Optimal discrete-time control system with cost for observation

The problem of how to select the total number and the spacings of the observations optimally when a constant cost is incurred for each observation taken is discussed. Approximate expressions for the criterion function with a fixed number of observations are obtained and are used to determine the optimal total number of observations. For a class of multidimensional systems with a dominant eigenvalue, the problem is shown to reduce to that for scalar systems. Detailed discussion is then carded out for scalar systems including some sensitivity study.