New results on semi-explicit and almost explicit MPC algorithms

Abstract

Abstract New results on a particular type of state-dependent parameterization for model predictive control (MPC) are presented. Based on such parameterizations efficient MPC algorithms can be formulated, which combine the advantages of explicit and online optimization-based MPC. The new results comprise an offline stability check for the parameterizations to decide if a closed-loop MPC scheme applying the parameterizations is asymptotically stabilizing. Second, a novel way of computing the parameterizations with improved scalability in the state space dimension is included. Furthermore, new results and simplifications of almost explicit MPC schemes based on univariate parameterizations are contributed. The results are presented in a common framework and are illustrated in numerical examples including an almost explicit controller for an eight-dimensional spring-damper system.