Differential equations are commonly used to model several engineering, science, and biological applications. Unfortunately, finding analytical solutions for solving higher-order Ordinary Differential Equations (ODEs) ...
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Differential equations are commonly used to model several engineering, science, and biological applications. Unfortunately, finding analytical solutions for solving higher-order Ordinary Differential Equations (ODEs) is a challenge. Numerical methods represent a leading candidate for solving such ODEs. This work presents an innovated adaptive technique that uses polynomials to solve linear or nonlinear third-order ODEs. The proposed technique adapts the coefficients of the polynomial to obtain an explicit analytical solution. A signed least mean square algorithm is exploited to enhance the adaptation process and decrease both computational requirements and time. The efficiency of the proposed adaptive Polynomial Method (APM) is illustrated through six well-known examples. The proposed technique is compared with recent analytical and numerical methods to validate its effectiveness in terms of Mean Square Error (MSE) and computation time. An application in a thin film flow system is modeled to a third-order ODE. The proposed technique is compared with recent numerical and analytical methods in solving the thin film flow equation, and it achieves better results. Furthermore, the proposed technique provides an analytical solution with an increased dynamic range and much lower computational time than those of the conventional numerical methods.
The noncooperative game with private constraints is studied, where heterogeneous players communicate over a weight-unbalanced digraph. A novel distributed Nash equilibrium (NE) seeking algorithm is adapted for this pr...
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This paper studies the problem of fast and accurate fault estimation for a class of descriptor systems with time-varying delays based on an adaptive finite time robust observer. This descriptor system is detectable, a...
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We apply control theoretic and optimization techniques to adaptively design incentives for principal-agent problems in which the principal faces adverse selection in its interaction with multiple agents. In particular...
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We apply control theoretic and optimization techniques to adaptively design incentives for principal-agent problems in which the principal faces adverse selection in its interaction with multiple agents. In particular, the principal's objective depends on data from strategic decision makers (agents) whose decision-making process is unknown a priori. We consider both the cases where agents play best response to one another (Nash) and where they employ myopic update rules. By parametrizing the agents' utility functions and the incentives offered, we develop an algorithm that the principal can employ to learn the agents' decision-making processes while simultaneously designing incentives to change their response to one that is more desirable. We provide convergence results for this algorithm both in the noise-free and noisy cases and present illustrative examples.
This paper focuses on aggregative games with local feasibility decision sets in a partial-decision information scenario. To seek the Nash equilibrium in a fully distributed manner, adaptive algorithms with edge-based ...
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This paper proposes Graph Signal adaptive Message Passing (GSAMP) by employing a distinct approach that utilizes localized computations at each node based on an adaptive solution obtained from an optimization problem ...
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This paper proposes Graph Signal adaptive Message Passing (GSAMP) by employing a distinct approach that utilizes localized computations at each node based on an adaptive solution obtained from an optimization problem designed to minimize the discrepancy between observed and estimated values. This localized approach distinguishes GSAMP from conventional graph methods derived from the entire graph. GSAMP efficiently handles real-world time-varying graph signals under Gaussian and impulsive noise, performing online prediction, missing data imputation, and noise removal simultaneously.
We prove that the iterates produced by, either the scalar step size variant, or the coordinatewise variant of AdaGrad algorithm, are convergent sequences when applied to convex objective functions with Lipschitz gradi...
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We prove that the iterates produced by, either the scalar step size variant, or the coordinatewise variant of AdaGrad algorithm, are convergent sequences when applied to convex objective functions with Lipschitz gradient. The key insight is to remark that such AdaGrad sequences satisfy a variable metric quasi-Fejer monotonicity property, which allows to prove convergence. (C) 2021 Elsevier B.V. All rights reserved.
One of the main fields of application of personal sound zones (PSZs) is the car industry. PSZ systems are usually designed assuming that the acoustic environment is not changing. However, due to variability in the car...
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One of the main fields of application of personal sound zones (PSZs) is the car industry. PSZ systems are usually designed assuming that the acoustic environment is not changing. However, due to variability in the car cabin's acoustic conditions, it is necessary to design a system capable of adapting to these variations. This paper introduces the use of the filtered-x least-mean-squares algorithm to adapt a PSZ system in a car cabin when the seat positions change. The article focuses on four aspects. First, the effect of the initial coefficients is investigated to help with the convergence of the adaptive algorithm. Second, a study is made on the definition of the desired pressure and its effect on the reproduction. Third, the system's sensitivity to external noise is also evaluated. Last, the possibility to reduce the number of microphones for the adaptive system is considered. The method's performance is evaluated using a two headrest system installed in a car cabin and when moving the seats to different positions. It is shown that the system is capable of maintaining the performance in the different seat positions. (C) 2021 Acoustical Society of America.
This paper introduces an online centered normalized least mean squares (OC-NLMS) algorithm for linear adaptive finite impulse response (FIR) filters and neural networks. As an extension of the normalized least mean sq...
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This paper introduces an online centered normalized least mean squares (OC-NLMS) algorithm for linear adaptive finite impulse response (FIR) filters and neural networks. As an extension of the normalized least mean squares (NLMS), the OC-NLMS algorithm features an approach of online input centering according to the introduced filter memory. This key feature can compensate the effect of concept drift in data streams, because such a centering makes the filter independent from the nonzero mean value of signal. This approach is beneficial for applications of adaptive filtering of data with offsets. Furthermore, it can be useful for real-time applications like data stream processing where it is impossible to normalize the measured data with respect to its unknown statistical attributes. The OC-NLMS approach holds superior performance in comparison to the NLMS for data with large offsets and dynamical ranges, due to its input centering feature that deals with the nonzero mean value of the input data. In this paper, the derivation of this algorithm is presented. Several simulation results with artificial and real data are also presented and analysed to demonstrate the capability of the proposed algorithm in comparison with NLMS.
In this work, a new class of stochastic gradient algorithm is developed based on fractional calculus. Unlike the existing algorithms, the concept of complex fractional gradient is introduced by employing Caputo's ...
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In this work, a new class of stochastic gradient algorithm is developed based on fractional calculus. Unlike the existing algorithms, the concept of complex fractional gradient is introduced by employing Caputo's fractional derivative which results in a fractional steepest descent algorithm and a fractional-order complex LMS (FoCLMS) algorithm. We demonstrate that with the Caputo's fractional gradient definition, the Weiner solution remains invariant. Convergence analysis of the proposed FoCLMS algorithm is presented for both transient and steady state scenarios. Consequently, expressions for the learning curves and steady state EMSE are derived. Our theoretical developments are validated by simulation experiments. Extensive simulations are presented to investigate all possible scenarios: channel with negative weights and real input data, channel with positive weights and complex input data, and channel with complex weights and complex input data.
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