Mathematics

Research

18 pages, 1582 KiB

Open AccessArticle

RBFNN-Based Distributed Coverage Control on an Unknown Region

by Ankang Zhang and Xiaoling Wang

Mathematics 2024, 12(1), 111; https://doi.org/10.3390/math12010111 - 28 Dec 2023

Viewed by 475

In this paper, we investigate the problem of achieving distributed coverage control of a mobile sensor network on an unknown region using local measurements. To accomplish this objective, each sensor is equipped with two-layer dynamics. The upper layer dynamic employs a completely distributed [...] Read more.

In this paper, we investigate the problem of achieving distributed coverage control of a mobile sensor network on an unknown region using local measurements. To accomplish this objective, each sensor is equipped with two-layer dynamics. The upper layer dynamic employs a completely distributed observer algorithm on the target region for state estimation of the density function. The lower layer dynamic utilizes a radial basis function neural network-based motion algorithm, which involves only the estimated state obtained by the upper layer dynamics, to guide the sensors towards an optimal coverage configuration. We demonstrate that with only the joint detectability of the partial outputs measurement, it is possible to achieve distributed coverage control in the unknown region without requiring additional information about the density function, communication topology associated with the sensors, or coupling gains. Finally, two examples are used to validate the theoretical findings. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

18 pages, 719 KiB

Open AccessArticle

Fixed-Time Synchronization of Complex-Valued Coupled Networks with Hybrid Perturbations via Quantized Control

by Enli Wu, Yao Wang, Yundong Li, Kelin Li and Fei Luo

Mathematics 2023, 11(18), 3845; https://doi.org/10.3390/math11183845 - 07 Sep 2023

Cited by 1 | Viewed by 631

Abstract

This paper considers the fixed-time synchronization of complex-valued coupled networks (CVCNs) with hybrid perturbations (nonlinear bounded external perturbations and stochastic perturbations). To accomplish the target of fixed-time synchronization, the CVCNs can be separated into their real and imaginary parts and establish real-valued subsystems, [...] Read more.

This paper considers the fixed-time synchronization of complex-valued coupled networks (CVCNs) with hybrid perturbations (nonlinear bounded external perturbations and stochastic perturbations). To accomplish the target of fixed-time synchronization, the CVCNs can be separated into their real and imaginary parts and establish real-valued subsystems, a novel quantized controller is designed to overcome the difficulties induced by complex parameters, variables, and disturbances. By means of the Lyapunov stability theorem and the properties of the Wiener process, some sufficient conditions are presented for the selection of control parameters to guarantee the fixed-time synchronization, and an upper bound of the setting time is also obtained, which is only related to parameters of both systems and the controller, not to the initial conditions of the systems. Finally, a numerical simulation is given to show the correctness of theoretical results and the effectiveness of the control strategy. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

12 pages, 452 KiB

Open AccessArticle

Global Stabilization of Delayed Feedback Financial System Involved in Advertisement under Impulsive Disturbance

by Xinggui Li and Xinsong Yang

Mathematics 2023, 11(9), 2120; https://doi.org/10.3390/math11092120 - 29 Apr 2023

Viewed by 772

Abstract

Diffusion is an inevitable important factor in advertising dynamic systems. However, previous literature did not involve this important diffusion factor, and only involved the local stability of the advertising model. This paper develops a global stability criterion for the impulsive advertising dynamic model [...] Read more.

Diffusion is an inevitable important factor in advertising dynamic systems. However, previous literature did not involve this important diffusion factor, and only involved the local stability of the advertising model. This paper develops a global stability criterion for the impulsive advertising dynamic model with a feedback term under the influence of diffusion. Since global stability requires the unique existence of equilibrium points, variational methods are employed to solve it in the infinite dimensional function space, and then a global stability criterion of the system is derived by way of the impulse inequality lemma and orthogonal decomposition of a class of Sobolev spaces. Numerical simulations verify the effectiveness of the proposed method. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

12 pages, 368 KiB

Open AccessArticle

Impulsive Destabilization Effect on Novel Existence of Solution and Global μ-Stability for MNNs in Quaternion Field

by Qingchao Meng and Huamin Wang

Mathematics 2023, 11(8), 1869; https://doi.org/10.3390/math11081869 - 14 Apr 2023

Viewed by 961

Abstract

In this paper, a novel memristor-based non-delay Hopfield neural network with impulsive effects is designed in a quaternion field. Some special inequalities, differential inclusion, Hamilton rules and impulsive system theories are utilized in this manuscript to investigate potential solutions and obtain some sufficient [...] Read more.

