Scalable Control of Positive Systems

Classical control theory does not scale well for large systems such as power networks, traffic networks and chemical reaction networks. However, many such applications in science and engineering can be efficiently modeled using the concept of positive systems and the nonlinear counterpart monotone systems. It is therefore of great interest to see how such models can be used for control. This paper demonstrates how positive systems can be exploited for analysis and design of large-scale control systems. Methods for synthesis of distributed controllers are developed based on linear Lyapunov functions and storage functions instead of quadratic ones. The main results are extended to frequency domain input–output models using the notion of positively dominated system. Applications to transportation networks and vehicle formations are provided.