Optimal Trajectory Tracking of Nonlinear Dynamical Systems

By establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be c...

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Main Author: Löber, Jakob
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2017, 2017
Edition:1st ed. 2017
Series:Springer Theses, Recognizing Outstanding Ph.D. Research
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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245 0 0 |a Optimal Trajectory Tracking of Nonlinear Dynamical Systems  |h Elektronische Ressource  |c by Jakob Löber 
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260 |a Cham  |b Springer International Publishing  |c 2017, 2017 
300 |a XIV, 243 p. 36 illus., 32 illus. in color  |b online resource 
505 0 |a Introduction -- Exactly Realizable Trajectories -- Optimal Control -- Analytical Approximations for Optimal Trajectory Tracking -- Control of Reaction-Diffusion System 
653 |a Dynamical Systems and Ergodic Theory 
653 |a Calculus of Variations and Optimal Control; Optimization 
653 |a Ergodic theory 
653 |a Statistical physics 
653 |a Vibration 
653 |a Vibration, Dynamical Systems, Control 
653 |a Applications of Nonlinear Dynamics and Chaos Theory 
653 |a Calculus of variations 
653 |a Dynamical systems 
653 |a Dynamics 
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490 0 |a Springer Theses, Recognizing Outstanding Ph.D. Research 
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520 |a By establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e.g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry