On a Representation of the Limit Occupational Measures Set of a Control System with Applications to Singularly Perturbed Control Systems

A representation of the limit occupational measures set of a control system in terms of the vector function defining the system's dynamics is established. Applications in averaging of singularly perturbed control systems are demonstrated.

[1]  Z. Artstein,et al.  The Value Function of Singularly Perturbed Control Systems , 2000 .

[2]  Fabio Bagagiolo,et al.  Singular Perturbation of a Finite Horizon Problem with State-Space Constraints , 1998 .

[3]  Warren B. Powell,et al.  Hierarchical Decision Making , 2004 .

[4]  J. Warga Optimal control of differential and functional equations , 1972 .

[5]  Y. Kabanov,et al.  On Convergence of Attainability Sets for Controlled Two-Scale Stochastic Linear Systems , 1997 .

[6]  A. Dontchev,et al.  A Tikhonov-type theorem for singularly perturbed differential inclusions , 1996 .

[7]  P. Kokotovic Applications of Singular Perturbation Techniques to Control Problems , 1984 .

[8]  R. Stockbridge Time-Average Control of Martingale Problems: Existence of a Stationary Solution , 1990 .

[9]  H. Kushner Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems , 1990 .

[10]  A. Vigodner Limits of Singularly Perturbed Control Problems with Statistical Dynamics of Fast Motions , 1997 .

[11]  V. A. Plotnikov Averaging of differential inclusions , 1979 .

[12]  Vladimir Gaitsgory,et al.  Multiscale Singularly Perturbed Control Systems: Limit Occupational Measures Sets and Averaging , 2002, SIAM J. Control. Optim..

[13]  Martino Bardi,et al.  Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control , 2001, SIAM J. Control. Optim..

[14]  F. Colonius,et al.  Controllability for Systems with Slowly Varying Parameters , 2003 .

[15]  ZVI ARTSTEIN,et al.  Singularly Perturbed Control Systems with One-Dimensional Fast Dynamics , 2002, SIAM J. Control. Optim..

[16]  Z. Artstein,et al.  The chattering limit of singularly perturbed optimal control problems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[17]  L. Segel,et al.  Introduction to Singular Perturbations. By R. E. O'MALLEY, JR. Academic Press, 1974. $ 16.50. , 1975, Journal of Fluid Mechanics.

[18]  M. Quincampoix,et al.  Singular perturbations in non-linear optimal control systems , 1995, Differential and Integral Equations.

[19]  Y. Kabanov,et al.  Two-scale stochastic systems , 2002 .

[20]  R. O'Malley Singular perturbations and optimal control , 1978 .

[21]  E. Altman,et al.  Asymptotic Optimization of a Nonlinear Hybrid System Governed by a Markov Decision Process , 1997 .

[22]  Arie Leizarowitz,et al.  Order Reduction Is Invalid for Singularly Perturbed Control Problems with a Vector Fast Variable , 2002, Math. Control. Signals Syst..

[23]  Desineni S Naidu,et al.  Singular perturbations and time scales in control theory and applications: An overview , 2002 .

[24]  V. Gaitsgory Suboptimization of singularly perturbed control systems , 1992 .

[25]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[26]  Z. Artstein,et al.  Tracking Fast Trajectories Along a Slow Dynamics: A Singular Perturbations Approach , 1997 .

[27]  G. Yin,et al.  Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach , 1997 .

[28]  Jean-Pierre Aubin,et al.  Viability theory , 1991 .

[29]  A. Bensoussan Perturbation Methods in Optimal Control , 1988 .

[30]  Asen L. Dontchev,et al.  Time-scale decomposition of the reachable set of constrained linear systems , 1992, Math. Control. Signals Syst..

[31]  Z. Artstein Anoccupational measure solution to a singularly perturbed optimal control problem , 2002 .

[32]  V. G. Gaitsgori,et al.  Theory of Suboptimal Decisions , 1988 .

[33]  Jerzy A. Filar,et al.  Control of singularly perturbed hybrid stochastic systems , 2001, IEEE Trans. Autom. Control..

[34]  Qing Zhang,et al.  Continuous-Time Markov Chains and Applications , 1998 .

[35]  G. Grammel Averaging of singularly perturbed systems , 1997 .

[36]  Z. Artstein,et al.  Convergence to convex compact sets in infinite dimensions , 2003 .

[37]  José G. Llavona,et al.  Approximation of Continuously Differentiable Functions , 1986 .

[38]  G. Grammel Periodic Near Optimal Control , 2000 .

[39]  T. Donchev,et al.  Averaging Method for One-Sided Lipschitz Differential Inclusions with Generalized Solutions , 1999 .

[40]  Qing Zhang,et al.  Hierarchical Decision Making in Stochastic Manufacturing Systems , 1994 .

[41]  A. Leizarowitz,et al.  Limit Occupational Measures Set for a Control System and Averaging of Singularly Perturbed Control Systems , 1999 .