Switching Control with Minimal Data

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This grant will allow breaking new ground in our understanding of the minimal amount of data required for solving control problems. For a given control objective, a modern control designer is faced not just with the task of developing a control algorithm, but also with deciding whether the objective is achievable with the available data, or with the question of what is the smallest amount of data with which the task is achievable by proper control design. By employing modern system-theoretic tools, centered around the notion of entropy for dynamical systems as well as methods for characterizing robustness of system response to perturbations, the project will develop systematic approaches to control design in the presence of data-rate constraints. The results are expected to have significant impact on several application domains, including population dynamics, control of mechanical systems, and synchronization of networks of electrical or mechanical systems. The project also includes components for integrating the research with personnel training and educational activities. The overarching goal of the project is to gain insight into the challenge of characterizing the minimal data with which a control task is achievable, and to translate this insight into synergistic methods for designing communication and control schemes. In advanced control problems of interest in modern theory and applications, one frequently encounters switching behavior in either the process dynamics, or in the controller dynamics, or in the control task itself. Switching dynamics present significant challenges, which the project plans to overcome by deploying novel generalizations and combinations of topological entropy and input-to-state robustness concepts. The project will initially focus on three benchmark classes of control problems: 1) control of switched systems; 2) control of nonholonomic mechanical systems; and 3) robust leader--follower synchronization. Building from specific case studies within each of these problem classes, the project aims to achieve a general methodology for designing switching controllers for complex systems which utilize available data in optimal or near-optimal fashion.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.