The research objective of this award is to create a unified control-theoretic framework and develop computationally tractable methods for optimal control and sensorless manipulation of complex ensemble systems. Many practical engineering and biomedical applications involve controlling large ensembles of structurally similar dynamical systems by the use of a common control input. Constructing robust external inputs that steer an ensemble of systems to form a desired dynamical condition, such as synchrony, is of fundamental importance. The research will result in methods that are general enough to apply across disciplines and can be exploited in diverse applications ranging from quantum physics to neuroscience. The research approach progresses from a fundamental investigation of controllability of ensemble systems based on geometric control techniques to the development of an efficient optimization-free computational method for optimal ensemble control synthesis. Deliverables include distributed computational routines for optimal ensemble control design, experimental demonstration and validation of the designed controls, documentation of research results, engineering student education, and engineering research experiences for pre-service teachers.
If successful, the results of this research will substantially advance our understanding of complex ensemble systems and directly contribute to new developments in control and systems theory. It will also broaden seminal applications by enabling analytically and numerically tractable methods for optimal control designs in atom cooling, deep brain stimulation for Parkinson's disease, and electrochemistry. This achievement has great potential to make significant impacts on the advancement of quantum science and technology, network sciences, biology, and neuroscience. Undergraduate and graduate engineering students and pre-service teachers will benefit through classroom instruction and involvement in multidisciplinary research, in particular gaining interactions with experimentalists. General public and pre-college K-12 students will also be engaged through, for example, Science Outreach Programs at Washington University.
