Distributed event-triggered scheduling of wireless networked control systems

Computer control systems are commonly designed in such way that observations are sampled equidistantly in time (time-triggered sampling). Networked control systems (NCS) are a special class of computer controlled systems, where sensors, controllers and actuators are spatially distributed and are only able to exchange information over a digital communication network. Due to the fact that these communicating devices are sharing a common medium, one of the major concerns of NCS is to minimize communication load, while preserving a certain level of control performance. It has been shown in [2] for multi-loop NCS that event-triggered sampling can be much more efficient than time-triggered sampling schemes in terms of resource usage of the communication system. While this approach presumes reliable communication systems, the focus of this work is to consider event-triggered scheduling schemes in unreliable communication networks. In [2], packet collisions in CSMA (carrier sense multiple access) protocols are resolved through arbitration mechanisms. If multiple senders access the shared medium at the same time, one sender will be elected to transmit information to its destination. In the absence of a global coordinator, arbitration mechanisms are hard to sustain in wireless communication networks [4]. We therefore consider in the following multi-loop NCS in CSMA communication networks without an arbitration mechanism, i.e. in case of multiple access to the medium at the same time collision occurs and all packets are lost. The NCS is given by N control loops which are closed over a common communication network. Each process i to be controlled is given by a stochastic linear discrete-time scalar system