Information-Theoretic Improvement of Model Predictive Control

An information-theoretic improvement of the stochastic Model Predictive Control has been proposed and examined. First, it was observed that optimal feedback must, if possible, actively generate information about the system state. Since standard MPC algorithm does not do this, it was hypothesized that adding a penalty for information deficit to the standard MPC cost function can generate a control strategy closer to the optimal one. An exact formula for the cost has been derived for a class of linear systems with control-dependent matrices. Then, it was shown on the basis of simple, two dimensional, example that the proposed modification generates significantly better strategy, for which the cost functional is more than five times smaller compared to the standard MPC algorithm.