Optimal Control

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The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automaton theory, operational research and industry. The more definite concept of a large-scale system is implicit in these applications, but is particularly evident in fields such as the study of communication networks, computer networks and neural networks. The Wiley-Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology. This is the first book-length treatment of risk-sensitive control, with many new results. The quadratic cost function of the standard LQG (linear/quadratic/Gaussian) treatment is replaced by the exponential of a quadratic, giving the so-called LEQG formulation allowing for a degree of optimism or pessimism on the part of the optimiser. The author is the first to achieve formulation and proof of risk-sensitive versions of the certainty-equivalence and separation principles. Further analysis allows one to formulate the optimization as the extremization of a path integral and to characterize the solution in terms of canonical factorization. It is thus possible to achieve the long-sought goal of an operational stochastic maximum principle, valid for a higher-order model, and in fact only evident when the models are extended to the risk-sensitive class. Additional results include deduction of compact relationsbetween value functions and canonical factors, the exploitation of the equivalence between policy improvement and Newton -- Raphson methods and the direct relation of LEQG methods to the H??? and minimum-entropy methods. This book will prove essential reading for all graduate stu