Optimal Trajectory Tracking of Nonlinear Dynamical Systems

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • Jakob Löber

   Pages 1-16

3. Exactly Realizable Trajectories

   • Jakob Löber

   Pages 17-78

4. Optimal Control

   • Jakob Löber

   Pages 79-118

5. Analytical Approximations for Optimal Trajectory Tracking

   • Jakob Löber

   Pages 119-193

6. Control of Reaction-Diffusion Systems

   • Jakob Löber

   Pages 195-220

7. Back Matter

   Pages 221-243

   PDF

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.

• Optimal Control
• Trajectory Tracking
• Nonlinear Control
• Exact Linearization
• Exactly Solvable Examples in Control Theory
• Controllability
• Affine Control Systems
• Systems Theory

• EW 7-1, Tech Univ Berlin EW 7-1, Berlin, Germany

  Jakob Löber

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