In my Ph.D. research we study nonlinear eigenfunction decompositions techniques for images based on PDE. We start by formulating a stable explicit scheme for solving nonlinear differential equations. Following that, we introduce a framework for analysis and processing such as decomposition, reconstruction, spectrum, and filtering. We began our research by formulating a numerical technique for solving eigenpair problems.

In my MSc study we proposed a control and guidance system for the autonomous execution of agile flight maneuvers, similar to those performed by a combat pilot and which utilize the entire lift capabilities of the aircraft while taking into account their limitations. This work has been motivated by applications to combat flight simulators but is also relevant to physical autonomous aircraft.

The control system we designed controls the velocity of the aircraft and angular velocities of the heading and elevation angle. This system using a feedforward-feedback structure which is calculated by using the inverse model of a simplified (3DOF) model or the aircraft. Control variables of this design model are the angle of attack, bank angle, and thrust. The controlled variables are acceleration, rate of change of heading angle and elevation angle.

The role of the guidance system is to generate combat-like maneuvers that arise during an air combat situation. In this part, we developed a repertoire of basic maneuvers with the characteristics mentioned above and guidance laws that imitate actions or mirror actions during the combat. The purpose of these laws is to lower the relative advantage of the enemy and increase the relative advantage of the guided aircraft.