Atomic norm denoising with applications to line spectral estimation

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials. We show that the associated convex optimization problem can be solved in polynomial time via semidefinite programming (SDP). We also show that the SDP can be approximated by an l1-regularized least-squares problem that achieves nearly the same error rate as the SDP but can scale to much larger problems. We compare both SDP and l1-based approaches with classical line spectral analysis methods and demonstrate that the SDP outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.Comment: 27 pages, 10 figures. A preliminary version of this work appeared in the Proceedings of the 49th Annual Allerton Conference in September 2011. Numerous numerical experiments added to this version in accordance with suggestions by anonymous reviewer

Computational aspects and applications of a new transform for solving the complex exponentials approximation problem

Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has been proposed in a theoretical framework. In this work some computational issues are addressed to make this new tool useful in practice. An algorithm is developed and used to solve a Nuclear Magnetic Resonance spectrometry problem, two time series interpolation and extrapolation problems and a shape from moments problem.Comment: 28 pages, 20 figure

A new transform for solving the noisy complex exponentials approximation problem

The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered. A random measure is defined whose expectation approximates the unknown measure under suitable conditions. An estimator of the approximating measure is then proposed as well as a new discrete transform of the noisy moments that allows to compute an estimate of the unknown measure. A small simulation study is also performed to experimentally check the goodness of the approximations.Comment: 42 pages, 5 figure

AI Applications to Power Systems

Today, the flow of electricity is bidirectional, and not all electricity is centrally produced in large power plants. With the growing emergence of prosumers and microgrids, the amount of electricity produced by sources other than large, traditional power plants is ever-increasing. These alternative sources include photovoltaic (PV), wind turbine (WT), geothermal, and biomass renewable generation plants. Some renewable energy resources (solar PV and wind turbine generation) are highly dependent on natural processes and parameters (wind speed, wind direction, temperature, solar irradiation, humidity, etc.). Thus, the outputs are so stochastic in nature. New data-science-inspired real-time solutions are needed in order to co-develop digital twins of large intermittent renewable plants whose services can be globally delivered

Automatic Landing of a Rotary-Wing UAV in Rough Seas

Rotary-wing unmanned aerial vehicles (RUAVs) have created extensive interest in the past few decades due to their unique manoeuverability and because of their suitability in a variety of flight missions ranging from traffic inspection to surveillance and reconnaissance. The ability of a RUAV to operate from a ship in the presence of adverse winds and deck motion could greatly extend its applications in both military and civilian roles. This requires the design of a flight control system to achieve safe and reliable automatic landings. Although ground-based landings in various scenarios have been investigated and some satisfactory flight test results are obtained, automatic shipboard recovery is still a dangerous and challenging task. Also, the highly coupled and inherently unstable flight dynamics of the helicopter exacerbate the difficulty in designing a flight control system which would enable the RUAV to attenuate the gust effect. This thesis makes both theoretical and technical contributions to the shipboard recovery problem of the RUAV operating in rough seas. The first main contribution involves a novel automatic landing scheme which reduces time, cost and experimental resources in the design and testing of the RUAV/ship landing system. The novelty of the proposed landing system enables the RUAV to track slow-varying mean deck height instead of instantaneous deck motion to reduce vertical oscillations. This is achieved by estimating the mean deck height through extracting dominant modes from the estimated deck displacement using the recursive Prony Analysis procedure. The second main contribution is the design of a flight control system with gust-attenuation and rapid position tracking capabilities. A feedback-feedforward controller has been devised for height stabilization in a windy environment based on the construction of an effective gust estimator. Flight tests have been conducted to verify its performance, and they demonstrate improved gust-attenuation capability in the RUAV. The proposed feedback-feedforward controller can dynamically and synchronously compensate for the gust effect. In addition, a nonlinear H1 controller has been designed for horizontal position tracking which shows rapid position tracking performance and gust-attenuation capability when gusts occur. This thesis also contains a description of technical contributions necessary for a real-time evaluation of the landing system. A high-infedlity simulation framework has been developed with the goal of minimizing the number of iterations required for theoretical analysis, simulation verification and flight validation. The real-time performance of the landing system is assessed in simulations using the C-code, which can be easily transferred to the autopilot for flight tests. All the subsystems are parameterized and can be extended to different RUAV platforms. The integration of helicopter flight dynamics, flapping dynamics, ship motion, gust effect, the flight control system and servo dynamics justifies the reliability of the simulation results. Also, practical constraints are imposed on the simulation to check the robustness of the flight control system. The feasibility of the landing procedure is confimed for the Vario helicopter using real-time ship motion data