Differential geometry has been successfully applied to nonlinear control theory, resulting in geometric control theory which was born in the mid 1960's. Around that same time, differential geometric methods were systematically applied to the formulations of classical mechanics. In the mid 1990's these two areas of research were fused with the result that significant advances were made in the control theory for mechanical systems. This continues to be an active area of research today.
This talk will be a survey of some of the advances in the area. The emphasis will be on the affine connection formulation of mechanics, and the application of this formulation to problems in control theory. The control theoretic problems discussed will include controllability (the study of states reachable, using controls, from an initial state), motion planning (the design of control laws to steer a system from one state to another), and stabilisation (the conversion of an unstable state into a stable state using feedback).
No background in control theory will be assumed.
Last Updated: Fri Jul 10 09:23:52 2020