Optimal minmax filtering and control in discontinuous Volterra systems

This paper presents solutions of the optimal minmax filtering problem for integral Volterra systems with deterministic uncertainties over discontinuous observations and the optimal linear-quadratic control problem for deterministic integral Volterra systems with discontinuous states. The equation for the optimal estimate in the filtering problem and the equation for the optimal gain matrix in both cases are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the duality principle for integral systems. The technical example illustrating application of the obtained results is finally given.