New Trends in Control Theory.

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New Trends in Control Theory is a graduate-level monographic textbook. It is a contemporary overview of modern trends in control theory. The introductory chapter gives the geometrical and quantum background, which is a necessary minimum for comprehensive reading of the book. The second chapter gives the basics of classical control theory, both linear and nonlinear. The third chapter shows the key role that Euclidean group of rigid motions plays in modern robotics and biomechanics. The fourth chapter gives an overview of modern quantum control, from both theoretical and measurement perspectives.

Machine generated contents note: 1. Introduction -- 1.1. Geometrical Preliminaries -- 1.1.1. Variational Method of Classical Mechanics -- 1.1.2. Lie Algebra Mechanics -- 1.1.3. Covariant Dynamics Modelling -- 1.1.4. Exterior Differential Forms -- 1.1.5. Hodge Theory Basics -- 1.1.6. Principal G-Bundles, Connections and G -- Snakes -- 1.1.7. Wei-Norman Exponential Method -- 1.2. Quantum Preliminaries -- 1.2.1. Basic Quantum Mechanics -- 1.2.2. Basic Quantum Fields -- 1.2.3. Wigner Function Basics -- 1.2.4. Path Integral Quantization -- 1.2.5. Gauge Path-Integral via Hodge Decomposition -- 2. Basics of Classical Control Theory -- 2.1. Linear Systems and Signals -- 2.1.1. Laplace Transform and Transfer-Function Methods -- 2.1.2. Fourier and Wavelet Transforms for Linear Signals -- 2.1.3. Kalman's Modular State-Space and Filtering Methods -- 2.1.4. Controllability of Linear Systems -- 2.1.5. Stability of Linear Systems -- 2.1.6. Naive Approaches to Nonlinear Systems -- 2.2. Nonlinear Control Systems -- 2.2.1. Command/Control in Human-Robot Interactions -- 2.2.2. Nonlinear Controllability -- 2.2.3. Basics of Geometric Nonlinear Control -- 2.2.4. Lie-Derivative Based Nonlinear Feedback Control -- 2.2.5. Hamiltonian Optimal Control and Maximum Principle -- 2.2.6. Path-Integral Optimal Control of Stochastic Systems -- 2.2.7. Fuzzy-Logic Control -- 3. Euclidean Group in Modern Robotics and Biomechanics -- 3.1. Introduction to Euclidean Group -- 3.1.1. Euclidean Kinematics -- 3.1.2. Basic Dynamics on SE(3) -- 3.1.3. Coupled Newton-Euler Dynamics on SE(3) -- 3.1.4. Introduction to Hamiltonian Biomechanics -- 3.1.5. Library of Basic Hamiltonian Systems -- 3.2. Euclidean Group in Modern Robotics -- 3.2.1. Constructive Controllability for Motion on Lie Groups -- 3.2.2. SE(3)-Group Control Example -- 3.2.3. Examples of SE(3)-Subgroups Control.

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