Abstract
A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation with variable coefficients and a linked rigid body governed by an ordinary differential equation, is considered. Various controllability/observability properties of the system under bounday control/observation are studied. It is shown that an open-loop smooth/singular controller of either torque control or force control is sufficient to make the system exactly controllable in arbitrarily short time duration.
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Balakrishnan A.V., Taylor L. The SCOLE Design Challenge, 3rd Annual NASA-SCOLE Workshop, NASA Technical Memorandum 89075, pp. 385–412, 1986.
W Littman L. Markus (1988) ArticleTitleExact Boundary Controllability of a Hybrid System of Elasticity Archive for Rational Mechanics and Analysis 103 193–235 Occurrence Handle10.1007/BF00251758
B.Z. Guo (2002) ArticleTitleOn the Boundary Control of a Hybrid System with Variable Co-efficients Journal of Optimization Theory and Applications 114 373–395 Occurrence Handle10.1023/A:1016039819069
B. Rao (2001) ArticleTitleExact Boundary Controllability of a Hybrid System of Elasticity by the HUM Method, ESAIM Control Optimization and Calculus Variations 6 183–199 Occurrence Handle10.1051/cocv:2001107
W Littman L. Markus (1988) ArticleTitleStabilization of a Hybrid System of Elasticity be Feedback Boundary Damping Annali di Matematica Pura ed Applicata 152 281–330
B. Rao (1995) ArticleTitleUniform Stabilization of a Hybrid System of Elasticity SIAM Journal on Control and Optimization 33 440–454 Occurrence Handle10.1137/S0363012992239879
S.A. Avdonin S.A. Ivanov (1995) Families of Exponentials: The Method of Moments in Controllability Problems for Distributed-Parameter Systems Cambridge University Press Cambridge, UK
K. Seip (1995) ArticleTitleOn the Connection between Exponential Bases and Certain Related Sequences in L2(−π, π) Journal of Functional Analysis 130 131–160 Occurrence Handle10.1006/jfan.1995.1066
D.L. Russell (1982) ArticleTitleOn Exponential Bases for the Sobolev Spaces over an Interval Journal of Mathematical Analysis and Applications 87 528–550 Occurrence Handle10.1016/0022-247X(82)90142-1
S Ivanov N. Kalton (2002) ArticleTitleInterpolation of Subspaces and Applications to Exponential Bases St. Petersburg Mathematical Journal 13 221–239
R.F. Curtain H.J. Zwart (1995) An Introduction to Infinite-Dimensional Linear Systems Theory Springer Verlag New York, NY
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The work was carried out with the support of the National Natural Science Foundation of China and the Russian Foundation for Fundamental Researches, Grant 02-01-00554.
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Guo, B.Z., Ivanov, S.A. Boundary Controllability and Observability of a One-Dimensional Nonuniform SCOLE System. J Optim Theory Appl 127, 89–108 (2005). https://doi.org/10.1007/s10957-005-6394-3
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DOI: https://doi.org/10.1007/s10957-005-6394-3