Suboptimal control of linear discrete stochastic systems with linear input constraints

Optimal control of linear discrete stochastic systems with linear input constraints is considered. A lower bound on the achievable minimum of the loss function is given. A suboptimal control strategy is derived by using a truncated Taylor series to approximate the expected future loss in the Bellman equation. The performance of the suboptimal controller is studied using Monte Carlo simulation and the obtained loss is compared with the lower bound.