In this paper, a novel memristor-based non-delay Hopfield neural network with impulsive effects is designed in a quaternion field. Some special inequalities, differential inclusion, Hamilton rules and impulsive system theories are utilized in this manuscript to investigate potential solutions and obtain some sufficient criteria. In addition, through choosing proper

μ (t)

and impulsive points, the global

μ

-stability of the solution is discussed and some sufficient criteria are presented by special technologies. Then, from the obtained sufficient criteria of global

μ

-stability, other stability criteria including exponential stability and power stability can be easily derived. Finally, one numerical example is given to illustrate the feasibility and validity of the derived conclusions. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

24 pages, 1431 KiB

Open AccessArticle

From Zeroing Dynamics to Zeroing-Gradient Dynamics for Solving Tracking Control Problem of Robot Manipulator Dynamic System with Linear Output or Nonlinear Output

by Zheng Zheng and Delu Zeng

Mathematics 2023, 11(7), 1605; https://doi.org/10.3390/math11071605 - 26 Mar 2023

Cited by 2 | Viewed by 1108

Abstract

With the vigorous development of mechanical intelligence in industrial manufacturing, tracking control dynamic systems have been widely applied in many aspects of industry. In this paper, we present one theorem to discuss the validity condition of a ZD model with order-n for solving [...] Read more.

With the vigorous development of mechanical intelligence in industrial manufacturing, tracking control dynamic systems have been widely applied in many aspects of industry. In this paper, we present one theorem to discuss the validity condition of a ZD model with order-n for solving the tracking control problem of a nonlinear problem by utilizing a Lie derivative. Moreover, we also give the unified formula of the ZD model with order-n and rigorously prove it mathematically. In addition, we present three other theorems to give the global exponential convergence property of the ZD controller u(t), and the steady-state tracking error bound of the ZGD controller u(t), and the radius bound where the steady-state tracking error converges exponentially. Finally, simulations are conducted to demonstrate the validity and parameter influences of the ZD model and ZGD model for solving the tracking control problem with a single linear or nonlinear output of the single-link manipulator with flexible joints. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

16 pages, 463 KiB

Open AccessArticle

Distributed Optimization Control for Heterogeneous Multiagent Systems under Directed Topologies

by Jingyi Wang, Danqi Liu, Jianwen Feng and Yi Zhao

Mathematics 2023, 11(6), 1479; https://doi.org/10.3390/math11061479 - 17 Mar 2023

Cited by 1 | Viewed by 1053

Abstract

This paper focuses on the solutions for the distributed optimization coordination problem (DOCP) for heterogeneous multiagent systems under directed topologies. To begin with, a different convex optimization problem is proposed, which implies a weighted average of the objective function of each agent. Sufficient [...] Read more.

This paper focuses on the solutions for the distributed optimization coordination problem (DOCP) for heterogeneous multiagent systems under directed topologies. To begin with, a different convex optimization problem is proposed, which implies a weighted average of the objective function of each agent. Sufficient conditions are set to ensure the unique solution for the DOCP. Then, despite the external disruption, a distributed control mechanism is constructed to drive the state of each agent to the auxiliary state in a finite time. Furthermore, it is demonstrated that the outputs of all agents can achieve the optimal value, ensuring global convergence. Moreover, the controller design rule is expanded with event-triggered communication, and there is no Zeno behavior. Finally, to exemplify the usefulness of the theoretical conclusions, a simulation example is offered. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

14 pages, 783 KiB

Open AccessArticle

Photovoltaic Power Prediction Based on VMD-BRNN-TSP

by Guici Chen, Tingting Zhang, Wenyu Qu and Wenbo Wang

Mathematics 2023, 11(4), 1033; https://doi.org/10.3390/math11041033 - 17 Feb 2023

Cited by 4 | Viewed by 1188

Abstract

Overfitting often occurs in neural network training, and neural networks with higher generalization ability are less prone to this phenomenon. Aiming at the problem that the generalization ability of photovoltaic (PV) power prediction model is insufficient, a PV power time-sharing prediction (TSP) model [...] Read more.

