Stability Under Finite-Rate Feedback

Sridevi Sarma is a potential faculty candidate in Mechanical Engineering.

Due to our information rich world, new applications, opportunities and challenges in control have emerged that remain largely untapped. One new area includes control in distributed, asynchronous, and networked environments, where computational components are connected via communication links. Communication links have rate limitations, cause delays, and are noisy, and their interactions with computational components cannot be ignored. Thus, a revolution in this area would be to generate a unifying theory for communication, computing, and control. The impact of such a theory would, for example, improve performance in automobiles, smart homes, large manufacturing systems, intelligent highways and networked city services. In addition, such a unified theory would provide valuable insight and enable powerful modeling of biological systems.

At the core of every network system there is a simple feedback loop that consists of a plant, a communication link and a controller. Over the past decade much effort has been devoted to analyzing a core system, in which a plant and feedback controller are separated by a noiseless finite-rate communication channel. Previous work derive conditions on the channel rate that guarantee some notion of asymptotic stability or input-output stability, when the encoder has memory, and more importantly, either has access to the control input or can compute it perfectly. We review these important results, and then consider a scenario in which the encoder does not have access to (and cannot compute) any signal in the system except for the plant output.