Mathematical Sciences: Geometric Methods in the Control of Nonlinear Systems

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This project will study optimal control and symmetry principles of nonlinear systems. In optimal control the principal investigator will attempt to develop a formal procedure to calculate the cut-loci between surfaces consisting of endpoints of trajectories with different switching structures. These cut-loci are the dominant geometric feature for local optimality of trajectories near a reference point. In symmetry principles the principal investigator will try to extend to singular systems recent results on the calculation of feedback functions. These studies will lead to further understanding of the optimal design of mechanical systems where symmetries (e.g. rotational) are present.