Multi-AUV Dynamic Maneuver Countermeasure Algorithm Based on Interval Information Game and Fractional-Order DE

Liu, Lu; Wang, Jian; Zhang, Lichuan; Zhang, Shuo

doi:10.3390/fractalfract6050235

Cited by 39 publications

(15 citation statements)

References 27 publications

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“…It is important to note that the suggested technique is very simple to use, quick convergent, and trustworthy, and it may be used to find both approximate and precise solutions to the issue under consideration. e Maple code is being created for this mentioned issue utilising a replicating kernel Hilbert space method, and it is being used to produce fresh findings as well as to make comparisons between results [34][35][36][37].…”

Section: Resultsmentioning

confidence: 99%

Convergence Analysis Hilbert Space Approach for Fuzzy Integro‐Differential Models

Zhang

2022

Journal of Mathematics

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In this paper, we present and demonstrate an innovative numerical method, which makes use of fuzzy numbers and fuzzy parameters that is effective in the solution of fuzzy type Volterra integro-differential equations, which was previously thought to be impossible using conventional methods. The first application of a technique for solving Volterra integro-differential equations of the fuzzy type, which was devised and tested in this paper, is shown here. This is the first time that this approach has been used. This system’s overall quality may be improved as a consequence of the use of the Hilbert space replicating kernel idea, which is a possibility. Separate evaluations are made of the algorithms’ correctness and sloppiness, as well as their foundations in the computationally effective kernel Hilbert space, which has been extensively researched in the past. Numerical examples are provided of the article to demonstrate how the technique outlined before may achieve convergence and accuracy. Here are a few illustrations to help understand that it is possible to deal with physical issues that require complicated geometric calculations with the assistance of the method explained in this article.

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Section: Resultsmentioning

confidence: 99%

Convergence Analysis Hilbert Space Approach for Fuzzy Integro‐Differential Models

Zhang

2022

Journal of Mathematics

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“…A fractional derivative is a generalization of the integer-order derivatives, which have been widely applied in different fields, such as dynamics, engineering, computer science, etc. [22][23][24][25][26][27][28]. Fractional derivative damping is usually utilized to describe the viscoelastic damping model.…”

Section: Fractional Derivativementioning

confidence: 99%

Stationary Response of a Kind of Nonlinear Stochastic Systems with Variable Mass and Fractional Derivative Damping

2022

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Viscoelasticity and variable mass are common phenomena in Micro-Electro-Mechanical Systems (MEMS), and could be described by a fractional derivative damping and a stochastic process, respectively. To study the dynamic influence cased by the viscoelasticity and variable mass, stationary response of a kind of nonlinear stochastic systems with stochastic variable-mass and fractional derivative, damping is investigated in this paper. Firstly, an approximately equivalent system of the studied nonlinear stochastic system is presented according to the Taylor expansion technique. Then, based on stochastic averaging of energy envelope, the corresponding Fokker–Plank–Kolmogorov (FPK) equation is deduced, which gives an approximated analytical solution of stationary response. Finally, a nonlinear oscillator with variable mass and fractional derivative damping is proposed in numerical simulations. The approximated analytical solution is compared with Monte Carlo numerical solution, which could verify the effectiveness of the obtained results.

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“…The TD method is necessarily convergent under the condition of a decreasing learning rate [32][33][34][35]. The multi-AUV cooperative navigation system needs to break through the underwater communication limitations, load restrictions, and interference in the complex ocean environment to propose a navigation method that meets the formation and mission requirements within the constraints [36]. The reinforcement learning method does not require a complete mathematical model but can solve the communication limitation problem, which can lay the foundation for AUV cooperative formation and clustering research.…”

Section: Markov Decision Processmentioning

confidence: 99%

Multi-AUV Cooperative Navigation Algorithm Based on Temporal Difference Method

Ren

Zhang

Liu

et al. 2022

JMSE

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To reduce the cooperative positioning error and improve the navigation accuracy, a single master–slave AUV cooperative navigation method is proposed in this paper, which mainly focuses on planning the optimal path of the master AUV by the time difference (TD) method, under the premise that the path of the slave AUV has been planned. First, the model of multi-AUV cooperative navigation is established, and the observable problem of the system is analyzed. Second, for the single master–slave AUV cooperative navigation system, a Markov decision process (MDP)-based multi-AUV cooperative navigation model is established, and the master AUV path planning method is designed based on the TD method. Finally, the extended Kalman filter (EKF) and unscented Kalman filter (UKF) nonlinear filtering algorithms are applied to simulate and verify the algorithm that is proposed in this paper. The results show that the theoretical positioning error of the slave AUV can be controlled to about 3.2m by planning the path of the master AUV using the TD method. This method can not only reduce the observation error and positioning error of the slave AUV during the whole cooperative navigation process, but also keep the relative measurement distance between the master AUV and the slave AUV within an appropriate range.

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Multi-AUV Dynamic Maneuver Countermeasure Algorithm Based on Interval Information Game and Fractional-Order DE

Cited by 39 publications

References 27 publications

Convergence Analysis Hilbert Space Approach for Fuzzy Integro‐Differential Models

Convergence Analysis Hilbert Space Approach for Fuzzy Integro‐Differential Models

Stationary Response of a Kind of Nonlinear Stochastic Systems with Variable Mass and Fractional Derivative Damping

Multi-AUV Cooperative Navigation Algorithm Based on Temporal Difference Method

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