Some aspects of constrained controllability of dynamical discrete-time systemsFootnote^*

^* The work was supported by the National Basic Program in Natural Science

References

• Ahmed , N.U. 1985 . Finite-time null controllability for a class of linear evolution equations . JOT A , 47 : 129 – 158 .
   Google Scholar
• Aubin , J.P. and Ekeland , I. 1984 . Applied nonlinear analysis , New York : Wiley-Interscience .
   Google Scholar
• Aubin , J.P. , Frankowska , H. and Olech , C. 1986 . Controllability of convex processes . SI AM J. Contr.Optim , 24 : 1192 – 1211 .
   Google Scholar
• Bartosiewicz , Z. 1984 . Approximate controllability of neutral systems with delays in controls . J. of Diff. Equations , 51 : 295 – 325 .
   Google Scholar
• Benzaid , Z. and Lutz , D.A. 1988 . Constrained controllability of pertubed discrete-time systems . Int. J.Control , 48 : 655 – 673 .
   Google Scholar
• Balachandran , H. and Dauer , J.P. 1987 . Controllability of nonlinear discrete-time systems via fixed point theorems . JOT A , 53
   Google Scholar
• Balachandran , K. and Murugesan , K. 1990 . Analysis of electronics circuits using Wash series approach . Int. J. of Electronics , 69 : 327 – 332 .
   Web of Science ®Google Scholar
• Brammer , R. 1972 . Controllability of linear autonomous system with positive controls . SI AM J.Contr , 10 : 339 – 353 .
   Web of Science ®Google Scholar
• Campbell , S.L. 1982 . Singular systems of differential equations , Vol. 2 , London Pitman .
   Google Scholar
• Clarke , F.H. 1983 . Optimization and nonsmooth analysis , New York : Wiley-Interscience .
   Google Scholar
• Conti , R. 1982 . Infinite dimensional linear autonomous controllability . Math. Reports Univer. Minnesota , : 82 – 127 .
   Google Scholar
• Conti , R. 1965 . Contribution to linear control theory . J. of Diff. Equations , 1 : 427 – 445 .
   Web of Science ®Google Scholar
• Chukwu , E.N. 1987 . Functional space controllability of linear delay systems with limited powers . J.Math. Anal Appl , 124 : 823 – 827 .
   Google Scholar
• Curtain , R.F. and Pritchard , A.J. 1978 . Infinite dimensional linear system theory Springer Verlag . Lecture Notes Contr. Inform. Sic , 8
   Google Scholar
• Chau , N.V. and Khai , P.H. 1985 . On controllability of linear discrete-time system and the pursuit process . Acta Math. Vietnamica , 10 : 58 – 74 .
   Google Scholar
• Dai , L. 1989 . Singular control systems. Springer Verlag . Lecture Notes Contr Inform. Sci , 118
   Google Scholar
• P.H , . 1983 . Locally Lipschit set-valued maps and generalized extremal problems . Acta Math.Vietnamica , 2 : 102 – 122 .
   Google Scholar
• Duong , P.C. and Tuy , H. 1978 . Stability, surjectivity and local invertibility of nondifferential mappings . Acta Math. Vietnamica , 1 : 89 – 105 .
   Google Scholar
• Evans , M.E. 1985 . The bounded controllers: controllability of finite time systems . Int. J. Syst. Sci , 16 : 31 – 47 .
   Web of Science ®Google Scholar
• Evans , M.E. and Murthy , D.M.D. 1977 . Controllability of discrete-time systems with positive controls . IEEE Trans. Aut. Contr , 6 : 924 – 951 .
   Google Scholar
• Grizzle , J.W. 1985 . Controlled invariance for discrete-time nonlinear systems with an application to the decoupling problems . IEEE Trans. Auto. Contr , AC-30 : 868 – 874 .
   Google Scholar
• Faradzev , R.G. , Phat , V.N. and Shapiro , A.V. 1986 . Controllability theory of dynamical discrete time systems: survey , Vol. 1 , 5 – 24 . Moscow : Avtomatika i Telemekhanika . (in Russian)
   Google Scholar
• Faradzev , R.G. and Phat , V.N. 1985 . Constrained controllability of nonlinear two parameter systems . Optimization , 5 : 869 – 877 .
   Google Scholar
• Fattorini , H.O. 1967 . On complete controllability of linear systems . J. Diff. Equations , 3 : 391 – 403 .
