Perturbation techniques for viability and control
- 96 Downloads
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.
Unable to display preview. Download preview PDF.
- Dontchev A. Perturbations, approximations and sensitivity analysis of optimal control systems, Lect. Notes in Contr.& Inform. Sciences,52, Springer-Verlag,1986Google Scholar
- 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)Google Scholar
- 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, 1986Google Scholar
- Krasovskii N.N. The control of a dynamic system, “Nauka”, Moscow, 1986 (in Russian)Google Scholar
- Kurzhanskii A.B. Control and observation under uncertainty, “Nauka”, Moscow, 1977 (in Russian)Google Scholar
- 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,1988,755–785Google Scholar
- Tikhonov A.N. On the dependence of the solutions of differential equations on small parameter, Mat.Sb.,22,1948,198–204 (in Russian)Google Scholar
- Tikhonov, A.N. Systems of differential equations containing a small parameter multiplying the derivative, Mat.Sb.,31,73,1952,575–586 (in Russian)Google Scholar