Gradient-based Iterative Algorithm Research Articles

Constrained solutions of generalized coupled discrete-time periodic matrix equations with application in state observer design for linear periodic systems

PurposeIt is desired to provide a diversified iterative scheme for solving the constrained solutions of the generalized coupled discrete-time periodic (GCDTP) matrix equations from the perspective of optimization.Design/methodology/approachThe paper considers generalized reflexive solutions of the GCDTP matrix equations by applying the Jacobi gradient-based iterative (JGI) algorithm, which is an extended variant of the gradient-based iterative (GI) algorithm.FindingsThrough numerical simulation, it is verified that the efficiency and accuracy of the JGI algorithm are better than some existing algorithms, such as the GI algorithm in Hajarian, the RGI algorithm in Sheng and the AGI algorithm in Xie and Ma.Originality/valueIt is the first instance in which the GCDTP matrix equations are solved applying the JGI algorithm.

Use of Deep-Learning-Accelerated Gradient Approximation for Reservoir Geological Parameter Estimation

The estimation of space-varying geological parameters is often not computationally affordable for high-dimensional subsurface reservoir modeling systems. The adjoint method is generally regarded as an efficient approach for obtaining analytical gradient and, thus, proceeding with the gradient-based iteration algorithm; however, the infeasible memory requirement and computational demands strictly prohibit its generic implementation, especially for high-dimensional problems. The autoregressive neural network (aNN) model, as a nonlinear surrogate approximation, has gradually received increasing popularity due to significant reduction of computational cost, but one prominent limitation is that the generic application of aNN to large-scale reservoir models inevitably poses challenges in the training procedure, which remains unresolved. To address this issue, model-order reduction could be a promising strategy, which enables us to train the neural network in a very efficient manner. A very popular projection-based linear reduction method, i.e., propel orthogonal decomposition (POD), is adopted to achieve dimensionality reduction. This paper presents an architecture of a projection-based autoregressive neural network that efficiently derives an easy-to-use adjoint model by the use of an auto-differentiation module inside the popular deep learning frameworks. This hybrid neural network proxy, referred to as POD-aNN, is capable of speeding up derivation of reduced-order adjoint models. The performance of POD-aNN is validated through a synthetic 2D subsurface transport model. The use of POD-aNN significantly reduces the computation cost while the accuracy remains. In addition, our proposed POD-aNN can easily obtain multiple posterior realizations for uncertainty evaluation. The developed POD-aNN emulator is a data-driven approach for reduced-order modeling of nonlinear dynamic systems and, thus, should be a very efficient modeling tool to address many engineering applications related to intensive simulation-based optimization.

Secure and covert communication strategy of UAV based on hybrid RF/FSO system

The hybrid radio frequency (RF)/free-space optical (FSO) system can improve communication security by using complimentary characteristics and mitigating the risks of RF links being susceptible to co-channel interference (CCI) and malicious eavesdropping. We investigate the secure and covert communication performance of unmanned aerial vehicles (UAVs) equipped with a hybrid RF/FSO system. In terms of secure communication, UAVs employ the strategy of transmitting private data concurrently through RF and FSO links, considering two modes based on active eavesdropping by a malicious user. Closed-form expressions for the secrecy outage probability (SOP) and effective secrecy throughput (EST) are derived. With respect to covert communication, the communication strategy is to utilize the RF link to generate interfering signals, thus aiding the FSO signals in accomplishing covert communication. We formulate an optimization problem that maximizes the EST while considering transmit power and user-acceptable detection error probability. A two-stage gradient-based iterative solution algorithm is proposed. The numerical results demonstrate the effectiveness of the proposed secure and covert communication strategy based on the hybrid RF/FSO system, which is expected to enhance the communication security of UAVs in the RF-challenged environment.

Highly efficient maximum-likelihood identification methods for bilinear systems with colored noises

This paper mainly discussed the highly efficient iterative identification methods for bilinear systems with autoregressive moving average noise. Firstly, the input-output representation of the bilinear systems is derived through eliminating the unknown state variables in the model. Then based on the maximum-likelihood principle, a maximum-likelihood gradient-based iterative (ML-GI) algorithm is proposed to identify the parameters of the bilinear systems with colored noises. For improving the computational efficiency, the original identification model is divided into three sub-identification models with smaller dimensions and fewer parameters, and a hierarchical maximum-likelihood gradient-based iterative (H-ML-GI) algorithm is derived by using the hierarchical identification principle. A gradient-based iterative (GI) algorithm is given for comparison. Finally, the algorithms are verified by a simulation example and a practical continuous stirred tank reactor (CSTR) example. The results show that the proposed algorithms are effective for identifying bilinear systems with colored noises and the H-ML-GI algorithm has a higher computational efficiency and a faster convergence rate than the ML-GI algorithm and the GI algorithm.