   Web of Science ®Google Scholar
• Fattorini , H.O. 1986 . Some remarks on complete controllability . SI AM J. Contr. Optim , 4 : 686 – 694 .
   Google Scholar
• Fliegner , T. , Nijmeijer , H. and Kotta , U. 1993 . Some aspects of nonlinear discrete-time descriptor systems. Memorandum , Vol. 1137 , 1 – 9 . University of Twente .
   Google Scholar
• Fliess , M. 1993 . Reversible linear and nonlinear discrete-time dynamics . IEEE Trans. Auto. Contr , 37 : 1144 – 1153 .
   Google Scholar
• Fliess , M. and Normand Cyrot , D. A group theoretic approach to discrete-time nonlinear controllability . Proc. 20th IEEE Conf Decision Contr . pp. 551 – 557 . San Diego, CA
   Google Scholar
• Fuhrmann , P.A. 1972 . On weak and strong reachability and controllability of infinite dimensional systems . JOT A , 9 : 77 – 89 .
   Google Scholar
• Gabasov , R. , Kirillova , F. , Krakhotko , V. and Miniuk , S. 1972 . Controllability theory of linear discrete-time systems . Diff. Equations, USSR , 8 : 767 – 773 . 1081-1091, 1282-1291
   Google Scholar
• Jakubsczyk , B. and Sontag , E.D. 1990 . Controllability of nonlinear discrete-time system: a Lie-algebraic approach . SIAM J. Contr. Optim , 28 : 1 – 33 .
   Google Scholar
• Jakubczyk , B. Invertible realization of nonlinear discrete-time systems . Proc. Princeton Conf. Inf.Sci . pp. 235 – 239 .
   Google Scholar
• Jakubczyk , B. 1987 . Feedback linearization of discrete-time systems . System Contr. Letters , 9 : 411 – 416 .
   Web of Science ®Google Scholar
• Heyman , H. 1975 . Controllability of linear systems with positive controls: a geometric considerration . J. Math. Anal. Appl , 52 : 36 – 41 .
   Google Scholar
• Ivanov , V.A. and Yushenko , A.C. 1983 . Theory of automatic control systems Moscow, Nauka (in Russian)
   Google Scholar
• Isidori , A. 1985 . Nonlinear control systems: introduction , Springer Verlag .
   Google Scholar
• Kalman , R.E. 1960 . Contribution to the theory of optimal control . Boll. Soc. Math. Mexicana , 5 : 102 – 119 .
   Google Scholar
• Kalman , R.E. , Ho , Y.C. and Narenda , K.S. 1963 . Controllability of linear dynamical systems . SI AM J. Contr. Optim , 1 : 152 – 193 .
   Google Scholar
• Klamka , J. 1976 . Relative controllability of nonlinear systems with delays in control . Automatica , 12 : 633 – 635 .
   Web of Science ®Google Scholar
• Klamka , J. 1980 . Controllability of nonlinear systems with distributed delays in control . Int. J. of Control , 31 : 811 – 819 .
   Web of Science ®Google Scholar
• Korobov , V.I. and Chuprina , V.E. Sufficient conditions for controllability of linear system to a subspace , 148 Vestnhik Kharkov University .
   Google Scholar
• Korobov , V.I. and Son , N.K. 1980 . Controllability of linear system with constrained controls in Banach spaces . Diff. Equations, USSR , 16 : 1010 – 1022 .
   Google Scholar
• Krein , M.G. and Rutman , M.A. 1948 . Linear operator leaving invariant a cone in Banach spaces . Uspekhi Math. Nauk, USSR , 1 : 3 – 95 .
   Google Scholar
• Lee , H. and Markus , S. 1987 . On input-output linearization of discrete-time nonlinear systems . System Contr. Letters , 1 : 249 – 266 .
   Google Scholar
• Luenberger , D.G. 1978 . Time-invariant descriptor systems . Automatica , 14 : 473 – 480 .
   Web of Science ®Google Scholar
• Martiniuk , D. Lectures on qualitative theory of differential equations , Nauka . (in Ruissan)
   Google Scholar
• Monaco , S. and Normand Cyrot , D. Algebraic and geometric methods in control theory 411 – 430 .
