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Volumn 16, Issue 7, 2006, Pages 2029-2041

An equation-free approach to nonlinear control: Coarse feedback linearization with pole-placement

Author keywords

Equation free; Feedback linearization; Microscopic stochastic systems; Nonlinear control

Indexed keywords

CATALYSIS; COMPUTATION THEORY; COMPUTER SIMULATION; FEEDBACK; MONTE CARLO METHODS; RANDOM PROCESSES;

EID: 33748520913     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406015878     Document Type: Article
Times cited : (16)

References (35)
  • 2
    • 0346685925 scopus 로고    scopus 로고
    • Time-steppers and coarse control of microscopic distributed processes
    • Armaou, A., Siettos, C. I. & Kevrekidis, I. G. [2004] "Time-steppers and coarse control of microscopic distributed processes," Int. J. Rob. Nonlin. Contr. 14, 89-111.
    • (2004) Int. J. Rob. Nonlin. Contr. , vol.14 , pp. 89-111
    • Armaou, A.1    Siettos, C.I.2    Kevrekidis, I.G.3
  • 3
    • 15944420251 scopus 로고    scopus 로고
    • Equation-free gaptooth-based controller design for distributed complex/multiscale processes
    • Armaou, A., Kevrekidis, I. G. & Theodoropoulos, C. [2005] "Equation-free gaptooth-based controller design for distributed complex/multiscale processes," Comp. Chem. Eng. 79, 731-740.
    • (2005) Comp. Chem. Eng. , vol.79 , pp. 731-740
    • Armaou, A.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 7
    • 19644394100 scopus 로고    scopus 로고
    • Geometric diffusions as a tool for harmonic analysis and structure definition of data. Part I, Diffusion maps
    • Coifman, Lafon, R. S., Lee, A. B., Maggioni, M., Nadler, B., Warner, F. & Zucker, S. [2005] "Geometric diffusions as a tool for harmonic analysis and structure definition of data. Part I, Diffusion maps," Proc. Natl. Acad. Sci. 102, 7426-7431.
    • (2005) Proc. Natl. Acad. Sci. , vol.102 , pp. 7426-7431
    • Coifman1    Lafon, R.S.2    Lee, A.B.3    Maggioni, M.4    Nadler, B.5    Warner, F.6    Zucker, S.7
  • 9
    • 0037104864 scopus 로고    scopus 로고
    • Coarse integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods
    • Gear, C. W., Kevrekidis, I. G. & Theodoropoulos, K. [2002] "Coarse integration/bifurcation analysis via microscopic simulators: Micro-Galerkin methods," Comp. Chem. Engng. 26, 941-963.
    • (2002) Comp. Chem. Engng. , vol.26 , pp. 941-963
    • Gear, C.W.1    Kevrekidis, I.G.2    Theodoropoulos, K.3
  • 10
    • 24644471938 scopus 로고    scopus 로고
    • Projecting on a slow manifold: Singularity perturbed systems and legacy codes
    • Gear, C. W., Kaper, T. J., Kevrekidis I. G. & Zagaris, A. [2005] "Projecting on a slow manifold: Singularity perturbed systems and legacy codes," SIADS 4, 711-732.
    • (2005) SIADS , vol.4 , pp. 711-732
    • Gear, C.W.1    Kaper, T.J.2    Kevrekidis, I.G.3    Zagaris, A.4
  • 11
    • 0017030517 scopus 로고
    • A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
    • Gillespie, D. T. [1976] "A general method for numerically simulating the stochastic time evolution of coupled chemical reactions," J. Comput. Phys. 22, 403-434.
    • (1976) J. Comput. Phys. , vol.22 , pp. 403-434
    • Gillespie, D.T.1
  • 12
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical reactions
    • Gillespie, D. T. [1977] "Exact stochastic simulation of coupled chemical reactions," J. Phys. Chem. 81, 2340-2361.
    • (1977) J. Phys. Chem. , vol.81 , pp. 2340-2361
    • Gillespie, D.T.1
  • 13
    • 0141736969 scopus 로고
    • Feedback linearization of discrete-time systems
    • Springer Verlag, Berlin, Germany
