Research for Parameter Estimation of Distributed Parameter Systems

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1. Mathematical Models of Stochastic Distributed Parameter Systems and Their Mathematical Aspects: Mathematical models have been established for describing several physical systems of diffusions and/or distributions of temperature, pressure, etc. as well as systems having moving boundaries. And conditions of the existence of unique solutions were studied for the established models from the mathematical point of view, and then the modelling of the distributed parameter systems has been established.2. Establishment of Mathematical Formulation of Parameter Estimation Theory: Several methods of the parameter estimation have been established for estimating unknown parameters appearing in the mathematical system models and/or in their boundary conditions. The main ideas were the introduction of the minimum variance estimate and the maximum likelihood one, and, during this Co-operative Research, the theory of parameter estimation was extensively developed from the lumped parameter systems to … More the distributed parameter ones.3. Adjustment and Development of Parameter Estimation Algorithms: Although the numerical computation for the parameter estimation is so massive and complicated, in this research, by introducing the finite element method and the boundary element method, a great contribution was made for establishing the method of numerical computation of parameter estimation. Also the investigation of the computational accuracy which is the central issue when the infinite-dimensional systems are approximated by suitable finite-dimensional ones was performed and contributed in the development of numerical algorithms.4. Application of Parameter Estimation Algorithms to Real Systems: Algorithms developed in this research were applied and tested in the field of remote-sensing using the LANDSAT data, solar energy collection system, space technology, estimation of meteorological field, and so on.5. Conclusion: As shown in the research report attached to this format, this Co-operative Research has achieved a great success in the systematic study of parameter estimation for the distributed parameter systems. Less