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In this paper, we present a novel linear model predictive control (MPC) scheme that relies on a continuous-time, barrier function based algorithm which asymptotically tracks the solution of a time-varying open-loop optimal control problem. In particular, the control input is obtained as the sampled output of a continuous-time dynamical system and no iterative optimization algorithm is needed in the on-line implementation. In addition, we present a new approach towards stabilizing MPC based on gradient recentered logarithmic barrier functions that allows enlargement of the employed terminal set.
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Feller et al. (2013) studied this question.