Robust and efficient feedback coding for communication based control: Operating under data-rate constraints

As the domain of applications of digital control systems expands, it has become important to understand the relationship between the feedback communication rate and the stability/performance of control systems. In applications such as wirelessly networked autonomous robots, embedded systems, MEMS (micro-electro-mechanical-system) device arrays, sensor networks, etc., the time constants of the underlying dynamics can be at the limit of what control electronics can accommodate. Correspondingly, there is a growing body of literature on communication constrained control systems. In this document, we discuss the design issues of such control systems in three parts: control of linear plants, control of nonlinear plants, and control with decentralized feedback communication.; Building on the basic ideas of the Data-Rate Theorem---which has been developed and become well-known in recent years---our research has gone on to explore the code-based control of linear systems that are robust and efficient in the presence of feedback communication capacity constraints and uncertain communication timing. First, in terms of a scalar linear system, we show that 1-bit control (the control action alphabet contains only two admissible actions during each control cycle) produces more robust system response than control strategies with larger alphabets but correspondingly less frequent updates. Then, we extend the desirable features of the 1-bit control to multidimensional linear systems by introducing a set of novel control design and coding techniques.; The data-rate problem for control of nonlinear plants is very rich. The time constants of nonlinear plants may not be easily related directly to system parameters and may strongly depend on where in the state space the system operates. We will first discuss such issues in the context of a broad class of nonlinear systems, then focus this discussion on the specific problem of maintaining an autonomous vehicle traveling in a prescribed lane.; Finally, the study will be extended to systems with decentralized feedback control implementations. We have observed that decentralization may magnify the uncertainty and degrade the performance in the presence of noise and mismatched timing among sensors. We will suggest solutions in terms of coding designs.