Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set, well adapted to a given closed set and prove a new attainability result.
Czasopismo
Rocznik
Tom
Strony
1411--1427
Opis fizyczny
Bibliogr. 39 poz., wykr.
Twórcy
autor
- Institute of Mathematics & Informatics, Sofia, Bulgaria
Bibliografia
- AGRACHEV, A. and GAMKRELIDZE, R. (1993) Local controllability and semigroups of diffeomorphisms. Acta Applicandae Mathematicae 32, 1-57.
- AUBIN, J.-P. H., FRANKOWSKA, H. and OLECH, Cz. (1986) Controllability of convex processes. SIAM J. Control Optimization 24, 1192-1211.
- BACCIOTTI, A. and STEFANI, G. (1980) Self-accessibility of a set with respect to a multivalued field. Journal of Optimization Theory and Applications 31, 535-552.
- BARDI, M. and CAPUZZO-DOLCETTA, I. (1997) Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equation. Birkhäuser.
- BIANCHINI, R. and STEFANI, G. (1990) Time optimal problem and time optimal map. Rend. Sem. Mat. Univers. Politecn. Torino 48, 401-429.
- BIANCHINI, R. and STEFANI, G. (1990) Graded approximation and controllability along a trajectory. SIAM J. Control and Optimization 28, 903-924.
- BIANCHINI, R. and STEFANI, G. (1993) Controllability along a trajectory: A variational approach. SIAM J. Control and Optimization 31, 900-927.
- BRUNOVSKY, P. (1974) Local controllability of odd systems. Banach Center Publications 1, Warsaw, 39-45.
- CARDALIAGUET, P., QUINCAMPOIX, M. and SAINT PIERRE, P. (1997) Minimal times for constrained nonlinear control problems without controllability. Appl. Math. Optimization 36, 21-42.
- CLARKE, F. (1983) Optimization and nonsmooth analysis. John Wiley & Sons, New York-Chichester-Brisbane-Toronto-Singapore.
- CLARKE, F. and WOLENSKI, P. (1996) Control of systems to sets and their interiors. Journal of Optimization Theory and Applications 88, 3-23.
- CLARKE, F., LEDYAEV, Yu., STERN, R. and WOLENSKI, P. (1998) Nonsmooth analysis and control theory. Graduate Text in Mathematics 178, Springer-Verlag, New York.
- COLOMBO, G., MARIGONDA, A. and WOLENSKI, P. (2006) Some new regularity properties for the minimal time function. SIAM J. Control and Optimization 44, 2285-2299.
- CORON, J.-M. (1994) Relations between nonlinear controllability and stabilizability (in French). In: H. Brezis et al., eds., Nonlinear partial differential equations and their applications. Coll’ege de France Seminar XI, Lectures presented at the weekly seminar on applied mathematics, Paris, France, 1989-1991. Pitman Res. Notes Math. Ser. 299, Longman Scientific & Technical, Harlow, 68-86.
- FRANKOWSKA, H. (1989) Local controllability of control systems with feedback. J. Opt. Theory and Application 60, 277-296.
- HERMES, H. (1978) Lie algebras of vector fields and local approximation of attainable sets. SIAM Journal on Control and Optimization 16, 715-727.
- HERMES, H. (1982) Control systems with decomposable Lie algebras. Journal of Differential Equations 44, 166-187.
- HIRSHORN, R. (1989) Strong controllability of nonlinear systems. SIAM J. Control and Optimization 16 264-275.
- JURDJEVIC, V. and KUPKA, I. (1985) Polynomial Control Systems. Mathematische Annalen 272, 361-368.
- KAWSKI, M. (1987) A Necessary Condition for Local Controllability. Contemporary Mathematics 68, 143-155.
- KAWSKI, M. (1988) Control variations with an increasing number of switchings. Bulletin of the American Mathematical Society 18, 149-152.
- KRASTANOV, M.I. (1998) A necessary condition for small time local controllability. Journal of Dynamical and Control Systems 4, 425-456.
- KRASTANOV, M.I. (2002) A sufficient condition for small-time local attainability of a set. Control and Cybernetics 31, 739-750.
- KRASTANOV, M.I. (2008) On the Constrained Small-Time Controllability of Linear Systems. Automatica 44 (9), 2370-2374.
- KRASTANOV, M.I. and QUINCAMPOIX, M. (2001) Local small-time controllability and attainability of a set for nonlinear control system. ESAIM: Control Optim. Calc. Variations 6, 499-516
- KRASTANOV, M.I. and VELIOV, V.M. (2005) On the controllability of switching linear systems. Automatica 41, 663-668.
- KUNITA, H. (1979) On the controllability of nonlinear systems with application to polynomial systems. Appl. Math. Optimization 5 (2), 89-99.
- LIVEROVSKIJ, A.A. and PETROV, N.N. (1988) Normal local controllability. Differ. Equations 24 (9), 996-1002.
- MARIGONDA, A. (2006) Second order conditions for the controllability of nonlinear systems with drift. Commun. Pure Appl. Analysis 5, 861-885.
- PETROV, N.N. (1976) Local controllability. Differ. Equations 12, 1545-1550.
- SORAVIA, P. (1978) Holder continuity of the minimal-time function for C1-manifold targets. Journal of Optimization Theory and Applications 75, 790-802.
- STEFANI, G. (1986) On the local controllability of a scalar input control system. In: C. Birnes and A. Lindquist, eds., Theory and Applications of Nonlinear Control Systems. North-Holland, Amsterdam, 167-179.
- SUSSMANN, H. (1978) A sufficient condition for local controllability. SIAM Journal on Control and Optimization 16, 790-802.
- SUSSMANN, H. (1983) Lie brackets and local controllability: a sufficient condition for scalar-input systems. SIAM Journal on Control and Optimization 21, 686-713.
- SUSSMANN, H. (1987) A general theorem on local controllability. SIAM Journal on Control and Optimization 25, 158-194.
- VELIOV, V.M. (1988) On the controllability of control constrained linear systems. Mathematica Balkanica, New Series 2, 147-155.
- VELIOV, V.M. (1994) Attractiveness and invariance: The case of uncertain measurement. Prog. Syst. Control Theory, 18, “Modeling Techniques for uncertain systems”. Birkhäuser, 277-288.
- VELIOV, V.M. (1997) On the Lipschitz continuity of the value function in optimal control. Journal of Optimization Theory and Applications 94, 335-361.
- VELIOV, V. M. and KRASTANOV, M. (1986) Controllability of piecewise linear systems. Systems & Control Letters 7, 335-341.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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