A linear framework on the distributed model predictive control of positive systems

Abstract

This paper investigates the distributed model predictive control (DMPC) for positive systems with interval and polytopic uncertainties, respectively. Different from the traditional quadratic DMPC, a new linear DMPC framework is established for positive systems. First, a linear cooperative cost function (performance index function) is introduced for the DMPC of positive systems. Accordingly, some linear constraint conditions are imposed on the systems. Then, a linear co-positive Lyapunov function is constructed. Using the linear Lyapunov function, the DMPC controllers are designed for interval positive systems and polytopic positive systems, respectively. The controller of each subsystem contains not only the state information of the subsystem but also the state information of other correlated subsystems. Linear programming based optimization algorithm is addressed to compute the controller parameters. To guarantee the feasibility and stability of the systems, a cone invariant set is proposed. Finally, two case studies are provided to illustrate the effectiveness of the theoretical findings.