Gradient-Based Optimization Method for Experimental Modal Parameter Estimation with Finite Element Model

This paper presents a novel gradient-based optimization algorithm for improving the accuracy of experimentally estimated modal parameters with the assistance of finite element models. Initially, we recast the discrete vibration response equation into a matrix form and formulate the parameter estimation problem in modal analysis as an optimization problem. Then the problem is solved with a gradient-based iterative algorithm, which explicitly exhibits the closed form of gradients used in optimization. Initial values for this iteration are parameters derived from finite element models, since every important engineering structure should be analyzed with a finite element model before it is constructed. Subsequently, the performance of this algorithm is validated by both pure numerical experiments, which simulate the physical world, and experiments using real measurement data gathered by sensors in the real physical world. The algorithm’s performance is further enhanced by incorporating gradient clipping and an adaptive iteration threshold. As a comparison, a discussion on classical least-squares time-domain method for the problem is provided. For practical applications, the Shi–Tomasi corner detection and Lucas–Kanade optical flow methods are deployed to detect corner points from videos taken during the vibration of a structure and track the motion of these points in the videos.

Optimal Parameter Estimation Techniques for Complex Nonlinear Systems

AbstractAccurate parameter estimation and state identification within nonlinear systems are fundamental challenges addressed by optimization techniques. This paper fills a critical gap in previous research by investigating tailored optimization methods for parameter estimation in nonlinear system modeling, with a particular emphasis on chaotic dynamical systems. We introduce and compare three optimization methods: a gradient-based iterative algorithm, the Levenberg-Marquardt algorithm, and the Nelder-Mead simplex method. These methods are strategically employed to simplify complex nonlinear optimization problems, rendering them more manageable. Through a comprehensive exploration of the performance of these methods in determining parameters across diverse systems, including the van der Pol oscillator, the Rössler system, and pharmacokinetic modeling, our study revealed that the accuracy and reliability of the Nelder-Mead simplex method were consistent. The Nelder-Mead simplex algorithm emerged as a powerful tool, that consistently outperforms alternative methods in terms of root mean squared error (RMSE) and convergence reliability. Visualizations of trajectory comparisons and parameter convergence under various noise levels further emphasize the algorithm’s robustness. These studies suggest that the Nelder-Mead simplex method has potential as a valuable tool for parameter estimation in chaotic dynamical systems. Our study’s implications extend beyond theoretical considerations, offering promising insights for parameter estimation techniques in diverse scientific fields reliant on nonlinear system modeling.

Penalized weighted smoothed quantile regression for high-dimensional longitudinal data.

Quantile regression, known as a robust alternative to linear regression, has been widely used in statistical modeling and inference. In this paper, we propose a penalized weighted convolution-type smoothed method for variable selection and robust parameter estimation of the quantile regression with high dimensional longitudinal data. The proposed method utilizes a twice-differentiable and smoothed loss function instead of the check function in quantile regression without penalty, and can select the important covariates consistently using the efficient gradient-based iterative algorithms when the dimension of covariates is larger than the sample size. Moreover, the proposed method can circumvent the influence of outliers in the response variable and/or the covariates. To incorporate the correlation within each subject and enhance the accuracy of the parameter estimation, a two-step weighted estimation method is also established. Furthermore, we prove the oracle properties of the proposed method under some regularity conditions. Finally, the performance of the proposed method is demonstrated by simulation studies and two real examples.

Modified and accelerated relaxed gradient-based iterative algorithms for the complex conjugate and transpose matrix equations

Modified and accelerated relaxed gradient-based iterative algorithms for the complex conjugate and transpose matrix equations

The Weighted, Relaxed Gradient-Based Iterative Algorithm for the Generalized Coupled Conjugate and Transpose Sylvester Matrix Equations

By applying the weighted relaxation technique to the gradient-based iterative (GI) algorithm and taking proper weighted combinations of the solutions, this paper proposes the weighted, relaxed gradient-based iterative (WRGI) algorithm to solve the generalized coupled conjugate and transpose Sylvester matrix equations. With the real representation of a complex matrix as a tool, the necessary and sufficient conditions for the convergence of the WRGI algorithm are determined. Also, some sufficient convergence conditions of the WRGI algorithm are presented. Moreover, the optimal step size and the corresponding optimal convergence factor of the WRGI algorithm are given. Lastly, some numerical examples are provided to demonstrate the effectiveness, feasibility and superiority of the proposed algorithm.

