Tradeoffs between quality-of-control and quality-of-service in large-scale nonlinear networked control systems

In this paper we study input-to-state stability (ISS) of large-scale networked control systems (NCSs) in which sensors, controllers and actuators are connected via multiple (local) communication networks which operate asynchronously and independently of each other. We model the large-scale NCS as an interconnection of hybrid subsystems, and establish rather natural conditions which guarantee that all subsystems are ISS, and have an associated ISS Lyapunov function. An ISS Lyapunov function for the overall system is constructed based on the ISS Lyapunov functions of the subsystems and the interconnection gains. The control performance, or “quality-of-control”, of the overall system is then viewed in terms of the convergence rate and ISS gain of the associated ISS Lyapunov function. Additionally, the “quality-of-service” of the communication networks is viewed in terms of the maximum allowable transmission interval (MATI) and the maximum allowable delay (MAD) of the network, and we show that the allowable quality-of-service of the communication networks is constrained by the required ISS gains and convergence rate of the hybrid subsystem corresponding to that network. Our results show that the quality-of-control of the overall system can be improved (or degraded) by improving (or relaxing) the quality-of-service of the communication networks. Alternatively, when relaxing the quality-of-service of one communication network, we can retain the quality-of-control of the overall system by improving the quality-of-service of one or more of the other communication networks. Our general framework will formally show these intuitive and insightful tradeoffs.