Distributed Parameter Systems: Theory and Applications

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.