Relaxed gradient-based iterative solutions to coupled Sylvester-conjugate transpose matrix equations of two unknowns

PurposeThis article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns.Design/methodology/approachThis article proposes a RGI algorithm to solve CSCTME with two unknowns.FindingsThe introduced (RGI) algorithm is more efficient than the gradient iterative (GI) algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.Research limitations/implicationsThe introduced (RGI) algorithm is more efficient than the GI algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.Practical implicationsIn systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.Social implicationsIn systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.Originality/valueThis article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester conjugate transpose matrix equations (CSCTME) with two unknowns. For any initial matrices, a sufficient condition is derived to determine whether the proposed algorithm converges to the exact solution. To demonstrate the effectiveness of the suggested method and to compare it with the gradient-based iterative algorithm proposed in [6] numerical examples are provided.

Enhancing the Transferability of Targeted Attacks with Adversarial Perturbation Transform

The transferability of adversarial examples has been proven to be a potent tool for successful attacks on target models, even in challenging black-box environments. However, the majority of current research focuses on non-targeted attacks, making it arduous to enhance the transferability of targeted attacks using traditional methods. This paper identifies a crucial issue in existing gradient iteration algorithms that generate adversarial perturbations in a fixed manner. These perturbations have a detrimental impact on subsequent gradient computations, resulting in instability of the update direction after momentum accumulation. Consequently, the transferability of adversarial examples is negatively affected. To overcome this issue, we propose an approach called Adversarial Perturbation Transform (APT) that introduces a transformation to the perturbations at each iteration. APT randomly samples clean patches from the original image and replaces the corresponding patches in the iterative output image. This transformed image is then used to compute the next momentum. In addition, APT could seamlessly integrate with other iterative gradient-based algorithms, incurring minimal additional computational overhead. Experimental results demonstrate that APT significantly enhances the transferability of targeted attacks when combined with traditional methods. Our approach achieves this improvement while maintaining computational efficiency.

Iterative parameter identification algorithms for transformed dynamic rational fraction input–output systems

The rational fraction system is a special nonlinear system, the existence of the denominator polynomial leads to the difficulty of identifying rational fraction models. Inspired by the gradient search and the Newton method, the gradient-based iterative algorithm and Newton iterative algorithm are presented to estimate the parameters of rational fraction system models. Furthermore, in order to avoid a large amount of calculation and complex equations encountered in the process of solving partial derivatives, the model transformation-based gradient iterative algorithm and the model transformation-based Newton iterative algorithm are proposed for parameter identification. Two examples are carried out to show the effectiveness of the proposed algorithms. This paper focuses on solving the identification problem of rational fraction systems.

Sensitivity-Based Iterative State-Feedback Tuning for MIMO Systems

In this paper, a new approach to tuning and optimisation of controlled systems regarding the tracking behaviour is presented. This approach can be understood as an extension to the iterative feedback tuning (IFT) approach known from the literature. Motivated by the sensitivity concept, the IFT algorithm is extended to both linear and nonlinear systems in state-space description with static state-feedback control, resulting in the proposed iterative state-feedback tuning (ISFT) method. The main contribution consists of the derivation of first and second-order sensitivity functions for quadratic cost functions, which is typical for control optimisation problems. The proposed approach results in a gradient-based iterative algorithm for control parameter adaptation. Finally, exemplary simulation results will be presented for a nonlinear system, demonstrating the usability of this new approach.

Gradient-descent iterative algorithm for solving exact and weighted least-squares solutions of rectangular linear systems

<abstract><p>Consider a linear system $ Ax = b $ where the coefficient matrix $ A $ is rectangular and of full-column rank. We propose an iterative algorithm for solving this linear system, based on gradient-descent optimization technique, aiming to produce a sequence of well-approximate least-squares solutions. Here, we consider least-squares solutions in a full generality, that is, we measure any related error through an arbitrary vector norm induced from weighted positive definite matrices $ W $. It turns out that when the system has a unique solution, the proposed algorithm produces approximated solutions converging to the unique solution. When the system is inconsistent, the sequence of residual norms converges to the weighted least-squares error. Our work includes the usual least-squares solution when $ W = I $. Numerical experiments are performed to validate the capability of the algorithm. Moreover, the performance of this algorithm is better than that of recent gradient-based iterative algorithms in both iteration numbers and computational time.</p></abstract>

Biomechanical Trajectory Optimization of Human Sit-to-Stand Motion With Stochastic Motion Planning Framework

Trajectory optimization has been an important approach in biomechanics for the analysis and prediction of the limb movement. Such approaches have paved the way for the motion planning of biped and quadruped robots as well. Most of these methods are deterministic, utilizing first-order iterative gradient-based algorithms incorporating the constrained differentiable objective functions. However, the limitation of prevailing methods concerning differentiability hinders the implementation of non-differentiable objective functions such as metabolic energy expenditure (MEE) function, which is highly relevant for physiological systems and can even be implemented across the muscular space. This paper consolidates the implementation of the prevalent direct collocation-based optimal control method with the stochastic trajectory optimization method based on Policy Improvement with Path Integral (PI2) for comprehending the human sit-to-stand (STS) motion. PI2 method, which utilizes reinforcement learning of Dynamic Movement Primitive (DMP) to learn a goal-based trajectory is implemented and validated by comparing with the experimental result in joint-space and muscle-space.

