Filtering in nonlinear time delay systems

Linear and nonlinear (extended Kalman-Bucy) filters are derived for systems governed by coupled partial and integro-differential equations. The framework used is sufficiently general that filters for 1) lumped parameter systems having multiple time varying or constant time delays, 2) coupled lumped and hyperbolic distributed parameter systems, and 3) lumped parameter systems with functional time delays, evolve as special cases. Although the filtering equations are the final result, the corresponding smoothing equations are developed as well. The performance of the filter is illustrated through application to a well stirred chemical reactor with external heat exchange.