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## Banach Center Publications

1996 | 35 | 1 | 193-205
Tytuł artykułu

### An Invariance Problem for Control Systems with Deterministic Uncertainty

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with a class of nonlinear control systems in $R^n$ in presence of deterministic uncertainty. The uncertainty is modelled by a multivalued map F with nonempty, closed, convex values. Given a nonempty closed set $K ⊂ R^n$ from a suitable class, which includes the convex sets, we solve the problem of finding a state feedback ū(t,x) in such a way that K is invariant under any system dynamics f. As a system dynamics we consider any continuous selection of the uncertain controlled dynamics F.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
193-205
Opis fizyczny
Daty
wydano
1996
Twórcy
autor
• Institute of Mathematics, University of N. Copernicus, ul. Chopina 12/18, 87100 Toruń, Poland
autor
• Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Via di S. Marta 3, 50139 Firenze, Italy
Bibliografia
• [1] J. P. Aubin, Viability Theory, Birkhäuser-Verlag, Berlin, 1991.
• [2] J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, 1984.
• [3] J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser-Verlag, Berlin, 1990.
• [4] J. P. Aubin and H. Frankowska, Observability of systems under uncertainty, SIAM J. Control and Optimization 27 (5) 1989, 949-975.
• [5] B. R. Barmish, Stabilization of uncertain systems via linear control, IEEE Trans. Autom. Contr. AC-28 (8) 1983, 848-850.
• [6] B. R. Barmish, M. Corless and G. Leitmann, A new class of stabilizing controllers for uncertain dynamical systems, SIAM J. Control and Optim. 21 (2) 1983, 246-255.
• [7] G. Bartolini and T. Zolezzi, Asymptotic linearization of uncertain systems by variable structure control, System, and Control Letters 10 1988, 111-117.
• [8] G. Bartolini and T. Zolezzi, Some new application of V.S.S. theory to the control of uncertain nonlinear systems, Proc. 27-th IEEE Conference on Decision and Control, Austin 1988.
• [9] R. Bielawski, L. Górniewicz and S. Plaskacz, Topological approach to differential inclusions on closed subsets of $R^n$, Dynamics Reported N.S. 1 1992, 225-250.
• [10] A. Bressan, Directionally continuous selections and differential inclusions, Funkc. Ekv. 31 1988, 459-470.
• [11] A. Bressan, Upper and lower semicontinuous differential inclusions: a unified approach, Nonlinear Controllability and Optimal Control, H. Sussmann Ed., M. Dekker, 1988, 21-31.
• [12] M. J. Corless and G. Leitmann, Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Trans. Autom. Contr. AC-26 (25) 1981, 1139-1144.
• [13] L. Górniewicz, P. Nistri and P. Zecca, Control problems in closed subset of $R^n$ via feedback controls, TMNA 2 1993, 163-178.
• [14] S. Hu and N. S. Papageorgiou, On the existence of periodic solutions of nonconvex valued differential inclusions in $R^n$, Technical Report.
• [15] I. Joong Ha and E. G. Gilbert, Robust tracking in nonlinear systems, IEEE Trans. Autom. Contr. AC-32 (9) 1987, 763-771.
• [16] M. Kisielewicz, Differential Inclusions and Optimal Control, PWN-Polish Scientific Publishers, Warszawa & Kluwer Academic Publishers, Dordrecht, Boston, London, 1991.
• [17] A. B. Kurzhanskiĭ, Control and observation under conditions of uncertainty, Nauka, Russia, 1997.
• [18] A. B. Kurzhanskiĭ, Advances in Nonlinear Dynamics and Control: A report from Russia, Verlag, Berlin, 1993.
• [19] J. W. Macki, P. Nistri and P. Zecca, A tracking problem for uncertain vector systems, Nonlinear Analysis TMA 14 1990, 319-328.
• [20] J. W. Macki, P. Nistri and P. Zecca, Corrigendum: A tracking problem for uncertain vector systems, Nonlinear Analysis TMA 20 1993, 191-192.
• [21] P. Nistri, V. Obukhovskiĭ and P. Zecca, Viability for feedback control systems in Banach spaces via Carathéodory closed-loop controls, Diff. Eqns and Dyn. Sys., (to appear).
• [22] J. Oxtoby, Measure and Category, Springer-Verlag, New York, 1971.
• [23] S. Plaskacz, Periodic solution of differential inclusions on compact subset of $R^n$, J. Math. Anal. and Appl. 148 1990, 202-212.
• [24] G. Stefani and P. Zecca, Properties of convex sets with application to differential theory of multivalued functions, Nonlinear Analysis TMA 2 1978, 581-593.
Typ dokumentu
Bibliografia
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