation de la réalisation minimale des systèmes dynamiques en Scratchpad
    • Paris, CNRS
    • N.E. Oussous and M. Petitot, Implantation de la réalisation minimale des systèmes dynamiques en Scratchpad, Proc. ACC Conf. (Paris, CNRS, 1991).
    • (1991) Proc. ACC Conf.
    • Oussous, N.E.1    Petitot, M.2
  • 20
    • 0023027733 scopus 로고
    • A product expansion for the Chen series
    • C. Byrnes and A. Lindquist, eds., North-Holland, Amsterdam
    • H.J. Sussmann, A product expansion for the Chen series, in: C. Byrnes and A. Lindquist, eds., Theory and Applications of Nonlinear Control Systems (North-Holland, Amsterdam, 1986) 323-335.
    • (1986) Theory and Applications of Nonlinear Control Systems , pp. 323-335
    • Sussmann, H.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.