Control under energy and time constraints

The performance of a control system is often limited by constraints on timing, bandwidth, and energy. This dissertation explores the trade-offs between constraints on these resources, the control system performance, and the system to be controlled.We begin by considering a networked control system in which the sensor sends its measurements to the controller over a limited-bandwidth communications channel. We explore the observation that the absence of communication nevertheless conveys information --- i.e., nothing communication-worthy occurred. This suggests that energy (or other resources consumed by communication) could be saved using the timing of messages to transmit information, rather than the normal practice of transmitting data in the messages themselves. We develop a framework to explore this idea and derive a condition for the existence of a stabilizing controller that captures the trade-off between bandwidth, resource consumption, and the unstable eigenvalues of the linear system to be controlled. A surprising result is that if this condition is satisfied, then one may design a stabilizing controller that consumes resources at an arbitrarily small rate, provided one has access to a sufficiently precise clock. In an extreme example, a large amount of data is encoded into the precise transmission time of a single bit, and the receiver decodes this data from the time the bit is received. This result quantifies the trade-off between bandwidth and time as resources for transmitting information.Next, we use our framework to analyze a family of event-based controllers. We show that these controllers can stabilize a system while consuming resources at a rate that is within 2.5 times the theoretically-minimum rate. These event-based controllers are intuitive and easy to implement, and our stability condition quantifies the cost (in additional required communication resources) that a control engineer pays for the convenience of implementing an event-based controller instead of the relatively more complicated controllers from the first section that use the theoretically-minimum communication rate.A takeaway from these results is that networked and distributed control systems can benefit from precise timing. However, even non-networked systems can benefit from precise timing. We explore this by developing a control architecture that allows a controller running on a non-real-time operating system to run with a high degree of determinacy, even when the OS task scheduler suspends the control task. The architecture employs a small microprocessor to be used as a "real-time processor" that runs independently from the OS and buffers sensor measurement and actuator commands. We implement this on a Beaglebone Black single-board computer and demonstrate that this architecture can significantly improve a controller's performance in the presence of OS preemption