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Controllability of semilinear systems. (English) Zbl 0674.93006

The most general results known about controllability of semilinear systems are found in A. Aronsson [SIAM J. Control 11, 607-619 (1973; Zbl 0271.49019)] and J. P. Dauer [J. Math. Anal. Appl. 54, 717-725 (1976; Zbl 0339.93004)]. The authors of these papers used different approaches, and no connection between them has ever been pointed out. The purpose of this paper is to present a general theorem under which these results easily follow.
Reviewer: V.N.Do

MSC:

93B05 Controllability
93C05 Linear systems in control theory
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References:

[1] Aronsson, G.,Global Controllability and Bang-Bang Steering of Certain Nonlinear Systems, SIAM Journal on Control, Vol. 15, pp. 607-619, 1973. · Zbl 0271.49019 · doi:10.1137/0311047
[2] Dauer, J.,Nonlinear Perturbations of Quasilinear Control Systems, Journal of Mathematical Analysis and Applications, Vol. 54, pp. 717-725, 1976. · Zbl 0339.93004 · doi:10.1016/0022-247X(76)90191-8
[3] Lukes, D. L.,Global Controllability of Nonlinear Systems, SIAM Journal on Control, Vol. 10, pp. 112-126, 1972; Erratum: Global Controllability of Nonlinear Systems, Vol. 11, pp. 186, 1973. · Zbl 0264.93004 · doi:10.1137/0310011
[4] Vidyasagar, M.,A Controllability Condition for Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 569-570, 1972. · Zbl 0262.93008 · doi:10.1109/TAC.1972.1100064
[5] Lee, E. B., andMarkus, L.,Foundation of Optimal Control Theory, John Wiley and Sons, New York, New York, 1967.
[6] Zeidler, E.,Nonlinear Functional Analysis and Its Applications, Part 1: Fixed-Point Theorems, Springer-Verlag, Berlin, Germany, 1986. · Zbl 0583.47050
[7] Aronsson, G.,A New Approach to Nonlinear Controllability, Journal of Mathematical Analysis and Applications, Vol. 44, pp. 763-772, 1973. · Zbl 0266.93003 · doi:10.1016/0022-247X(73)90015-2
[8] Mirza, K. B., andWomack, B. F.,On the Controllability of a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-16, pp. 497-498, 1971. · doi:10.1109/TAC.1971.1099795
[9] Folland, G.,Real Analysis, Modern Techniques, and Their Applications, Wiley-Interscience, New York, New York, 1984. · Zbl 0549.28001
[10] Do, V. N,Stabilizability, and Controllability of Semilinear Systems, University of California, Los Angeles, PhD Thesis, 1988.
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