Abstract
The paper deals with the perturbation techniques for dynamic systems described by differential inclusions and state constraint relations. We replace the phase restrictions by a new differential inclusion with a small parameter multiplying the derivative and study the limit behaviour of the system combining two groups of differential inclusions, the former to be the given differential inclusion and the latter to be the introduced one. The idea based upon consideration of all matrix time-varying perturbations to this system allows one to describe the attainability sets of the primary differential inclusion under state constraints. Applications to the control and observation problems are also discussed.
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References
Aubin J.-P., and Cellina A. Differential inclusions, Heidelberg, Springer-Verlag,1984
Dontchev A. Perturbations, approximations and sensitivity analysis of optimal control systems, Lect. Notes in Contr.& Inform. Sciences,52, Springer-Verlag,1986
Klimushev A.I., and Krasovskii N.N. Uniform asymptotic stability of systems of differential equations with a small parameter in the derivative term, Prikl. Mat. Mech.,25,1,1962,1011–1025 (in Russian)
Kokotovic P., Bensoussan A., and Blankeship G. Eds., Singular perturbations and asymptotic analysis in control systems, Lect. Notes in Contr. & Inform. Sciences, 90, Springer-Verlag, 1986
Krasovskii N.N. The control of a dynamic system, “Nauka”, Moscow, 1986 (in Russian)
Kurzhanskii A.B. Control and observation under uncertainty, “Nauka”, Moscow, 1977 (in Russian)
Kurzhanskii A.B., and Filippova T.F. On the description of the set of viable trajectories of a differential inclusion, Doklady AN SSSR,289,1986,38–41 (in Russian)
Kurzhanskii A.B., and Valye I. Set-valued solutions to control problems and their approximations, in:A.Bensoussan, J.L.Lions Eds., Analysis and Optimization of systems, Lect.Notes in Contr.& Inform. Sciences,111,Springer-Verlag,1988,755–785
Tikhonov A.N. On the dependence of the solutions of differential equations on small parameter, Mat.Sb.,22,1948,198–204 (in Russian)
Tikhonov, A.N. Systems of differential equations containing a small parameter multiplying the derivative, Mat.Sb.,31,73,1952,575–586 (in Russian)
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© 1992 International Federation for Information Processing
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Kurzhanski, A.B., Filippova, T.F. (1992). Perturbation techniques for viability and control. In: Davisson, L.D., et al. System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113306
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DOI: https://doi.org/10.1007/BFb0113306
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-540-47220-9
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