Distributed parameter systems : theory and applications
著者
書誌事項
Distributed parameter systems : theory and applications
（Oxford mathematical monographs）
Ohmsha , Clarendon Press , Oxford University Press, 1989
大学図書館所蔵 全36件
注記
Includes index and bibliographies
内容説明・目次
内容説明
Many problems in control and systems theory are formulated in terms of partial differential equations and these are known as distributed parameter systems. This book aims to present the major aspects of the control, estimation and identification of distributed parameter sytems. The book was written for all those applied mathematicians, control theorists and engineers whose work involves such systems and the authors have tried to present a comprehensive account of the essential results in both deterministic and stochastic systems. Part one develops the mathematical theory of distributed parameter systems. The results of the theory of deterministic and stochastic partial differential equations are developed and then applied to the optimal control and estimation theories for the distributed parameter systems. Controllability and observability problems are also discussed. Part two contains applications of the theory to engineering problems. The optimal sensor and actuator location problems are discussed from the engineering viewpoint. There then follows a treatment of computational techniques for the identification of distributed parameter systems.
The book is intended for applied mathematicians, control theorists and engineers interested in distributed parameter systems.
目次
- Part 1 Mathematical theory: some basic results in the theory of partial differential equations - Bellman-Gronwall inequality, Sobolev spaces, Green's formula
- stochastic partial differential equations - radon measures, cylindrical probability, Gaussian cylindrical probability, nuclear and Hilbert-Schmidt operators, conditional expectation, Hilbert- space-valued Wiener processes
- optimal control of deterministic distributed parameter systems - elliptic systems, the Dirichlet problem, the Neumann problem, parabolic systems, Riccati equation, Hamilton-Jacobi equation, hyperbolic systems
- controllability and observability
- linear estimation theory - finite-dimensional estimation theory, estimation for random linear functionals
- optimal filter for distributed parameter systems - the filtering problems, Wiener filter, Kalman-Bucy filter, recursive formula for the optimal filter, innovation theory, duality between estimation and control, optimal filter for hyperbolic systems
- stochastic optimal control of distributed parameter systems
- formulation of the model, the stochastic optimal control problem, necessary and sufficient conditions for optimality, the separation principle
- identification of distributed parameter systems - the basic concept of system identification, modal approximation for identification, regularization. Part 2 Engineering Applications: formal approach to optimal filtering and control of distributed parameter systems - Wiener-Hopf theorem, the optimal filter, predictor and smoothing estimator, various approaches to linear estimation problems
- stochastic optimal control problems
- optimal sensor and actuator location problems - optimal sensor location problems, optimal actuator locations
- computational techniques for identification of distributed parameter systems - stochastic approximation, least squares identification, the Galerkin finite-element model, discrete regularization and minimization.
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