The objective of this EArly-concept Grants for Exploratory Research (EAGER)research project is the control design for complex multi-input multi-output systems with very large state-space dimension, partially unknown state-space models, and in which the unknown part of the model, although identifiable in practice, requires a time-consuming or costly process to be estimated. This class of plants covers a large number of industrial and cyberphysical systems, from chemical processes to manufacturing systems to high-quality multi- machine xerographic reproduction systems, which constitute the main driving application and testbed for our work. For such systems in which precise model identification is possible but costly, the control engineer typically faces a trade-off between identification and closed-loop performance. Finding the appropriate ``critical parameters? to be identified for a particular regulation task and determining a ``good" identification/performance trade-off has traditionally been mostly a matter of experience and rules of thumb, and often occupies a significant portion of the practicing control engineer's time. This project proposes a new approach for developing practical techniques that can help the practitioner explore the identification/control performance trade-off. The key idea is to build on novel and fast ``compressed sensing" algorithms from the field of signal processing, and combine them with more traditional control design ideas.
This research will be conducted in close collaboration with scientists at Xerox Corporation?s Research Center in Webster (NY, which will ensure the relevance and practical applicability of the developed algorithms, and provide access to an actual xerographic printing testbed. This collaboration will also actively engage a graduate student. We expect the tools resulting from this research to be widely applicable in industrial control design contexts. Their dissemination will be facilitated by the organization of tutorial workshops at leading control conferences, and the initial development of an open-source software toolbox.
The general goal of this project was to assess the use of compressed sensing / nuclear norm-based optimization technique for identification and control of "easy-but-costly-to-model" processes. Two specific systems and application classes were treated as case studies to develop and validate the tools: (1) identification of a printer's tone reproduction curve's parameters (which is typically a measurement intensive task, and for which the approach was expected to reduce the required number of samples) and (2) blind source separation for low-cost human vitals identification and monitoring. While sampling-based techniques did not prove efficient at significantly reducing the burden of tone-reproducing curve identification and, as a result, did not readily transfer to industrial application, a new blind source separation algorithm was developed and validated, which significantly outperforms existing alternatives in situations where the sources are not statistically independent (the traditional assumption in the literature) but, instead, are assumed to each be the impulse response of low dimensional dynamical systems. This assumption is particularly relevant for bio-medical applications, where sources (typically a patient's vitals) are all typically correlated. In turn, the developed new blind source separation techniques may have an impact on low-cost webcam-based vitals and diagnostics technology for remote biomedical applications, and help provide partially automated healthcare to populations that are either physically isolated or for whom access to information technology is easier than to health services (e.g., in growing economies).
