A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao, Kaihong; Liu, Juqing; Lv, Xiaojun

doi:10.3390/fractalfract8020111

Cited by 13 publications

(4 citation statements)

References 72 publications

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“…Meanwhile, Figures 2, 4 and 6 also indicate that the solution of ( 1) is sensitive and dependent on parameters p i , α i and β i , i = 1, 2. In addition, inspired by recently published papers [9,47,48], we will investigate the Lyapunov stability of fractional differential equations, the coincidence theory of fractional differential equations, and fractional differential equations involving fractional derivative impulses in the future.…”

Section: Discussionmentioning

confidence: 99%

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

Lv,

Zhao,

Xie

2024

Symmetry

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The Hadamard fractional derivative and integral are important parts of fractional calculus which have been widely used in engineering, biology, neural networks, control theory, and so on. In addition, the periodic boundary conditions are an important class of symmetric two-point boundary conditions for differential equations and have wide applications. Therefore, this article considers a class of nonlinear Hadamard fractional coupling (p1,p2)-Laplacian systems with periodic boundary value conditions. Based on nonlinear analysis methods and the contraction mapping principle, we obtain some new and easily verifiable sufficient criteria for the existence and uniqueness of solutions to this system. Moreover, we further discuss the generalized Ulam–Hyers (GUH) stability of this problem by using some inequality techniques. Finally, three examples and simulations explain the correctness and availability of our main results.

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Section: Discussionmentioning

confidence: 99%

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

Lv,

Zhao,

Xie

2024

Symmetry

Self Cite

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“…It can be seen that compared to the basic distributed control methods, such as IQL and DDQNPER, the centralized control method based on DQN obviously has better control effects, and DQN converged at the 82nd generation, while IQN and DDQNPER converged at the 127th and 131st generations, respectively. In terms of system stability, some researchers have used a nonlinear analysis and inequality techniques to discuss the stability of system solutions and have combined numerical simulation algorithms to test the correctness and effectiveness of the theoretical results and simulation algorithms through examples [44,45]. In the work related to reinforcement learning, researchers have generally evaluated the control effect and stability of the built model based on the mean, standard deviation, median, and other parameters of multiple test experimental results for different random seed environments after the algorithm's convergence [4,46,47].…”

Section: Comparative Experimentsmentioning

confidence: 99%

CVDMARL: A Communication-Enhanced Value Decomposition Multi-Agent Reinforcement Learning Traffic Signal Control Method

Chang,

Ji,

Wang

et al. 2024

Sustainability

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Effective traffic signal control (TSC) plays an important role in reducing vehicle emissions and improving the sustainability of the transportation system. Recently, the feasibility of using multi-agent reinforcement learning technology for TSC has been widely verified. However, the process of mapping road network states onto actions has encountered many challenges, due to the limited communication between agents and the partial observability of the traffic environment. To address this problem, this paper proposes a communication-enhancement value decomposition, multi-agent reinforcement learning TSC method (CVDMARL). The model combines two communication methods: implicit and explicit communication, decouples the complex relationships among the multi-signal agents through the centralized-training and decentralized-execution paradigm, and uses a modified deep network to realize the mining and selective transmission of traffic flow features. We compare and analyze CVDMARL with six different baseline methods based on real datasets. The results show that compared to the optimal method MN_Light, among the baseline methods, CVDMARL’s queue length during peak hours was reduced by 9.12%, the waiting time was reduced by 7.67%, and the convergence algebra was reduced by 7.97%. While enriching the information content, it also reduces communication overhead and has better control effects, providing a new idea for solving the collaborative control problem of multi-signalized intersections.

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“…The interaction force between the robot and the external environment is approximately equivalent to the step signal. The step response of a first-order system is always stable without oscillation, so the admittance control model is stable [ 31 , 32 ].…”

Section: Admittance Control Modelmentioning

confidence: 99%

Robot Learning Method for Human-like Arm Skills Based on the Hybrid Primitive Framework

Li,

Han,

et al. 2024

Sensors

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This paper addresses the issue of how to endow robots with motion skills, flexibility, and adaptability similar to human arms. It innovatively proposes a hybrid-primitive-frame-based robot skill learning algorithm and utilizes the policy improvement with a path integral algorithm to optimize the parameters of the hybrid primitive framework, enabling robots to possess skills similar to human arms. Firstly, the end of the robot is dynamically modeled using an admittance control model to give the robot flexibility. Secondly, the dynamic movement primitives are employed to model the robot’s motion trajectory. Additionally, novel stiffness primitives and damping primitives are introduced to model the stiffness and damping parameters in the impedance model. The combination of the dynamic movement primitives, stiffness primitives, and damping primitives is called the hybrid primitive framework. Simulated experiments are designed to validate the effectiveness of the hybrid-primitive-frame-based robot skill learning algorithm, including point-to-point motion under external force disturbance and trajectory tracking under variable stiffness conditions.

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A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Cited by 13 publications

References 72 publications

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

CVDMARL: A Communication-Enhanced Value Decomposition Multi-Agent Reinforcement Learning Traffic Signal Control Method

Robot Learning Method for Human-like Arm Skills Based on the Hybrid Primitive Framework

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