My current research interests are in the areas of systems and control theory and their applications in optics, bio-engineering, and cyber-security of critical infrastructure systems.
In the area of smart structures and material modeling, I am interested in the modeling and control of actuators that are based on smart materials. A key difficulty in this area is that the systems exhibit a phenomenon called hysteresis. My contribution to this area includes development of theory of hysteresis, model development from basic principles for smart materials; developing efficient and fast system identification techniques, and control design over a wide range of operating frequencies in the presence of saturation hysteresis and frequency dependent power-losses. More recently, in collaboration with researchers from University of Sannio, Benevento, Italy, I have been researching energy harvesting schemes for advanced engineering structures.
During 2000-2005, I worked with US Air Force Research Laboratory on problems relating to control of hypersonic, and unmanned air vehicles. I realized that existing inertial navigation systems were inadequate for micro air vehicles and developed a completely novel sensing idea based on insect vision. This led to an enduring interest in optics. Since 2010, I have been working on the development of custom designed contact lenses for keratoconic patients, with Dr. Steven Matthews, O.D., Ph.D.. Here, my contributions include developing a smoothing spline method on disk domains for the reconstruction of the corneal surface from optical coherence tomography measurements, and robust front surface design for contact lenses that take into account translation and rotation of the lenses while providing significant vision correction. From a mathematical perspective, this project has led me and my student to develop theoretical understanding of dissipation processes in low dimensional Reynolds number flow involving capillary surfaces, and contact angle hysteresis. A series of grants by Texas Tech University let us set up a laboratory for mathematical and clinical research in this area. During the last few years, I have advised several M.S. and Ph.D. students in the area of modeling the dynamics of human eye motion; smoothing of RGP lenses after wavefront aberration correction; smoothing spline models for creating 3D model of the cornea from optical coherence tomography (OCT) measurement; correction of lower and higher order aberrations; and mathematical modeling and analysis of the static and dynamic stability of the contact lens/tear/lens system.
Recently, I have been working with a large group of faculty from Engineering, Arts and Sciences, and Business, on the cybersecurity of networked critical infrastructure systems. Critical infrastructure such as oil, gas, and water pipelines; the smart electricity grid; and the national highway network, are vulnerable to cyberattacks due to their networked nature. Although features of information assurance apply to this area due to its networked nature, the key feature that can be exploited to defend networked critical infrastructure systems is the constraint imposed by its physical nature. Our group's aim is to understand vulnerabilities due to legacy systems, make the networks resilient to cyberattacks with designed-in security features, and educate the next generation of cybersecurity engineers.