In control, a large number of applications are mechanical in nature. These application areas include robotics, aerospace systems, and autonomous vehicles. In existing practice, these systems are often dealt with in an ad hoc manner, with the methodology for one system possibly having little bearing on a methodology for any other system. A significant portion of my research is devoted to developing a unified theory for dealing with large classes of mechanical systems. To do this, one wishes to understand what aspects of these systems constitute a minimal physical description, and develop control methodologies based upon this minimal structure. This, it turns out, is a nontrivial undertaking. In the talk, I shall present my research essentially by a collection of simple "toy" systems. Each system, while innocuous both in terms of its physical complexity and in terms of the complexity of its mathematical model, is not easy to control.
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