   Google Scholar
• Nieuwenhuis , J.W. and Willems , J.C. 1991 . On the nature of descriptor systems , Vol. 27 , 282 – 288 . Kybernetica .
   Google Scholar
• Nijmeijer , H. and Van der Schaft , A.J. 1990 . Nonlinear dynamical control systems , New York : Springer Verlag .
   Google Scholar
• Olbrot , A. and Sonsowski , A. 1981 . Duality theorems in control and observation of discrete time systems . Math. Syst. Theory , 14 : 173 – 187 .
   Google Scholar
• Park , J.Y. , Nakagiri , S. and Yamamoto , M. 1989 . Admissible controllability for linear systems in banach spaces—A problem in game theory . Sci. Papers of the Univer. of Tokyo , 39 : 5 – 55 .
   Google Scholar
• Park , J.Y. 1990 . Max-min controllability of delay differentiable games . Kobe J. Math , 7
   Google Scholar
• Pandolfi , L. 1976 . Linear control systems: controllability with restrained controls . JOTA , 19 : 577 – 585 .
   Google Scholar
• Przyluski K. Infinite-dimensional discrete-time systems: theory and application to linear hereditary control systems IPEPW, Technical Reports Warsaw 1979
   Google Scholar
• Przyluski , K. and Rolewicz , S. 1984 . On stability of linear infinite-dimensional discrete-time systems . System Contr. Letters , 4
   Google Scholar
• Pshenhichnyi , N. Convex analysis and extremal problems , Nauka : Moscow . (in Russian)
   Google Scholar
• Pshenhichnyi , N. Necessary conditions for extremums , Nauka : Moscow . (in Russian)
   Google Scholar
• Peichl , G. and Schappacher , W. 1986 . Constrained controllability in Banach spaces . SI AM J. Contr. Optim , 24 : 1261 – 1275 .
   Web of Science ®Google Scholar
• Robert , van Til. and Schmitendorf , W.E. 1986 . Constrained controllability of discrete-time systems . Int. J. of Control , 43 : 941 – 956 .
   Google Scholar
• Robert van Til Van , P. Constrained controllability holding of discrete-time systems. Ph.D. thesis , Evanston, IL : Ph.D. thesis Northweston University .
   Google Scholar
• Robinson , S.M. 1976 . Regularity and stability for convex multi valued functions . Math. Oper. Research , 11 : 130 – 143 .
   Google Scholar
• Rockafellar , T. 1970 . Convex analysis , Princeton Press .
   Google Scholar
• Rudin , W. 1990 . Functional Analysis New York
   Google Scholar
• Sontag , E.D. 1990 . Mathematical control theory New Brunswick
   Google Scholar
• Sontag , E.D. 1986 . An eigenvalue conditions for sampled weak controllability of bilinear systems . System Contr. Letters , 7 : 313 – 316 .
   Web of Science ®Google Scholar
• Schmitendorf , W.E. and Barmish , B.R. 1980 . Null-controllability of linear systems with constrained controls . SI AM J. Contr. Optim , 4 : 327 – 345 .
   Google Scholar
• Son , N.K. 1981 . Controllability of linear discrete-time systems with constrained controls in Banach spaces . Control and Cybernetics , 10 : 5 – 16 .
   Google Scholar
• Son , N. K. 1986 . On the controllability of linear discrete-time systems with restrained controls . JOT A , 50 : 313 – 329 .
   Google Scholar
• Son , N.K. and Su , N.V. 1986 . Linear periodic control systems: Controllability with restrained controls . Appl. Math. Optim , 14 : 173 – 185 .
   Web of Science ®Google Scholar
• Sampei , M. , Kato , F. and Furuta , K. Approximate input-output linearization of nonlinear systems . Proc. 26th IEEE Conference on Decision Control . Los Angles, CA.
   Google Scholar
• Sussmann , H.J. Jurdjevic , . 1980 . “ Les point reguliersdes application multivoques commandabilité dans les systems discrets ” . In Analyse Appl. et Inf , Vol. 8022 , 1 – 47 . University Bordeaur .
   Google Scholar
• Ngoc Phat , Vu. 1984 . Controllability theory of Nonlnear discrete-time systems , USSR : Ph. D. thesis, Bacu Universty .
   Google Scholar
• Ngoc Phat , Vu. 1983 . Controllability of discrete-time system with nonconvex controls . Math. Oper. u Stat.Ser. Optimization , 14 : 571 – 379 .