    • Grizzle, J. W. [1986] "Feedback linearization of discrete-time systems," in Lecture Notes in Control and Information Sciences (Springer Verlag, Berlin, Germany).
    • (1986) Lecture Notes in Control and Information Sciences
    • Grizzle, J.W.1
  • 16
    • 0023455846 scopus 로고
    • Feedback linearization of discrete-time systems
    • Jakubczyck, B. [1987] "Feedback linearization of discrete-time systems," Syst. Contr. Lett. 9, 441.
    • (1987) Syst. Contr. Lett. , vol.9 , pp. 441
    • Jakubczyck, B.1
  • 17
    • 0034918631 scopus 로고    scopus 로고
    • A functional equations approach to nonlinear discrete-time feedback stabilization through pole-placement
    • Kazantzis, N. [2001] "A functional equations approach to nonlinear discrete-time feedback stabilization through pole-placement," Syst. Contr. Lett. 43, 361.
    • (2001) Syst. Contr. Lett. , vol.43 , pp. 361
    • Kazantzis, N.1
  • 18
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and non-linear eigenvalue problems
    • ed. Rabinowitz, P. H. (Academic Press, NY)
    • Keller, H. B. [1977] "Numerical solution of bifurcation and non-linear eigenvalue problems," in Applications of Bifurcation Theory, ed. Rabinowitz, P. H. (Academic Press, NY), pp. 359-384.
    • (1977) Applications of Bifurcation Theory , pp. 359-384
    • Keller, H.B.1
  • 21
    • 85128858890 scopus 로고    scopus 로고
    • Equation-free coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level tasks
    • original version can be obtained as physics/0209043 at arXiv.org.
    • Kevrekidis, I. G., Gear, C. W., Hyman, J. M., Kevrekidis, P. G., Runborg, O. & Theodoropoulos, K. [2003] "Equation-free coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level tasks," Comm. Math. Sciences 1, 715-762; original version can be obtained as physics/0209043 at arXiv.org.
    • (2003) Comm. Math. Sciences , vol.1 , pp. 715-762
    • Kevrekidis, I.G.1    Gear, C.W.2    Hyman, J.M.3    Kevrekidis, P.G.4    Runborg, O.5    Theodoropoulos, K.6
  • 22
    • 3042720018 scopus 로고    scopus 로고
    • Equation-free: The computer-assisted analysis of complex, multiscale systems
    • Kevrekidis, I. G., Gear, C. W. & Hummer, G. [2004] "Equation-free: The computer-assisted analysis of complex, multiscale systems," AIChE J. 50, 1346-1354.
    • (2004) AIChE J. , vol.50 , pp. 1346-1354
    • Kevrekidis, I.G.1    Gear, C.W.2    Hummer, G.3
  • 23
    • 0023345206 scopus 로고
    • On the linearization of discrete-time systems
    • Lee, H. G., Arapostathis, A. & Marcus, S. I. [1987] "On the linearization of discrete-time systems," Int. J. Contr. 45, 1783.
    • (1987) Int. J. Contr. , vol.45 , pp. 1783
    • Lee, H.G.1    Arapostathis, A.2    Marcus, S.I.3
  • 24
    • 0029639346 scopus 로고
    • Remarks on linearization of discrete-time autonomous systems and nonlinear observer design
    • Lin, W. & Byrnes, C. I. [1995] "Remarks on linearization of discrete-time autonomous systems and nonlinear observer design," Syst. Contr. Lett. 25, 31.
    • (1995) Syst. Contr. Lett. , vol.25 , pp. 31
    • Lin, W.1    Byrnes, C.I.2
  • 25
    • 84886166390 scopus 로고
    • Observing the state of a linear system
    • Luenberger, D. G. [1963] "Observing the state of a linear system," IEEE Trans. Milit. Electr. 8, 74.
    • (1963) IEEE Trans. Milit. Electr. , vol.8 , pp. 74
    • Luenberger, D.G.1
  • 27
    • 0037162264 scopus 로고    scopus 로고
    • Coarse stability analysis using stochastic simulators: Kinetic Monte Carlo examples
    • Makeev, A., Maroudas, D. & Kevrekidis, I. G. [2002] "Coarse stability analysis using stochastic simulators: Kinetic Monte Carlo examples," J. Chem. Phys. 116, 10083-10091.
