This book addresses the mathematical and the practical aspects of motion implied by advanced control theory. The richness and power of the theory are demonstrated by separate analyses of single-model and multi-modal repertoires, consisting of verities of estimation and control facets. Starting with purely mathematical concepts, specifically, abstract probability and information theories, model control theory is gradually revealed as a rather amazing domain. The mathematical equations, taking essentially simple forms, are exposed as powerful generators of motion. Moreover, seemingly obvious applications of the theory, such as high-performance aircraft control make room for unexpected virtual reality feedback in control of motion for the neurologically impaired.Following the presentation of some historical milestones and mathematical preliminaries, the book is divided into four parts. The first deals with minimal-order models of state estimation and control. The second addresses multi-modal estimation and control, which facilitates the operation of high-performance aircraft in large flight envelopes. The third presents the transition from naturally nonlinear control of movement in obstacle avoidance and object targeting to virtually linear control of movement in the neurologically impaired. The fourth and final part of the book addresses the application of virtual sensory feedback in walking with specific neurological impairment. While the clinical studies reported were all based on a single-model paradigm, a later reflection reveals that, given the variety of neurological symptoms associated with the relevant disorders, a multi-modal approach, as that addressed in the control of high-performance aircraft in a large flight envelope, would be similarly applicable in the treatment of neurological disorders.Key FeaturesThe focus of the book, presented and explained here for the first time, is that the technological wisdom of control theory is naturally embedded in cortical control of biological motionThe notion of a single-model selection from a multi-modal set addressed in Chapters 9 – 12, was first suggested in the author’s PhD thesis (Baram, 1976), but its extension to virtually driven motion control in neurologically impaired patients is suggested here for the first timeThe mathematical evolution from the fundamentals of probability, statistics, and information to the technology of virtual reality, supported by extensive clinical tests, is also presented here for the first time

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