Geometric Control Theory: linear control theory has its limitations, more particularly, with under-actuated nonlinear control systems. Geometric control theory allows for revealing new information/directions/mechanisms within the system's vector fields that otherwise will not be discovered. Utilizing geometric control theory is very appealing to analyze and re-frame some very interesting under-actuated nonlinear systems. Nonlinear geometric control, for example, helps significantly with understanding the flight physics of soaring birds and, therefore, advancing research attempting at mimicking soaring birds by UAVs. We are also investigating gliding physics through geometric control formulation. Take a look at the following publication:
-A Controllability Perspective of Dynamic Soaring. Nonlinear Dynamics, Springer, DOI: 10.1007/s11071-018-4493-6. (2018).

Non-Smooth and Discontinuous Sensitivity Theory: control systems in general and power/energy control systems in particular have many interesting situations in which computing the sensitivity of the states with respect to any of the system's parameters, initial condition,...etc, is of great importance; for example series of faults hitting the system can be modeled as series of jumps which posses discontinuities. Our interests is to advance and utilize new non-smooth, discontinuous, and hybrid sensitivity theory (generalized-derivatives concept) that is also computationally-relevant and implementable to analyze dynamic sensitivities for cases where non-smoothness or even discontinuities are present in the right hand side of differential-algebraic systems due to the control input or parametric profiles. This, for example, is very useful in wind turbine systems when non-smooth/discontinuous parametric profiles are used to model extreme/sudden changes in wind speed or the power grid parameters. Take a look at the following publication:
-Sensitivity Analysis of Nonsmooth Power Control Systems with an Example of Wind Turbines. Communications in Nonlinear Science and Numerical Simulations, Elsevier, DOI: 10.1016/j.cnsns.2020.105633. (2021).

Extremum Seeking Control: ESC has been researched for long time because it is a very powerful adaptive control design that allows for steering dynamical systems toward the extrema (maximum or minimum) of a given objective function that, ideally, is unknown - expression wise. Not surprising, this has been introduced to multi agent systems which seek minimizations of, often the case, unknown objective functions. ESC formulation can be approximated by tools from differential geometrical control, in particular, Lie brackets. We are investigating the viability and the expansion of such approximation to solve/enhance some of the persistent problems in the structures of ESC such as its oscillatory behavior and how much information it requires on the objective function in order to guarantee stability characteristics. We also are interested in applying ESC to original fields, particularly bio-inspired systems. Below is an initial work we have done in the lab, which introduced original class of ESC that involve Lie brackets to obtain adaptation laws of the excitation signal, which in return, resulted in attenuation of the oscillations and without requiring information on the objective function unlike many very recent approaches:
-Class of Extremum Seeking Controls with Adjustable Oscillations. https://arxiv.org/abs/2105.03985 (2021).

Wind turbine modeling: in order to have better understanding of how to utilize best wind energy, we have to have very reliable wind turbine models that allows for all kind of studies concerned with wind turbines implementation and stable power generation. We built a strong modeling framework that has been recognized by energy news platforms (such as Energy Daily News) and manufacturers such as General Electric (click here). Many aspects of the model and developing new parts/designs in it still have to be done. Major interests are toward improving the performance of the pitch control and the unstable behaviors when the wind turbine connected to the grid faces sudden drops in the power grid loads. Take a look at the following publications:
-Nonlinear Modeling, Analysis and Simulation of Wind Turbine Control System with and without Pitch as in Industry. Invited Book Chapter to the Power Systems Series ISSN: 1612-1287, Advanced Control and Optimization Paradigms for Wind Energy Systems, Springer , (2019). DOI: 10.1007/978-981-13-5995-8, eBook ISBN: 978-981-13-5995-8, and Hardcover ISBN: 978-981-13-5994-1.
-Modeling Dynamics and Control of Type-3 DFIG Wind Turbines: Stability, Q Droop Function, Control Limits and Extreme Scenarios Simulation. Electric Power Systems Research, Elsevier, DOI: 10.1016/j.epsr.2018.09.018. (2019).
-Investigating the Problem of Oscillatory Orbits and Attractors in Wind Turbines System Under Control Limits Imposed by Industry. Electric Power Systems Research, Elsevier, DOI: 10.1016/j.epsr.2019.106098. (2020).

Power Maximization and Increased Resilience of Wind Turbines: it is not very obvious or easy to how we can place wind turbines together and to what degree they should be communicating/deciding altogether certain performances. For example, power generation is not maximum if every wind turbine in the complex having its pitch control set for maximum individual power extraction. This is simply due to the very nonlinear and complex aerodynamics effects. We are interested in researching this problem by not only examining the physical-based wind turbine model, but by combining a learning (AI) and modeling efforts.

UAVs mimicking soaring birds: dynamic soaring is an exceptional phenomenon that basically allows for full/partial energy harvesting from the wind shear, and as a result, flying almost for free as done by Albatross (click here). We built a nonlinear modeling, studied controllability, and advanced morphing studies to have UAVs mimicking soaring birds and perform dynamic soaring optimally. This work is ongoing as there is a space of applying dynamic soaring in forward flights instead of periodic orbits and also advance studies to how this phenomenon can be applied practically in real situations. Also, stable-feed back controllers benefiting from some controllability and stability work we performed is under investigation. Additionally, reinforcement learning can be used broadly with dynamic soaring, but particularly, with control decision taking and transitions between operating states in cases where dynamic soaring process may be interrupted by poor wind condition. Take a look at the following publications:-Review of Dynamic Soaring: Technical Aspects, Nonlinear Modeling Perspectives and Future Directions. Nonlinear Dynamics, Springer, DOI: 10.1007/s11071-018-4540-3. (2018).-Optimal Morphing-Augmented Dynamic Soaring Maneuvers for Unmanned Aerial Vehicle Capable of Span and Sweep Morphologies. Aerospace Science and Technology, Elsevier, DOI: 10.1016/j.ast.2018.05.024. (2018).-A Controllability Perspective of Dynamic Soaring. Nonlinear Dynamics, Springer, DOI: 10.1007/s11071-018-4493-6. (2018).

Dynamic Soaring inspiration to Gliding: dynamic soaring partially was realized by gliders who try to take advantage of wind shear to glide for larger distances. We are working on studying the flight physics involved with gliding and optimally formulating gliding problem that takes advantage from wind shear in a controllable way to enhance the gliding performance. Control designs and implementation is part of the project.

Hooping Robots are used to study different animals locomotion. Also, it is inspiring for studying many characteristics about humans walking and many related medical/biological subjects.