The concepts of entropy, chaos, and control engineering, to familiarize the reader with the key notions of the book. Chapter 2, discusses a new derivation of the theory of optimal estimation and control by associating the cost of performance with entropy. This new theory produced two results: first the derivation of the Generalized Hamilton-Jacobi-Bellman equation which describes the behavior of control systems for a fixed but arbitrary controller.This volume attempts to couple control engineering with the modern developments in science, through the concept of entropy. Such disciplines like Intelligent Machines, Economics, Manufacturing, Environmental Systems, Waste etc. can be favorably affected and their performance can be improved or actually their catastrophic effects minimized. Entropy is used as the unifying measure of the various, seemingly disjoint, disciplines to represent the cost of producing work that improves the standards of living, both in engineering and in science. Modeling is done through probabilistic methods, thus establishing the irreversibility of the processes involved. This is in accordance with the modern point of view of science. In addition the behavior of control for an arbitrary but fixed controller away from the optimal (equilibrium) was obtained, the analytic expression of which should lead to chaotic solutions.
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