Markov chain model of fault-tolerant wireless networked control systems

Wireless networked control systems (WNCS) are composed of spatially distributed sensors, actuators, and controllers communicating through wireless networks instead of conventional point-to-point wired connections. While WNCSs have a tremendous potential to improve the efficiency of many critical control systems, for instance, in building automation and process control, the systems are fundamentally constrained by the packet losses and the functional faults of the underlying wireless sensor and actuator networks. Understanding the interaction between wireless networks and control systems is essential to characterize the performance limitations of the critical control systems and optimize its wireless network resources. This paper presents an analytical framework for modeling the behavior of the control loop over lossy and faulty network. The control loop over wireless networks is modeled through a Markov chain taking into account sensing links, actuating links, and recovery mechanism to compensate the faulty nodes. By using this model, the novel performance metrics are mathematically derived and are evaluated through both theoretical analysis and simulation results. The performance evaluation shows the critical tradeoff between the average performance when the control loop is in the normal operation mode and the recovery performance when it is in the abnormal operating mode due to the faulty nodes.