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Reducing conservativeness in predictive control of constrained systems with disturbances

Predictive controllers which are able to guarantee constraint fulfilment in the presence of input disturbances, typically based on min-max formulations, often suffer excessive conservativeness. One of the main reasons for this is that the control action is based on the open-loop prediction of the evolution of the system, because the uncertainty due to the disturbance grows as time proceeds on the prediction horizon. On the other hand, such an effect can be moderated by adopting a closed-loop prediction. In this paper, closed-loop prediction is achieved by including a free feedback matrix gain in the set of optimization variables. This allows one to balance computational burden and reduction of conservativeness.