9,988 research outputs found
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
In this paper, we address the stability of a broad class of discrete-time
hypercomplex-valued Hopfield-type neural networks. To ensure the neural
networks belonging to this class always settle down at a stationary state, we
introduce novel hypercomplex number systems referred to as real-part
associative hypercomplex number systems. Real-part associative hypercomplex
number systems generalize the well-known Cayley-Dickson algebras and real
Clifford algebras and include the systems of real numbers, complex numbers,
dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as
particular instances. Apart from the novel hypercomplex number systems, we
introduce a family of hypercomplex-valued activation functions called
-projection functions. Broadly speaking, a
-projection function projects the activation potential onto the
set of all possible states of a hypercomplex-valued neuron. Using the theory
presented in this paper, we confirm the stability analysis of several
discrete-time hypercomplex-valued Hopfield-type neural networks from the
literature. Moreover, we introduce and provide the stability analysis of a
general class of Hopfield-type neural networks on Cayley-Dickson algebras
GPU-accelerated stochastic predictive control of drinking water networks
Despite the proven advantages of scenario-based stochastic model predictive
control for the operational control of water networks, its applicability is
limited by its considerable computational footprint. In this paper we fully
exploit the structure of these problems and solve them using a proximal
gradient algorithm parallelizing the involved operations. The proposed
methodology is applied and validated on a case study: the water network of the
city of Barcelona.Comment: 11 pages in double column, 7 figure
Low-Complexity Iterative Methods for Complex-Variable Matrix Optimization Problems in Frobenius Norm
Complex-variable matrix optimization problems (CMOPs) in Frobenius norm
emerge in many areas of applied mathematics and engineering applications. In
this letter, we focus on solving CMOPs by iterative methods. For unconstrained
CMOPs, we prove that the gradient descent (GD) method is feasible in the
complex domain. Further, in view of reducing the computation complexity,
constrained CMOPs are solved by a projection gradient descent (PGD) method. The
theoretical analysis shows that the PGD method maintains a good convergence in
the complex domain. Experiment results well support the theoretical analysis.Comment: This paper has been submitted to IEEE signal processing letter for
possible publicatio
Model reduction for the dynamics and control of large structural systems via neutral network processing direct numerical optimization
Three neural network processing approaches in a direct numerical optimization model reduction scheme are proposed and investigated. Large structural systems, such as large space structures, offer new challenges to both structural dynamicists and control engineers. One such challenge is that of dimensionality. Indeed these distributed parameter systems can be modeled either by infinite dimensional mathematical models (typically partial differential equations) or by high dimensional discrete models (typically finite element models) often exhibiting thousands of vibrational modes usually closely spaced and with little, if any, damping. Clearly, some form of model reduction is in order, especially for the control engineer who can actively control but a few of the modes using system identification based on a limited number of sensors. Inasmuch as the amount of 'control spillover' (in which the control inputs excite the neglected dynamics) and/or 'observation spillover' (where neglected dynamics affect system identification) is to a large extent determined by the choice of particular reduced model (RM), the way in which this model reduction is carried out is often critical
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