Control, Stabilization and Dynamics of Mechanical Systems

Abstract
This project involved the study of control and dynamics of various physical and engineering systems. The Principal Investigator analyzed the stability of mechanical systems in the presence of dissipation, as well as the stabilization of mechanical systems by using nonlinear controls. He studied in particular a method of control that involves matching a feedback controlled system by an autonomous controlled Lagrangian system by adjusting parameters. He analyzed control of satellite dynamics by this method. He studied the geometry, control and stabilization of systems with nonholonomic constraints - systems such as wheeled vehicles or contour following robots. He derived an energy-based method for analyzing such nonholonomic systems, even in the case when the system has natural dissipation. He also studied the role of conservation laws in nonholonomic systems. He studied optimal control problems and, in particular, solvable optimal control problems, and derived a novel form of the equations for the rigid body using the optimal control approach. These equations were linked with discrete rigid body equations and numerical analysis. He also worked on the stabilization of systems with complex dynamics arising in anti-corrosion processes.

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