Towards a separation principle in closed-loop predictive control

In closed-loop MPC a feedforward signal and a feedback law are optimized simultaneously over a finite time horizon. This solution can be implemented without any reoptimization yet, reoptimization using recent measurements could improve the cost to go for the remainder of the horizon. In this paper, we explore the possibility to separate this reoptimization problem into an estimation problem and a prediction problem. We propose to solve the new prediction problem with an updated state-estimate with corresponding error-covariance matrix and to apply an offset on the future control moves depending on the control law from the past.