    • (2002) J. Chem. Phys. , vol.116 , pp. 10083-10091
    • Makeev, A.1    Maroudas, D.2    Kevrekidis, I.G.3
  • 28
    • 0024480625 scopus 로고
    • Linearization of discrete-time nonlinear systems and a canonical structure
    • Nam, K. [1989] "Linearization of discrete-time nonlinear systems and a canonical structure," IEEE Trans. Autom. Contr. 34, 119.
    • (1989) IEEE Trans. Autom. Contr. , vol.34 , pp. 119
    • Nam, K.1
  • 29
    • 0038824886 scopus 로고    scopus 로고
    • Microscopic/stochastic timesteppers and coarse control: A kinetic Monte Carlo example
    • Siettos, C. I., Armaou, A., Makeev, A. G., Kevrekidis, I. G. [2003a] "Microscopic/stochastic timesteppers and coarse control: A kinetic Monte Carlo example," AIChE J. 49, 1922-1926.
    • (2003) AIChE J. , vol.49 , pp. 1922-1926
    • Siettos, C.I.1    Armaou, A.2    Makeev, A.G.3    Kevrekidis, I.G.4
  • 30
    • 0038608279 scopus 로고    scopus 로고
    • Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration and control via stochastic simulation
    • Siettos, C. I., Graham, M. & Kevrekidis, I. G. [2003b] "Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration and control via stochastic simulation," J. Chem. Phys. 118, 10149-10157.
    • (2003) J. Chem. Phys. , vol.118 , pp. 10149-10157
    • Siettos, C.I.1    Graham, M.2    Kevrekidis, I.G.3
  • 31
    • 3042713738 scopus 로고    scopus 로고
    • Coarse bifurcation diagrams via microscopic simulators: A state-feedback control-based approach
    • Siettos, C. I., Maroudas, D. & Kevrekidis, I. G. [2004a] "Coarse bifurcation diagrams via microscopic simulators: A state-feedback control-based approach," Int. J. Bifurcation and Chaos 14, 207-220.
    • (2004) Int. J. Bifurcation and Chaos , vol.14 , pp. 207-220
    • Siettos, C.I.1    Maroudas, D.2    Kevrekidis, I.G.3
  • 32
    • 33748550928 scopus 로고    scopus 로고
    • Nonlinear feedback linearization with pole placement in one step: An equation-free approach for discrete time systems and microscopic simulators
    • 22-26 July, Ancient Olympia, Greece
    • Siettos, C. I., Kevrekidis, I. G. & Kazantzis, N. [2004b] "Nonlinear feedback linearization with pole placement in one step: An equation-free approach for discrete time systems and microscopic simulators," Complexity in Science & Society European Advanced Studies Conf., 22-26 July, Ancient Olympia, Greece.
    • (2004) Complexity in Science & Society European Advanced Studies Conf.
    • Siettos, C.I.1    Kevrekidis, I.G.2    Kazantzis, N.3
  • 33
    • 0034730149 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using timesteppers: A reaction diffusion example
    • Theodoropoulos, K., Qian, Y. H. & Kevrekidis, I. G. [2000] "Coarse stability and bifurcation analysis using timesteppers: A reaction diffusion example," Proc. Natl. Acad. Sci. 97, 9840-9843.
    • (2000) Proc. Natl. Acad. Sci. , vol.97 , pp. 9840-9843
    • Theodoropoulos, K.1    Qian, Y.H.2    Kevrekidis, I.G.3
  • 34
    • 0141900705 scopus 로고    scopus 로고
    • Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation
    • Pope, S. B. [1997] "Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation," Comb. Theor. Model. 1, 41-63.
    • (1997) Comb. Theor. Model. , vol.1 , pp. 41-63
    • Pope, S.B.1
  • 35
    • 0021787301 scopus 로고
    • GMRES acceleration of computational fluid codes
    • Wington, L. B., Yu, N. J. & Young, D. P. [1985] "GMRES acceleration of computational fluid codes," 1985 AIAA Conf., pp. 67-74.
    • (1985) 1985 AIAA Conf. , pp. 67-74
    • Wington, L.B.1    Yu, N.J.2    Young, D.P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.