Adaptive robust model predictive control of nonlinear systems using tubes based on interval inclusions

Abstract

This article considers the adaptive robust constrained regulation problem for a class of nonlinear plants with bounded additive disturbances. The nonlinear dynamics of the plant are approximated as an uncertain Quasi-Linear Parameter Varying (Q-LPV) system in which the time varying parameter consist of an on-line adaptation of weights of multiple linear models. The overall multiple model representation consists of a convex combination of the individual models. The uncertainty bounds on the Q-LPV system are “designed” to include the plant-model mismatch in addition to the disturbance bounds. In particular, these uncertainty bounds are computed based on inclusion functions obtained using Bernstein polynomial and interval based bounding. The resulting robust regulation problem of the nonlinear plant is posed as Robust Tube Based Model Predictive Control (RTBMPC) of the uncertain Q-LPV system with “designed” uncertainty bounds. The proposed control strategy is demonstrated for robust regulation of Van de Vusse reactor, a significantly nonlinear system.