Stochastic control with continuously variable observation costs for a class of discrete nonlinear systems

The discrete stochastic linear servomechanism problem is reformulated to include the costs of observations. The optimal control solution to this modified problem is identical to that of the standard servomechanism problem, but the optimal observations policy requires the solution of a TPBVP which may be computed a priori. The problem is further extended to include the class of nonlinear systems suggested by dynamic populations. The solution presented for the nonlinear problem is an iterative solution involving the second-order conditional-mean estimation and prediction algorithms and the linear control algorithms which are applied about the linearized predicted trajectories. A nonlinear example problem is included.