Parameter-dependent Lyapunov function based model predictive control for positive systems and its application in urban water management

This paper is concerned with model predictive control of positive systems with polytope uncertainty. A parameter-dependent Lyapunov function is constructed for such systems and by employing the Lyapunov function, a new and less conservative model predictive control approach is presented. The new approach employs a linear framework in the performance index, the Lyapunov function, and the present conditions whereas the classic model predictive control always uses the quadratic form in those ones. The advantages of the proposed approach lie in the fact that: (i) it is more suitable for positive systems since the essential property of the systems is sufficiently considered, and (ii) the present model predictive control algorithm is easily implemented whether for off-line or on-line. A practical example is provided to illustrate the effectiveness of the proposed model predictive control design.