Optimal cross-layer resource allocation in fog computing: A market-based framework

The potential upsides of fog computing are undeniable, including better near-real-time response, reduced transmission costs and analysis for IoT, which will further have a significant impact on operation of factories, enterprises, organizations and even the quality of our life. However, due to the resource-constrained nature, heterogeneity and distributed nodes, how to manage the extraordinarily complex fog computing resources is necessary to improve the QoE of users. This paper investigates the rational resource allocation for fog computing from the cross-layer point of perspective, and formulates the resource allocation scenario as Cloud–Fog–User market which is composed of cloud center devices, fog nodes, and user devices. Firstly, the resource market is divided into Cloud–Fog market containing cloud layer and fog layer, and Fog–User market containing fog layer and user layer based on different scenarios separately. The paper proposes a market-based framework for fog computing networks, which enables the cloud layer and the fog layer to allocate their resources in the form of pricing, payment and supply–demand relationship, while analyzes the relationship among resource allocation participants in the market. Then the paper investigates the utility optimization models from the viewpoints of both the participants of respective markets, so as to optimize optimal payment and optimal resource allocation via convex optimization techniques, and proposes a gradient-based iterative algorithm to optimize the utilities, respectively. Finally, experimental results have displayed the performance of convex analysis results and effectiveness of the proposed algorithm.

Conjugate gradient-based iterative algorithm for solving generalized periodic coupled Sylvester matrix equations

This paper focuses on constructing a conjugate gradient-based (CGB) method to solve the generalized periodic coupled Sylvester matrix equations in complex space. The presented method is developed from a point of conjugate gradient methods. It is proved that the presented method can find the solution of the considered matrix equations within finite iteration steps in the absence of round-off errors by theoretical derivation. Some numerical examples are provided to verify the convergence performance of the presented method, which is superior to some existing numerical algorithms both in iteration steps and computation time.

Stackelberg-Game-Based Computation Offloading Method in Cloud–Edge Computing Networks

Offloading computation tasks through cloud–edge collaboration has been a promising way to improve the Quality of Service (QoS) of applications. Usually, cloud server (CS) and edge server (ES) are selfish and rational and, therefore, it is imperative to develop incentive mechanisms, which can encourage idle ESs or the CS to participate in the task offloading process. In this article, we propose a computation offloading method based on the game theory, which is suitable for cloud–edge computing networks. It is considered that the CS has a lot of computation tasks to conduct, and ESs usually have idle computational resources. The CS can offload computation tasks to ESs with idle computational resources to reduce its own cost and pressure, and ESs can profit by selling their computational resources. The interaction between the CS and ESs is modeled as a Stackelberg game, and the proposed game is analyzed by using the backward induction method. It is proved that the game can achieve a unique Nash equilibrium. Then, a gradient-based iterative search algorithm (GISA) is proposed to obtain the optimal solution in order to maximize the utility of the CS and ESs. Finally, numerical simulation results show that our proposed method greatly outperforms other benchmark schemes under different scenarios, and can encourage ESs to trade their computational resources with the CS effectively.

A relaxed gradient based iterative algorithm of the generalized Sylvester-conjugate matrix equation over centro-symmetric and centro-Hermitian matrices

The main purpose of this paper is to establish two relaxed gradient-based iterative (RGI) algorithms extending the Jacobi and Gauss–Seidel iterations for solving the generalized Sylvester-conjugate matrix equation , over centro-symmetric, and centro-Hermitian matrices. It is shown that the iterative methods, respectively, converge to the centro-symmetric and centro-Hermitian solutions for any initial centro-symmetric and centro-Hermitian matrices. We report numerical tests to show the effectiveness of the proposed approaches.

On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations

In this paper, we propose the full-rank and reduced-rank relaxed gradient-based iterative algorithms for solving the generalized coupled Sylvester-transpose matrix equations. We provide analytically the necessary and sufficient condition for the convergence of the proposed iterative algorithm and give explicitly the optimal step size such that the convergence rate of the algorithm is maximized. Some numerical examples are examined to confirm the feasibility and efficiency of the proposed algorithms.