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Register a new userInvariant-based inverse engineering for fast and robust load transport in a double pendulum bridge crane
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We set a shortcut-to-adiabaticity strategy to design the trolley motion in a double-pendulum bridge crane. The trajectories found guarantee payload transport without residual excitation regardless of the initial conditions within the small oscillations regime. The results are compared with exact dynamics to set the working domain of the approach. The method is free from instabilities due boundary effects or to resonances with the two natural frequencies.
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By applying invariant-based inverse engineering in the small-oscillations regime, we design the time dependence of the control parameters of an overhead crane (trolley displacement and rope length), to transport a load between two positions at different heights with minimal final energy excitation for a microcanonical ensemble of initial conditions. The analogies between ion transport in multisegmented traps or neutral atom transport in moving optical lattices and load manipulation by cranes opens a route for a useful transfer of techniques among very different fields.
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these coupled systems 2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic waveguides; and (ii) we design the state transfer from one coupled oscillator to another.
The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the very same system of equations, each of them with particular initial conditions. We compare with the common two--dimensional approximations in textbooks. A previously unnoticed pattern in the three--dimensional Foucault pendulum attractor is presented.
Inverse problems are essential to imaging applications. In this paper, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) and strong regularization and tuning-free advantages of the data-driven neural network. By unfolding the FISTA into a deep network, the architecture of FISTA-Net consists of multiple gradient descent, proximal mapping, and momentum modules in cascade. Different from FISTA, the gradient matrix in FISTA-Net can be updated during iteration and a proximal operator network is developed for nonlinear thresholding which can be learned through end-to-end training. Key parameters of FISTA-Net including the gradient step size, thresholding value and momentum scalar are tuning-free and learned from training data rather than hand-crafted. We further impose positive and monotonous constraints on these parameters to ensure they converge properly. The experimental results, evaluated both visually and quantitatively, show that the FISTA-Net can optimize parameters for different imaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT). It outperforms the state-of-the-art model-based and deep learning methods and exhibits good generalization ability over other competitive learning-based approaches under different noise levels.
The load-flow equations are the main tool to operate and plan electrical networks. For transmission or distribution networks these equations can be simplified into a linear system involving the graph Laplacian and the power input vector. We show, using spectral graph theory, how to solve this system efficiently. This spectral approach gives a new geometric view of the network and power vector. This formulation yields a Parseval-like relation for the $L_2$ norm of the power in the lines. Using this relation as a guide, we show that a small number of eigenvector components of the power vector are enough to obtain an estimate of the solution. This would allow fast reconfiguration of networks and better planning.
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