Bang-bang controls in the singular perturbations limit

• Autorzy: Artstein Z.
• Języki publikacji: EN

Abstrakty

EN

A general form of the dynamics obtained as a limit of trajectories of singularly perturbed linear control systems is presented. The limit trajectories are described in terms of probability measure-valued maps. This allows to determine the extent to which the bang-bang principle for linear control systems is carried over to the singular limit.

Słowa kluczowe

EN

bang-bang; singular perturbations; Young measures

PL

zaburzenia osobliwe; miara Younga

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 3
• Strony: 645--663
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Artstein Z.

• Department of Mathematics The Weizmann Institute of Science Rehovot 76100, Israel

Bibliografia

• Artstein, Z. (1999) Invariant measures of differential inclusions applied to singular perturbations. J. Differential Equations 152, 289-307.
• Artstein, Z. (2000) The chattering limit of singularly perturbed optimal control problems. Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 564-569.
• Artstein, Z. (2002) An occupational measure solution to a singularly perturbed optimal control problem. Control and Cybernetics 31, 623-642.
• Artstein, Z. (2004a) On impulses induced by singular perturbations. In: M. de Queiroz, M. Malisoff and P. Wolenski, eds., Optimal Control, Stabilization, and Nonsmooth Analysis, Lecture Notes in Control and Information Sciences 301, Springer-Verlag, Heidelberg, 61-72.
• Artstein, Z. (2004b) Invariant measures and their projections in nonautonomous dynamical systems. Stochastics and Dynamics 4, 439-459.
• Artstein, Z. (2004c) On the value function of singularly perturbed optimal control systems. Proceedings of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, 432-437.
• Artstein, Z. and Gaitsgory, V. (1997) Linear-quadratic tracking of coupled slow and fast targets. Math. Cont. Sign. Syst. 10, 1-30.
• Artstein, Z. and Vigodner, A. (1996) Singularly perturbed ordinary differential equations with dynamic limits. Proceedings of the Royal Society of Edinburgh 126A, 541-569.
• Balder, E.J. (2000) Lectures on Young measure theory and its applications to economics. Rend. Istit. Mat. Univ. Trieste 31, supplemento 1, 1-69.
• Dontchev, A.L. and Veliov, V.M. (1983) Singular perturbation in Mayer’s problem for linear systems. SIAM J. Control Optim. 21, 566-581.
• Dontchev, A.L. and Veliov, V.M. (1985a) Singular perturbations in linear control systems with weakly coupled stable and unstable fast subsystems. J. Math. Anal. Appl. 110, 1-30.
• Dontchev, A.L. and Veliov, V.M. (1985b) On the order reduction of linear optimal control systems in critical cases. In: A. Bagehi and H.Th. Jongen, eds., Systems and optimization. Lecture Notes in Control and Inform. Sci. 66, Springer, Berlin, 61-73.
• Hermes, H. and LaSalle, J.P. (1969) Functional Analysis and Time Optimal Control. Academic Press, New York.
• Kokotovic, P.V., Khalil, H.K. and O’Reilly, J. (1999) Singular Perturbation Methods in Control: Analysis and Design. Academic Press, London, 1986. Reprinted as Classics in Applied Mathematics 25, SIAM Publications, Philadelphia.
• LaSalle, J.P. (1959) The time optimal control problem. Theory of Nonlinear Oscillations, 5, Princeton University Press, Princeton, NJ, 1-24.
• Olech, C. (1966) Extremal solutions of a control system. J. Differential Equations 2, 74-101.
• Olech, C. (1967) Lexicographical order, range of integrals and ”bang-bang” principle. In: A.V. Balakrishnan and L.W. Neustadt, eds., Mathematical Theory of Control, Proc. Conf. in Univ. of Southern California, Jan. 30–Feb. 1, 1967, 35-45, Academic Press, New York.
• Valadier, M. (1994) A course on Young measures. Rend. Istit. Mat. Univ. Trieste 26 supp., 349-394.
• Vigodner, A. (1997) Limits of singularly perturbed control problems with statistical dynamics of fast motions. SIAM J. Control Optim. 35, 1-28.