Robust model predictive control for nonlinear parameter varying systems without computational delay

Abstract

SummaryThis article proposes a one‐step ahead robust model predictive control (MPC) for discrete‐time Lipschitz nonlinear parameter varying (NLPV) systems subject to disturbances. Within the proposed design framework, the optimization that generates the MPC policy to be implemented at next time instant is executed in advance during the current sampling period based on future state prediction. This new feature allows avoidance of the online computational delay existing in the traditional MPC settings and improves the control performance. The proposed MPC is proved to be recursively feasible with the guarantee for robust closed‐loop system stability and satisfaction of input and output constraints. A tractable linear matrix inequality (LMI) optimization problem is formulated to compute the control gains at each time instant. The computational complexity of the obtained LMI problem is also analyzed. The one‐step ahead robust MPC is further developed to cover discrete‐time Lipschitz NLPV systems with disturbance compensation. Efficacy and performance improvement of the design are demonstrated through a numerical example and an application to adaptive cooperative cruise control for automated vehicles under variable road geometry.