Computational Methods in Laser Molecular Control and Parameter Estimation

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The investigator will spend a year at the Center for Control Engineering and Computation (CCEC) of the University of California at Santa Barbara. This will allow him to obtain a sound foundation in the fields of control systems and signal processing and apply this knowledge in his subsequent research. The proposed work emphasizes the positive interactions between mathematics and engineering, and between theory and application. The investigator will initiate and collaborate on interdisciplinary research projects with members of the CCEC. In particular, he will work with Professor Dahleh, the research director at the CCEC, in the area of control of molecular systems. Based on the quantum models of the molecular systems they seek to answer the question of whether a certain chemical reaction rate is possible, and if so what sort of control input is needed. This work will involve the determination of efficient computational algorithms for the assessment of controllability of realistic molecular systems. Along with Professor Chandrasekaran, also a member of the CCEC, the investigator will also develop fast and efficient algorithms for estimation and filtering problems. A critical issue in estimation concerns the uncertainty model used. If the uncertainty model does not give an accurate representation of the true uncertainty in the problem but rather overbounds it, then it will lead to overly conservative results with poor performance. The investigator and Professor Chandrasekaran will explicitly include structured data uncertainties into least-squares type estimation problems. Examples of structured uncertainties are displacement-structured (Toeplitz, Hankel and etc.) and block-structured uncertainties. Displacement structures arise where there are LTI (linear time-invariant) systems. Block structures are more common and will occur when there are sub-systems. The investigator will apply the newly acquired expertise in engineering and applied mathematics to supervise interdisciplinary senior projects for both mathematics and engineering majors and to better integrate mathematics into the engineering curriculum. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).