Singularly perturbed differential inclusions: An averaging approach

Set-Valued Analysis

Volumn 4, Issue 4, 1996, Pages 361-374

  Grammel, Götz ^a  

^a UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Averaging method; Controlability; Differential inclusion; Singular perturbation; Stability

Indexed keywords

EID: 0001110622     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00436111     Document Type: Article

References (11)

1. Anosov, D. V.: Oscillations in systems of ODE with rapidly oscillating solutions, Izvest. Akad. Nauk SSSR Math. 24(5) (1960), 721-742.
2. Artstein, Z. and Vigodner, A.: Singularly perturbed ordinary differential equations with dynamic limits, Royal Society of Edinburgh Proceedings A, to appear.
3. Aubin, J. P.: Viability Theory, Birkhäuser, Basel, 1991.
4. Aubin, J. P. and Cellina, A.: Differential Inclusions, Springer-Verlag, New York, 1984.
5. Deimling, K.: Multivalued Differential Equations, Walter de Gruyter, Berlin, 1992.
6. Dontchev, A. L. and Slavov, I. I.: Upper semicontinuity of solutions of singularly perturbed differential inclusions, in: H.-J. Sebastian and K. Tammer (eds), System Modelling and Optimization, Lecture Notes in Control Info. Sci. 143, Springer-Verlag, New York, 1991.
7. Gaitsgory, V. G.: Suboptimization of singularly perturbed control systems, SIAM J. Cont. Optimiz. 30(5) (1992), 1228-1249.
8. Grammel, G.: Averaging of singularly perturbed systems, Nonlinear Analysis, TMA, to appear.
9. Lochak, P. and Meunier, C: Multiphase Averaging for Classical Systems, Springer-Verlag, New York, 1988.
10. Plotnikov, V. A.: Averaging method for differential inclusions and its application to optimal control problems, Differential Equations 15 (1979), 1013-1018.
11. Tychonov, A. N.: Systems of differential equations containing small parameters in the derivatives, Mat. Sb. 31 (1952), 575-586.