Currently, my research focuses on three main areas: (a) estimation and control of stochastic systems with non-Gaussian noises, (b) air traffic control, and (c) robust, adaptive and nonlinear control of aerospace systems.
Estimation and Control of Stochastic Systems with Non-Gaussian Noises
In many engineering, telecommunications, and science applications the underlying random processes or noises have significant volatility, which are not captured by Gaussian distributions. Rather than light-tailed Gaussian distributions, heavy-tailed distributions have been shown to better represent these volatile random fluctuations in applications like radar and sonar sensor noises, and the air turbulent environment. The objective of this research effort is to develop estimation and stochastic control techniques for linear dynamic systems with heavy-tail distributed noises while using a particular case of symmetric alpha-stable distributions, the Cauchy noise model. To date, impressive results were attained in the area of estimation for single state and multivariable systems. Although a closed analytical solution was derived, it suffers from increasing complexity with processing time. The current research effort is devoted in understanding the complex characteristics of the derived estimators, to yield more practical implementations. Among things that are tested is parallel implementation on multi-processor computing units (GPU-s) and finite dimensional approximations. In the stochastic control of such systems, currently we have only single state results. An effort is devoted to extend those results to the multivariable case. Here too, the complexity of the solution, in part affected by the estimation result discussed above, requires special consideration.
Air Traffic Control
Continuous growth in the air traffic density, mainly over Europe and the U.S., introduces a need for new air-traffic control concepts. One such concept involves air-traffic management using four dimensional (4D, i.e., 3D spatial and time) contracts. According to this approach, all the air traffic is pre-planned and optimized in advance in four dimensions. This stage is called strategic planning. Before take-off each aircraft is given a flyable conflict-free flight plan, called 4D contract, which it is responsible to comply with. Whenever, for any reason, the aircraft can not respect its prescribed 4D contract, a new 4D contract should be re-computed for it in a matter of minutes. This stage is called tactical re-planning. Our current research effort addresses efficient tactical re-planning. Most of our work so far has concentrated on planar en-route re-planning. We now turn to 3 dimensional deviations and possible change of aircraft speed. These provide more flexibility, but at the same time, increase the complexity of the solution. In addition, these variations may reduce the flight efficiency, i.e., cause larger fuel use. Those solutions will be explored, focusing also on the more complicated terminal area of flight. In this context, we intend to address efficient 4D autopilots to accommodate the requirements of the 4D contract operation.
Robust, Adaptive and Nonlinear Control of Aerospace Systems
Since I joined the Faculty, I have always carried research activities in the area of practical applications of advance control design techniques for aerospace applications. This included missile guidance (e.g., nonlinear guidance and trajectory planning for imposing interception geometry), integrated missile guidance and control using nonlinear, sliding mode design methods, adaptive neural network based control for space applications, robust control of motion based flight simulator, and more. Today, I continue spending time also in this area. Currently, with my graduate student, we are exploring the advantages of using advance nonlinear control methods for controlling simple seeker heads. The challenge in the problem results from a very simple design that leads to significant nonlinearities and noisy measurements with unknown characteristics. The goal is to regain performance of such a rough system while use advanced control methods. In addition, the 4D autopilot design activity mentioned in the air traffic control section above falls also into this discipline. Here, we intend to explore, e.g., integrated guidance and control for this problem while using nonlinear control methods.