Current scientific research interests:
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Modeling and simulation of complex aircrafts. Modeling of unmanned quadcopter drones and helicopters, and simulating
numerically their behavior by manifold calculus.
Animation by A. Tarsi: Simulation of a helicopter take-off.
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Modeling, simulation and control of complex underwater vehicles. Modeling of unmanned underwater vehicles, designing appropriate
controllers for trajectory following, and simulating numerically their behavior by manifold calculus.
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Modeling, simulation and control of complex spacecrafts. Modeling of unmanned spacececraft, designing appropriate controllers
for reorientation and rendezvous maneuvers, and simulating numerically their behavior by manifold calculus.
Animation by E. Sampaolesi: Simulation of a spacecraft effecting a rendezvous to a space station.
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Simulation and control of DC2DC power converters. Modeling of DC-to-DC electrical power converters, designing appropriate controllers
to achieve conversion, and simulating numerically their behavior by manifold calculus.
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Optimization on manifolds and Lie groups. Geometrical
(pseudo-) Riemannian-gradient optimization methods and numerical calculus techniques. Dynamical systems on manifolds to optimize smooth criteria.
Symplex (Amoeba) methods on manifolds to optimize non-smooth criteria.
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Statistics on smooth manifolds: Generation of pseudo-random clouds and pseudo-random processes on differentiable manifolds
and Lie groups. ARMA-type models on differentiable manifolds and Lie groups. Cross- and auto-correlation functions on
differentiable manifolds and Lie groups.
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Non-linear oscillators on Lie groups and smooth manifolds. Continuous-time, second-order dynamical systems on Lie groups and
manifolds exhibiting periodic oscillatory behavior as well as continuous-time, second-order chaotic systems.
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Non-linear control on smooth manifolds and related numerical calculus techniques. Extension of PID-like control theories.
Minimum effort control theories. Consensus and virtual-potential control. Numerical techniques to implement non-linear control theories on
manifolds. Synchronization of dynamical systems on manifolds. Animation by A. Saccuti: Synchronization of two
satellites when one of them gets hit repeatedly.
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Statistical data modeling and regression. Statistical isotonic modeling and data regression. Non-linear transformations
to extend isotonic modeling to non-monotonic data.
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MATLAB-based implementation.
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Application of numerical calculus on manifolds to machine learning and signal/data processing. Foundations of machine
learning and signal/data processing on smooth manifolds.
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Artificial neural systems and algorithms for signal/data processing.
(Here is a scanned version of a stamp with a portrait
issued by the USSR in 1983 to commemorate the 1200th anniversary of Muhammad
al-Khowarizmi, after whom algorithms are named).
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Unsupervised learning theory (principal/independent component/subspace
analysis, information-theoretic learning) and neural units with adaptive
activation functions.
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Linear and non-linear adaptive discrete-time filtering. Blind
deconvolution of non-minimum phase systems, blind image deblurring.
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Non-linear and non-stationary continuous-time circuits with stochastic excitations.
Statistical isotonic modeling and data regression.
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