Gaussian sum approximation for non-linear fixed-point prediction

Fixed-point prediction is the estimation of the state of a system at a future fixed time based on a noisy measurement with sequence length that increases with current time. A recursive algorithm for generating fixed-point prediction is given using the integrated form of the chain rule. For non-linear systems no general filter solution exists ; thus a gaussian sum approximation is developed. The method provides a numerical approximation for the time-dependant a posteriori density from which a filter can be generated.     

Optimization of weakly coupled subsystems by a two-level method

A two-level method to find the optimal control of a linear system is presented. We consider that the system is composed of coupled subsystems. And we solve two decoupled first-level problems and one coordinating second-level problem iteratively. When the system can be decoupled into weakly coupled subsystems, the solution fast converges to the optimal.