Nearly Optimal Controls of Markovian Systems

[1]  Tamer Basar,et al.  H infintity control of large-scale jump linear systems via averaging and aggregation , 1999 .

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

[3]  W. Miranker,et al.  Multitime Methods for Systems of Difference Equations , 1977 .

[4]  Tomasz R. Bielecki,et al.  Ergodic Control of a Singularly Perturbed Markov Process in Discrete Time with General State and Compact Action Spaces , 1998 .

[5]  Cyrus Derman,et al.  Finite State Markovian Decision Processes , 1970 .

[6]  Dimitri P. Bertsekas,et al.  Dynamic Programming: Deterministic and Stochastic Models , 1987 .

[7]  R. H. Liu Nearly optimal control of singularly perturbed Markov decision processes in discrete time , 2001 .

[8]  Harold J. Kushner,et al.  Stochastic Approximation Algorithms and Applications , 1997, Applications of Mathematics.

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

[10]  F. Delebecque A Reduction Process for Perturbed Markov Chains , 1983 .

[11]  P. Billingsley,et al.  Convergence of Probability Measures , 1970, The Mathematical Gazette.

[12]  Xi-Ren Cao,et al.  A unified approach to Markov decision problems and performance sensitivity analysis , 2000, at - Automatisierungstechnik.

[13]  Qing Zhang,et al.  Control of singularly perturbed Markov chains: A numerical study , 2003, The ANZIAM Journal.

[14]  Marius Iosifescu,et al.  Finite Markov Processes and Their Applications , 1981 .

[15]  G. Blankenship Singularly perturbed difference equations in optimal control problems , 1981 .

[16]  Gang George Yin,et al.  Singularly Perturbed Discrete-Time Markov Chains , 2000, SIAM J. Appl. Math..

[17]  Xi-Ren Cao The Maclaurin series for performance functions of Markov chains , 1998, Advances in Applied Probability.

[18]  Gang George Yin,et al.  On nearly optimal controls of hybrid LQG problems , 1999, IEEE Trans. Autom. Control..

[19]  A. A. Pervozvanskiĭ,et al.  Theory of Suboptimal Decisions: Decomposition and Aggregation , 1988 .

[20]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[21]  Xi-Ren Cao,et al.  Semi-Markov decision problems and performance sensitivity analysis , 2003, IEEE Trans. Autom. Control..

[22]  J. Filar,et al.  Algorithms for singularly perturbed limiting average Markov control problems , 1990, 29th IEEE Conference on Decision and Control.

[23]  Zhiyuan Ren,et al.  A time aggregation approach to Markov decision processes , 2002, Autom..

[24]  Optimal Control of Perturbed Markov Chains: The Multitime Scale Case , 1982 .

[25]  R. Rishel Control of systems with jump Markov disturbances , 1975 .

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

[27]  Q. Zhang,et al.  NEARLY OPTIMAL CONTROL OF NONLINEAR MARKOVIAN SYSTEMS SUBJECT TO WEAK AND STRONG INTERACTIONS , 2001 .

[28]  Eitan Altman,et al.  Control of a hybrid stochastic system , 1993 .

[29]  R. Z. Khasminskii,et al.  Constructing asymptotic series for probability distributions of Markov chains with weak and strong interactions , 1997 .

[30]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[31]  M. Mariton,et al.  Robust jump linear quadratic control: A mode stabilizing solution , 1985 .

[32]  D. Naidu Singular Perturbation Methodology in Control Systems , 1988 .

[33]  J. Filar,et al.  Perturbation and stability theory for Markov control problems , 1992 .

[34]  J. Filar,et al.  Singularly perturbed Markov control problem: Limiting average cost , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[35]  R. H. Liu,et al.  Asymptotically optimal controls of hybrid linear quadratic regulators in discrete time , 2002, Autom..

[36]  Xi-Ren Cao,et al.  The Relations Among Potentials, Perturbation Analysis, and Markov Decision Processes , 1998, Discret. Event Dyn. Syst..

[37]  Qing Zhang,et al.  Asymptotic properties of a singularly perturbed Markov chain with inclusion of transient states , 2000 .

[38]  D. Sworder,et al.  Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria , 1975 .

[39]  Qing Zhang,et al.  Finite state markovian decision processes with weak and strong interactions , 1996 .

[40]  François Delebecque,et al.  Optimal control of markov chains admitting strong and weak interactions , 1981, Autom..

[41]  P. Caines,et al.  Optimal adaptive LQG control for systems with finite state process parameters , 1985, The 23rd IEEE Conference on Decision and Control.

[42]  Qing Zhang,et al.  Hybrid filtering for linear systems with non-Gaussian disturbances , 2000, IEEE Trans. Autom. Control..

[43]  G. Yin,et al.  Asymptotic Properties and Associated Control Problems of Discrete-Time Singularly Perturbed Markov Chains , 2002 .

[44]  H. Chizeck,et al.  Jump Linear Quadratic Gaussian Control in Continuous Time , 1991, 1991 American Control Conference.

[45]  Gang George Yin,et al.  Asymptotic Expansions of Singularly Perturbed Systems Involving Rapidly Fluctuating Markov Chains , 1996, SIAM J. Appl. Math..