Nonlinear filtering and control of Stochastic descriptor systems with applications to PDAES

By means of Riccati transformation we recently have generalized the Kalman-Bucy filter, LQG, and H_\infty filter and control to stochastic descriptor systems in continuous-time. The so-called direct discretization method for optimal control problems is applied to constrained multi-body systems. Derivations, structural issues, and numerical results are sketched. We point out directions for future research and a descriptor systems approach to filtering and control of the Navier-Stokes equation.