AbstractsMathematics

Communication networks increase flexibility of industrial monitoring, supervisory and control systems. However, they introduce delays or even dropouts on the transmitted information that affect the performance and robustness on the decision and control mechanisms in the system. This thesis contributes theoretically to the state estimation and fault diagnosis problem over networks. First, we study the state estimation problem. Motivated by reducing the implementation computational load of Luenberger-type estimators, we focus on predefined gain approaches for different network transmission conditions. In general, we propose jump estimators whose gains are related to the different network-induced data reception scenarios. We define the estimator complexity in terms of the number of different stored gains. Considering constant successful transmission probabilities, our main contribution here is the design of jump linear estimators to attain favorable trade-offs between estimation performance and estimator complexity. We show that one can reduce the estimator complexity while guaranteeing a similar performance than the optimal Kalman Filter. When dropouts are governed by a non-stationary stochastic process, the successful transmission probability is time-varying and may be unknown. For this case, we propose an estimator whose gains are scheduled in real-time with rational functions of the estimated packet arrival rate. We turn the design procedure into an optimization problem over polynomials that is numerically solved employing sum-of-squares (SOS) decomposition techniques. Second, motivated by reducing the network resource consumption without considerably degrading the estimation performance, we study the jointly design of jump linear estimators and predefined network operation conditions (co-design) to guarantee a favorable trade-off. Focusing on wireless networks with self-powered nodes, where transmitting is the most energy consuming task, we analyze two approaches for the network operation: event-based transmissions and power control. For the event-based approach, we use a Send-on-Delta protocol which reduces the number of transmissions with respect to transmitting at each sampling instant. However, it leads to an unknown successful transmission probability. For this framework, we contribute by characterizing this uncertainty and including it on the stochastic behavior of the estimator by means of a SOS-based design. Power control strategies are developed over a multi-hop wireless network with fading channels. Instead of reducing the number of transmission, power control acts directly on the transmission power. Higher transmission powers imply higher successful transmission probability values. Finally, motivated by the need of assuring a reliable operation of the networked system, we study the fault diagnosis problem. We explore and point out the trade-offs between fast fault detection and fault tracking conditions. We design jump estimatorbased fault diagnosers in which we can specify the minimum…