My main field of research is Optimal Control Theory essentially from the Calculus of Variations point of view, following the path of my teacher H. J. Kelley. Thus gradient methods, adjoint analysis, singular perturbations, singular control, etc. are all topics in my research works. Modern direct optimization tools are also employed for this purpose in mine and my students’ work, such as collocation and pseudo-spectral methods.
The applications of the theory to real aerospace problems have been at the center of my attention. It includes some major problems in atmospheric flight (e.g. minimum time to fly between points; minimum time to climb)), in rocket performance (Goddard problem, maximal rocket range), in missile guidance (Proportional Navigation, Linear Quadratic Pursuit-Evasion games) and more.
The main threats of the country are ballistic missiles (especially with nuclear warheads) and rockets. The challenges are to provide nearly hermetic defense against the former and cost effective defense against the later. Most of my graduate students come from the aerospace industry (Rafael, Elbit, IMI and IAI) and are involved in this national effort. We direct our research work toward solving problems arising in their industrial activities. Some of our research results have been incorporated in new missile defense systems.