Optimal stopping for updating controls
Year: 2009
Type: conference-paper
Abstract: We study a problem of sampled-data control for an Ito diffusion process. In particular, we allow the sampling of the state process to be event-triggered and place a bound on the sampling rate. Such limits arise in Networked control systems where, the sensors, the controller and the actuators may be connected to each other over data networks. Although these networked control loops suffer from degraded communication, they offer several cost savings and the advantages of fast installation, easy maintenance, deployment in mobile environments etc. (see [1] for an overview). In practical situations such as in wireless industrial control, frequently, it is the link from sensors to controllers that have restricted rates. Consider such a loop consisting of three components: the plant, a sensor and a controller (see fig. 1(a)). The link from the sensor to the controller is over a data network and so, its communication rate is limited. The other links in the loop have no such limits and can be considered ideal. Assume that the sensor obtains perfect and continuous measurements of the state process. Because of the rate limit, continuous transmission of the sensor observations to the controller is impossible; only a sampled version of the observations can be forwarded to the controller. The control process is hence generated with some compressed information about the state process. It is generated based on the timed sequence of samples received, and, is forced to be piecewise deterministic. The traditional solution is to sample sensor observations periodically choosing a sampling rate equalling the average communication rate permitted by the channel. Here, we pursue the more efficient strategy of letting the sensor choose sampling times to be stopping times w.r.t. its observations. The rate of arrival of the stopping times then should be no greater than the rate permitted by the channel. This pursuit boils down to designing two elements namely, an Event detector at the sensor end which applies a set of stopping rules to generate samples, and, a Control generator inside the controller node which produces piece-wise deterministic waveforms derived from the sequence of received samples. In mathematical terms, we get a sequential decision problem for a two person team where, the control signal, and, sampling times are decision variables. Moreover, this decision problem has a non-standard information pattern with the control values and the stopping times being chosen based on different information.
Authors: Maben Rabi, Karl Henrik Johansson
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W618603157