Leseprobe
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Adaptive Control of Parabolic PDEs
Miroslav Krstic, Andrey Smyshlyaev
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others.
Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.
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Eigenfunction, Transfer function, Error term, Adaptive system, Eigenvalues and eigenvectors, Integral equation, Dirichlet boundary condition, Linearization, Frequency domain, Bounded operator, Measurement, Integrator, Theorem, Gradient method, Least squares, Estimator, Instability, Observability, Rate of convergence, Uncertainty, Parameter, Actuator, Accuracy and precision, Categorization, Symbolic computation, Inverse Laplace transform, Deterministic system, Differential equation, Parametrization, Optimal control, Derivative, Linear differential equation, Discretization, Phase margin, Extended Kalman filter, Wave equation, Pointwise, Sensor, Backstepping, Initial condition, Change of variables, Laplace transform, Mathematical optimization, Adaptive control, Estimation theory, Asymptotic analysis, Boundary value problem, Control variable, Robustification, Variable (mathematics), Computation, Bode plot, Minimum phase, Volterra operator, Coefficient, Feedback linearization, Identifiability, Nonlinear control, Dimension (vector space), Separation principle, Control engineering, System identification, Linear programming, Parametric model, Estimation, Lyapunov function, Reynolds number, Identifier, Nonlinear system, Riccati equation