The Separation Principle for Stochastic Evolution Equations

The separation principle is proved for a general class of linear infinite dimensional systems. The dynamical system is modeled as an abstract evolution equation, which includes linear ordinary equations, classes of linear partial differential equations and linear delay equations. The noise process in the, control system is modeled using a stochastic integral with respect to a class of Hilbert space valued Gaussian stochastic processes, which includes the Wiener process as a special case. The observation process is finite dimensional and is corrupted by Gaussian type white noise, which is modeled using the Wiener integral. The cost functional to be minimized is quadratic.