Constructions of Lyapunov functions for large-scale networked control systems with packet-based communication

Abstract

In this tutorial presentation we focus on the construction of Lyapunov or storage functions for 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. Within each packet-based communication network only one node can communicate at a given transmission time (requiring communication protocols) and the transmission intervals and delays may vary over time. These artefacts cause network-induced communication errors in the overal closed-loop system and can be detrimental for stability and performance. For these NCSs we provide explicit constructions of Lyapunov functions by modelling the large-scale NCS as an interconnection of a finite or even an infinite number of hybrid subsystems, and combining ‘local’ Lyapunov functions for the controlled dynamics (including network-induced errors) and the protocols in a systematic manner. These constructions lead to the numerical computation of maximum allowable transmission intervals (MATIs) and maximum allowable delays (MADs) for each of the individual networks. The availability of the Lyapunov or storage functions guarantee properties such as global asymptotic or exponential stability, input-to-state stability (ISS) and L p -stability for the large-scale NCS. Interestingly, the control performance expressed in terms of ISS and L p -gains can be traded with the network parameters (MATIs and MADs). Hence, tradeoffs can be made between the quality-of-control of the overal hybrid system and the required quality-of-service of the underlying communication infrastructure. Also event-triggered communication schemes will be shortly discussed. The results are illustrated with an example of vehicle platooning.