In the light of the increasingly complex nature of dynamical systems requiring controls, the predominant considerations in control law design for modern engineering systems have focused on general hierarchical nonlinear switching control architectures that minimize control law complexity subject to the achievement of overall system stability and performance. These systems, classified as hybrid dynamical systems, include dynamical switching systems, nonsmooth impact mechanical systems, biological systems, sampled-data systems, discrete-event systems, intelligent vehicle/highway systems, constrained mechanical systems, and flight control systems, to cite but a few examples. The proposed research program focuses on stability and control of general hybrid dynamical systems. In this research, first, we will focus on the development of a unified dynamical systems approach for solving the problems of stability analysis, disspativity theory, optimal control, robust stability and performance of hybrid/impulsive dynamical systems. Next, a general modeling framework for mechanical impact systems described by impulsive differential equations will be developed. Furthermore, based on an ongoing research effort, we will develop a passivity-based control framework for stabilization of mechanical impact systems, more generally, Euler-Lagrange systems involving impacts. Finally, to transition the proposed theoretical developments to cutting-edge engineering technology, we propose to validate our results on a very important engineering problem; namely, active control of nanoprocesses.
As part of his educational activities, we propose to introduce a novel web-based numerical experimental component in the undergraduate control education. Specifically, using the new enabling multimedia technology, we propose to develop several numerical experiments to train students in applying the analytical skills on computer generated models. Finally, inspired by an optimal control approach for biological processes, we propose a teaching philosophy/model to study and hopefully maximize freshmen retention.
