Stabilization of linear stochastic systems with a discount: Modeling and estimation of the long-term effects from the application of optimal control strategies

Abstract

The paper is devoted to the problem of stabilizing a linear stochastic control system. The quadratic cost functional measures the total loss caused by deviation from the fixed (target) levels and control trajectories, as well as a decision-maker’s time preferences expressed in the discount function. The long-term impacts of the use of decision-making, optimal on average, over an infinite-time horizon are taken as estimates of the deviation of the optimal trajectory from its target in the mean square sense and with the probability of 1.