Minmax filtering in Volterra systems

Examines the minmax filtering problem for linear integral Volterra systems with deterministic uncertainties over observations given by either a differential equation or an integral Volterra equation as well. The solution is based on the Pontryagin minimum (maximum) principle, the Lagrange multipliers method, and the duality principle in Volterra systems. First, the optimal control (regulator) problem is solved and the Riccati equation for the optimal gain matrix is obtained for integral Volterra systems, and, second, the minmax filtering equation for the optimal estimate of a Volterra system state and the Riccati equation for its ellipsoid matrix are obtained over both differential and integral observations. Thus, in the case of deterministic uncertainties, it is possible to form a closed system of the minmax filtering equations for an integral system state over integral observations, using only two filtering variables, the optimal estimate and its ellipsoid matrix, although the analogous result cannot be reached in stochastic systems.