Overfitting often occurs in neural network training, and neural networks with higher generalization ability are less prone to this phenomenon. Aiming at the problem that the generalization ability of photovoltaic (PV) power prediction model is insufficient, a PV power time-sharing prediction (TSP) model combining variational mode decomposition (VMD) and Bayesian regularization neural network (BRNN) is proposed. Firstly, the meteorological sequences related to the output power are selected by mutual information (MI) analysis. Secondly, VMD processing is performed on the filtered sequences, which is aimed at reducing the non-stationarity of the data; then, normalized cross-correlation (NCC) and signal-to-noise ratio (SNR) between the components obtained by signal decomposition and the original data are calculated, after which the key influencing factors are screened out to eliminate the correlation and redundancy of the data. Finally, the filtered meteorological sequences are divided into two datasets based on whether the irradiance of the day is zero or not. Meanwhile, the predictions are performed using BRNN for each of the two datasets. Then, the results are reordered in chronological order, and the prediction of PV power is realized conclusively. It was experimentally verified that the mean absolute value error (

M A E

) of the method proposed in this paper is

0.1281

, which is reduced by

40.28 %

compared with the back propagation neural network (BPNN) model on the same dataset, the mean squared error (

M S E

) is

0.0962

, and the coefficient of determination (

R^{2}

) is

0.9907

. Other error indicators also confirm that VMD is of much significance and TSP is contributive. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

21 pages, 2555 KiB

Open AccessArticle

Prescribed Settling Time Adaptive Neural Network Consensus Control of Multiagent Systems with Unknown Time-Varying Input Dead-Zone

by Wenqiang Wu, Jiarui Liu, Fangyi Li, Yuanqing Zhang and Zikai Hu

Mathematics 2023, 11(4), 988; https://doi.org/10.3390/math11040988 - 15 Feb 2023

Viewed by 1036

Abstract

For a class of multiagent systems with an unknown time-varying input dead-zone, a prescribed settling time adaptive neural network consensus control method is developed. In practical applications, some control signals are difficult to use effectively due to the extensive existence of an input [...] Read more.

For a class of multiagent systems with an unknown time-varying input dead-zone, a prescribed settling time adaptive neural network consensus control method is developed. In practical applications, some control signals are difficult to use effectively due to the extensive existence of an input dead-zone. Moreover, the time-varying input gains further seriously degrade the performance of the systems and even cause system instability. In addition, multiagent systems need frequent communication to ensure a system’s consistency. This may lead to communication congestion. To solve this problem, an event-triggered adaptive neural network control method is proposed. Further, combined with the prescribed settling time transform function, the developed consensus method greatly increases the convergence rate. It is demonstrated that all followers of multiagent systems can track the virtual leader within a prescribed time and not exhibit Zeno behavior. Finally, the theoretical analysis and simulation verify the effectiveness of the designed control method. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

18 pages, 610 KiB

Open AccessArticle

New Results on Finite-Time Synchronization Control of Chaotic Memristor-Based Inertial Neural Networks with Time-Varying Delays

by Jun Wang, Yongqiang Tian, Lanfeng Hua, Kaibo Shi, Shouming Zhong and Shiping Wen

Mathematics 2023, 11(3), 684; https://doi.org/10.3390/math11030684 - 29 Jan 2023

Cited by 18 | Viewed by 1467

Abstract

In this work, we are concerned with the finite-time synchronization (FTS) control issue of the drive and response delayed memristor-based inertial neural networks (MINNs). Firstly, a novel finite-time stability lemma is developed, which is different from the existing finite-time stability criteria and extends [...] Read more.

In this work, we are concerned with the finite-time synchronization (FTS) control issue of the drive and response delayed memristor-based inertial neural networks (MINNs). Firstly, a novel finite-time stability lemma is developed, which is different from the existing finite-time stability criteria and extends the previous results. Secondly, by constructing an appropriate Lyapunov function, designing effective delay-dependent feedback controllers and combining the finite-time control theory with a new non-reduced order method (NROD), several novel theoretical criteria to ensure the FTS for the studied MINNs are provided. In addition, the obtained theoretical results are established in a more general framework than the previous works and widen the application scope. Lastly, we illustrate the practicality and validity of the theoretical results via some numerical examples. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

21 pages, 435 KiB

Open AccessArticle

Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays

by Wenjun Dong, Yujiao Huang, Tingan Chen, Xinggang Fan and Haixia Long

Mathematics 2022, 10(13), 2157; https://doi.org/10.3390/math10132157 - 21 Jun 2022

Viewed by 1044

Abstract

This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neural networks with time delays. By separating the quaternion-valued [...] Read more.

This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neural networks with time delays. By separating the quaternion-valued neural networks into a real part and three imaginary parts, separating the quaternion field into

3^{4 n}

subregions, and using the intermediate value theorem, sufficient conditions are proposed to ensure quaternion-valued neural networks have

3^{4 n}

equilibrium points. According to the Halanay inequality, the conditions for the existence of

2^{4 n}

local Lagrange exponentially stable equilibria of quaternion-valued neural networks are established. The obtained stability results improve and extend the existing ones. Under the same conditions, quaternion-valued neural networks have more stable equilibrium points than complex-valued neural networks and real-valued neural networks. The validity of the theoretical results were verified by an example. Full article

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematic Control and Artificial Intelligence

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (10 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI