Distributed Model Predictive Control with Linear Gain and Mixed Performances for Positive Systems*

This paper proposes a distributed model predictive control design approach to positive systems with disturbances. Using decomposition technique, a positive system are transformed into a distributed system consisting of positive subsystems. Polytopic uncertainty and norm-bounded disturbance are imposed on the considered systems. Different from tradition quadratic performance indexes, the performance index of distributed model predictive control of positive systems is defined via a linear form called linear gain performance. Using linear copositive Lyapunov functions, a control framework for the distributed model predictive controller of constrained positive systems is established. Thus, the required linear gain performance is satisfied under the proposed controller. Furthermore, a mixed performance index is introduced for positive systems. A distributed model predictive controller is designed to obtain the mixed performance index. The corresponding distributed model predictive control algorithms are given by virtue of some linear programming conditions. Finally, an simulation example is given to verify the presented design.