Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains

This Springer brief addresses the challenges encountered in the study of  the optimization of time-nonhomogeneous Markov chains. It develops new insights and new methodologies for systems in which concepts such as stationarity, ergodicity, periodicity and connectivity do not apply.

This brief introduces the novel concept of confluencity and applies a relative optimization approach. It develops a comprehensive theory for optimization of the long-run average of time-nonhomogeneous Markov chains. The book shows that confluencity is the most fundamental concept in optimization, and that relative optimization is more suitable for treating the systems under consideration than standard ideas of dynamic programming. Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived. These results are presented in a book for the first time and so may enhance the understanding of optimization and motivate new research ideas in the area.

• Markov Decision Processes
• Blackwell Optimality
• Branching States
• Confluencity
• Multi-Class Optimization
• Nth-Bias Optimality
• Performance Potentials
• State Classification
• Time-Nonhomogeneous Markov Chain
• Markov Chains

• Department of Automation, Shanghai Jiao Tong University, Shanghai, China

  Xi-Ren Cao

Professor Xi-Ren Cao gained his B.S. in 1967 from the University of Sciences and Technology of China, and his M.S. and Ph.D. from Harvard University, in 1982 and 1984, respectively. He has worked in numerous industrial, teaching, and research positions since then, and is now a Professor Emeritus, The Hong Kong University of Science and Technology. He has acted as an Industry Consultant, was Editor-in-Chief of Discrete Event Dynamic Systems: Theory and Applications for 9 years, and is a Fellow of IFAC and the IEEE. He has published 125 peer-reviewed journal papers, 12 invited book chapters, and four books. 

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