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This book investigates abstraction of dynamical systems for the purpose of designing controllers. Abstraction is a means to reduce a system model's complexity while retaining the important behavior of that system. The motivating example throughout this text is the robotic car. Two topics are introduced in this text: control design using abstraction and propagation of uncertainty in abstracted systems. First, this book investigates the conditions for which controllers can be designed in abstracted systems and then transferred to the original dynamical system, taking advantage of design using the simpler model. This book also studies the relationship between the evolution of uncertain initial conditions in abstracted control systems. It is shown that a control system abstraction can capture the time evolution of the uncertainty in the original system by an appropriate choice of control input. This book provides a comprehensive review of the theory behind abstraction and applies the results to general nonlinear dynamical systems. In particular, the following topics are presented: * An overview of the history and current research in mobile robotic control design. * A mathematical review that provides the tools used in this research area. * The development of the robotic car model and both controllers used in the new control design. * A review of abstraction and an extension of these ideas into new system relationship characterizations called traceability and E-traceability. * A framework for designing controllers based on abstraction. * An open-loop control design with simulation results. * An investigation of system abstraction with uncertain initial conditions.


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