Optimal Feedback Control Laws Using Random Sampling of the Observation

摘要

It is assumed that a control object is described by the system of nonlinear stochastic equations dx = f(x) + v(z)dt + sigma(x)dW, t O, x, z epsilon R sub n, where W is a vector of independent standard Wiener processes and v is the control vector. It is further assumed that the process Z is observed, described by dz(i)=x(i)dN(i) + gamma (i) (x)dB(i), 1,...,n, x,z epsilon R sup n, where B = col. B (1), ...B(n) is a vector of independent standard Wiener processes and N = col. N(1), ...,N(n) is a vector of doubly stochastic Poisson processes with intensity (lambda (1) Z (t), ..., lambda (n) Z (sub t), t or equals O. It is shown how the process N can be constructed, and for a given sampling process N, sufficient conditions are derived on optimal controls. In addition, the problem is dealt with in selecting an optimal sampling process N for a given admissible control law.