Interference Management for Stabilization of Dynamical Systems over Wireless Channels

Abstract: In networked control systems, dynamical systems are stabilized by actions of remotely placed controllers. This involves communication between plants and controllers over wireless channel(s). The communication channel(s) are subjected to interfering signals, caused by some external radio devices in the neighborhood or by the other wireless components within the same networked control system. Interference in the communication channel is a major problem which drastically affects performance of the dynamical systems that are to be controlled over the wireless channels. This thesis in particular focuses on such a problem; it aims to improve stabilizability of linear systems by managing interference in the wireless channels. We propose an idea of using dedicated sensor nodes in a networked control system whose sole purpose is to manage interferences. Such a dedicated sensor node is termed as a relay node in this thesis, as it relays its received information to the other components in networked control system. We assume first order linear time invariant plants with arbitrary distributed initial state and model all the communication links as white Gaussian channels. We study two related setups. In the first setup, we study the remote stabilization of a first order linear plant over a wireless channel in which the communication between the plant’s sensor (state encoder) and controller is disturbed by an independent interference signal. The relay node observes this interference information and sends it to the state encoder and the controller, which then utilize this information to mitigate interference. In the second setup, we consider two separate plants that communicate with two separate controllers using a shared spectrum. Due to the common communication medium, the signals transmitted by the state encoders of the two plants interfere with each other. In this setup, the relay node observes the signals transmitted by the encoders of both plants. It then assists by communicating its observations to the two controllers. The fundamental difference between the two setups is that in the former, the interference is independent of the signal transmitted by the encoder, whereas in the later, the interference becomes correlated with the signals transmitted by the encoders of the two plants. In both setups, we use delay-free linear sensing and control schemes. By employing these schemes, we derive sufficient conditions for mean square stability. We show that the achievable stability region significantly enlarges with the relay assisted interference cancelation schemes.