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Continuous-time linear MPC algorithms based on relaxed logarithmic barrier functions

Abstract In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. In particular, barrier function based continuous-time algorithms are considered, in which the control input is obtained as the sampled output of a continuous-time dynamical system. We present suitable barrier function relaxations as well as results on closed-loop stability and the satisfaction of state and input constraints. The results also apply to conventional barrier function based model predictive control schemes.