Optimal Stochastic SD Control With Preview

The problem of H₂-optimal sampled-data (SD) preview control is considered. It is assumed that a stochastic reference signal corrupted with additive colored noise acts upon the system so that future values of this input are known within a preview window tau . A rigorous frequency-domain solution of the problem is given for SISO SD systems on the basis of the parametric transfer function concept. Numerator and denominator degrees of the optimal controller are calculated explicitly on the basis of initial data. The dependence of the optimal cost function on tau is investigated and the limiting value as tau rarr infin is found. Moreover, it is shown that this limit depends on the relation between tau and the sampling period.