Optimal feedback control laws using random sampling of the observation

Abstract

Abstract It is assumed that a control object is described by the system of non-linear stochastic equations dx= [f(x) + v(z)] dt+ σ(x) dW, t>0, x, zεRn, where Wis a vector of independent standard Wiener processes and vis the control vector. It is further assumed that the process Zis observed, described by dzt = xt dNt + yt (x) dB t i= 1,[tdot] n, x, zεFt n i, where B= col (B1 [tdot], Bn ) is a vector of independent standard Wiener processes and N= col (N1 [tdot], Nn ) is a vector of doubly stochastic Poisson processes with intensity process {(λ1(Zt ), [tdot], λ n (Zt <)), t 0}. It is then shown how the process Ncan be constructed, and for a given sampling process N, sufficient conditions are derived on optimal controls. In addition, the problem is dealt with of selecting an optimal sampling process Nfor a given admissible control law.