A barrier function based continuous-time algorithm for linear model predictive control

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.