Constrained model predictive control for positive systems

This article is devoted to the problem of model predictive control (MPC) design for discrete-time and continuous-time positive systems with state and input constraints. The proposed controllers are so designed that the closed-loop constrained systems are positive and stable, meanwhile, linear infinite horizon cost functions through their upper bounds are minimised. In the discrete-time case, the performance of the control system compared to existing studies is remarkably improved. Moreover, in the continuous-time case, the proposed MPC is such that can be directly applied to the continuous-time positive system without discretisation. The merit of this method is that the sampling interval has nothing to do with the stability of the system, just a shorter sampling period results in better optimality and performance. In addition, by defining a slack variable and accounting it in the minimisation problems, a fast rate of convergence will be obtained. In order to solve the optimisation problem of MPC, linear programming (LP) is used which needs to be solved at each iteration. All conditions are derived in the form of LP. Finally, to demonstrate the effectiveness of the proposed method, comparisons with the existing studies are presented through practical and numerical examples.