Finite-Dimensional Observation and Control of Ensembles of Linear Systems

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Ensemble control is an emerging field of mathematical systems and control theory that refers to the task of controlling a large, potentially infinite, number of states, or systems, using a single input function or a single feedback controller. A prototype of an ensemble is determined by a parameter dependent family of systems and initial states which has to be controlled by a single input or feedback controller. Applications of ensemble control arise in, e.g., quantum control, systems biology, sensor networks and robotics, where control actions and measurements are performed in a distributed way. Classical methods from robust control do not suffice to study ensembles of systems and a new theory is needed. Except for few rudimentary contributions, no rigorous control theory of ensembles exists so far. The ensemble control problem area presents a new connection between control theory, complex analysis and approximation theory. We propose to establish fundamental concepts and tools for a system theoretic analysis of linear parametric ensembles. Thus we aim at a comprehensive structure theory for parameter dependent linear systems, by addressing the fundamental tasks of controllability and observability, constructive ensemble control and state estimation for ensembles.