Closing the loop around sensor networks: Optimal estimation and control of networked systems

The following dissertation explores issues related to the modeling and analysis of control systems over Wireless Sensor Networks (WSNs).;Recent technological advances in electronic components design, radio technology and networking have given rise to a new class of systems, composed of networked embedded subsystems.;Coordination between such systems can improve the performance of existing applications as well as pave the road to the conception of new ones. Inventory monitoring and control, home and building automation, precision agriculture, power generation, SCADA and security systems, drive by-wireless automotive systems can all benefit from the use of a network connecting its components, by reducing cost and improving performance.;This flexibility comes at the cost of complexity. In particular, when dealing with control applications, the design issues are exacerbated by the effect that communication delays and loss of information have on the closed loop performance. Classical control theory assumes that delays are bounded and information is never lost. Therefore, control systems designed upon this assumption are bound to fail in this context.;This dissertation provides some key results towards the understanding of systems-theoretic implications of using unreliable networks for estimation and control.;It starts by addressing the discrete-time Kalman filtering problem, modeling the arrival of the observation as a random process. The statistical convergence properties of the estimation error covariance is studied, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. Also upper and lower bounds on the expected state error covariance are provided.;For the control problem two classes of communication protocols are considered. Packet networks communication channels typically use one of two kinds of protocols: Transmission Control (TCP) or User Datagram (UDP). In the first case there is acknowledgment of received packets, while in the second case no confirmation feedback is provided on the communication link.;The effect of data losses, due to the unreliability of the network links under these two protocols, is analyzed. The Linear Quadratic Gaussian (LQG) optimal control problem is generalized, by modeling the arrival of both observations and control packets as random processes whose parameters are related to the characteristics of the communication channel. Accordingly, two independent Bernoulli processes are used to model packet losses between the sensors and the estimation-control unit, and between the latter and the actuation points. It is shown that for protocols where successful transmissions of packets are acknowledged at the receiver (e.g. TCP-like protocols), the separation principle holds. For these protocols, the optimal LQG control is a linear function of the estimated state. Further, there exists a critical probability for the successful delivery of packets, below which the optimal controller fails to stabilize the system. In stark contrast, it is shown that when there is no acknowledgment of successful delivery of control packets (e.g. UDP-like protocols), the LQG optimal controller is in general nonlinear.