   Google Scholar
• Ngoc Phat , Vu. Controllability of convex processes 62
   Google Scholar
• Ngoc Phat , Vu. 1988 . On approximate controllability of nonlinear discrete-time systems . Acta Math. Vietnamica , 2 : 81 – 88 .
   Google Scholar
• Ngoc Phat , Vu. 1988 . Controllability of nonstationary discrete-time systems with phase constraints , Vol. 8 , 51 Moscow : Av-tomatika i Telemekhanika .
   Google Scholar
• Ngoc Phat , Vu. 1989 . Controlability of linear discrete-time systems with multiple delays on control and states in Banach spaces . Int. J. of Control , 5 : 1645 – 1654 .
   Google Scholar
• Ngoc Phat , Vu. 1989 . Controllability of linear discrete-time systems with multiple delays on control and states in Banach spaces . Int. J. of Control , 5 : 1645 – 1654 .
   Google Scholar
• Ngoc Phat , Vu. 1990 . An application of theorem on implicit function to Controllability problem , Vol. 4 , 55 – 59 . Kiev, USSR : Kibernetika .
   Google Scholar
• Ngoc Phat , Vu. 1988 . Controllability of nonlinear discrete-time systems without differentiability assumption . Optimization , 1 : 133 – 142 .
   Google Scholar
• Ngoc Phat Vu Some remarks on controllability of discrete-time convex processes Optimization 1994 accepted
   Google Scholar
• Ngoc Phat Vu Constrained controllability of linear infinite-dimensional systems:A set-valued analysis approach IMAJ. of Math. Control and Inform 1994 accepted
   Google Scholar
• Ngoc Phat , Vu. and Khoa Son , Nguyen. 1990 . Linear nonstationary discrete-time systems: Nullcontrollability with restrained controls . Optimization , 21 : 271 – 279 .
   Google Scholar
• Ngoc Phat , Vu. and Balachandran , K. 1992 . On the controllability of linear descriptor systems in Banach spaces . Acta Math. Vietnamica , 1 : 67 – 76 .
   Google Scholar
• Ngoc Phat , Vu. 1992 . Local controllability of linear discrete-time systems with constrained controls and states in Banach spaces . SI AM J. Contr. Optim , 30 : 1311 – 1319 .
   Google Scholar
• Ngoc Phat , Vu. 1992 . Linear control systems with additive disturbances: Constrained controllability to a subset . Optimization , 24 : 319 – 327 .
   Google Scholar
• Ngoc Phat , Vu. 1994 . On the Krein-Rutman's theorem and its application in controllability . Proceedings of the AMS , 124 : 495 – 501 .
   Google Scholar
• Ngoc Phat , Vu. and Murugesan , K. 1992 . A note on constrained controllability of linear descriptor systems . Optimization , 25 : 77 – 82 .
   Google Scholar
• Yorke , J. and Saperstones. 1971 . Controllability of oscillatory systems with using positive controllers . SI AM. Contr , 9 : 253 – 262 .
   Google Scholar
• Zabczyk , J. 1976 . Remarks on the algebraic Riccati-equations in Hilbert space . Appl. Math. Optim , 2 : 251 – 258 .
   Google Scholar
• Zabczyk , J. Mathematical Control Theory. Institute of Math , Polish Academy of Science .
   Google Scholar
• Warga , J. 1978 . Controllability of nondifferentiable hereditary prosesses . SI AM J. Contr. Optim , 16 : 813 – 831 .
   Google Scholar
• Weiss , L. 1972 . Controllability, realization and stability of linear discrete-time systems . SI AM J. Contr , 10 : 230 – 251 .
   Web of Science ®Google Scholar
• Wonham , W.M. Linear multivariable control: a geometric approach , Springer Verlag .
   Google Scholar
• Wing , C. and Desoer , C. A. 1963 . The multible input minimal regulator problem . IEEE Trans. Auto. Contr , AC-5 : 125 – 136 . general theory
   Google Scholar
• Yen , N.D. 1986 . Local controllability for Lipschite discrete-time systems . Acta Math. Vietnamica , 11 : 172 – 179 .
   Google Scholar
• Yen , N.D. and Dieu , T.C. 1989 . On local controllability of nondifferentiable discrete-time system with nonconvex constrained controls . Optimization , 20 : 889 – 899 .
   Google Scholar