Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm

Li, Leong Kwan; Shao, Sally S. L.; Yiu, Ka Fai Cedric

doi:10.3934/jimo.2011.7.385

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…The reverse propagation process starts if the errors do not satisfy the predefined condition, going from the output layer back to the hidden layer and finally to the input layer (Soybilgen, 2020). The weights and thresholds of the BPNN are continuously adjusted through this loop until the error satisfies the imposed requirements (Li et al. , 2011).…”

Section: Ppr Prediction Modelmentioning

confidence: 99%

GA-BP neural network modeling for project portfolio risk prediction

Bai

Wei

Zhang

et al. 2022

JEIM

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PurposeProject portfolio risk (PPR) management plays an important role in promoting the smooth implementation of a project portfolio (PP). Accurate PPR prediction helps managers cope with risks timely in complicated PP environments. However, studies on accurate PPR impact degree prediction, which consists of both risk occurrence probabilities and risk impact consequences considering project interactions, are limited. This study aims to model PPR prediction and expand PPR prediction tools.Design/methodology/approachIn this study, the authors build a PPR prediction model based on a genetic algorithm and back-propagation neural network (GA-BPNN) integrated with entropy-trapezoidal fuzzy numbers. Then, the authors verify the proposed model with real data and obtain PPR impact degrees.FindingsThe test results indicate that the proposed method achieves an average absolute error of 0.002 and an average prediction accuracy rate of 97.8%. The former is reduced by 0.038, while the latter is improved by 32.1% when compared with the results of the original BPNN model. Finally, the authors conduct an index sensitivity analysis for identifying critical risks to effectively control them.Originality/valueThis study develops a hybrid PPR prediction model that integrates a GA-BPNN with entropy-trapezoidal fuzzy numbers. The authors use this model to predict PPR impact degrees, which consist of both risk occurrence probabilities and risk impact consequences considering project interactions. The results provide insights into PPR management.

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Section: Ppr Prediction Modelmentioning

confidence: 99%

GA-BP neural network modeling for project portfolio risk prediction

Bai

Wei

Zhang

et al. 2022

JEIM

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“…Li, Shao and Yiu (( [7]) developed a novel learning algorithm WSSSA, a derivative-free and non-random learning algorithm, to solve the least square problems with recurrent neural dynamic constraints. The method is based on approximating a new trajectory which is a convex combination of the system output of the RNN and the desired trajectory with a ratio α ( [7]). This approach provides the best feasible solution for the nonlinear optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of the weighted state space search algorithm for recurrent neural networks

Li¹,

Shao²

2014

Numerical Algebra, Control &Amp; Optimization

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Recurrent neural networks (RNNs) have emerged as a promising tool in modeling nonlinear dynamical systems. The convergence is one of the most important issues of concern among the dynamical properties for the RNNs in practical applications. The reason is that the viability of many applications of RNNs depends on their convergence properties. We study in this paper the convergence properties of the weighted state space search algorithm (WSSSA)a derivative-free and non-random learning algorithm which searches the neighborhood of the target trajectory in the state space instead of the parameter space. Because there is no computation of partial derivatives involved, the WSSSA has a couple of salient features such as simple, fast and cost effective. In this study we provide a necessary and sufficient condition that required for the convergence of the WSSSA. Restrictions are offered that may help assure convergence of the of the WSSSA to the desired solution. The asymptotic rate of convergence is also analyzed. Our study gives insights into the problem and provides useful information for the actual design of the RNNs. A numerical example is given to support the theoretical analysis and to demonstrate that it is applicable to many applications.

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Analyzing the Impact of Wind on Trajectory Tracking for Unmanned Vehicles Based on Road Adhesion Coefficient Estimation

Luo,

Zheng

2024

Processes

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This paper presents a novel approach to address the challenge of trajectory tracking control in unmanned vehicles (UVs) operating on roads with varying ad hesion coefficients and subject to wind disturbances. The proposed method integrates real-time estimation of road adhesion coefficients with a wind disturbance model, embedding both into the trajectory tracking control system. Specifically, the Unscented Kalman Filter (UKF) is employed to dynamically estimate the road adhesion coefficients. These estimates are then combined with the wind disturbance model and incorporated into a Model Predictive Control (MPC) framework, enhancing the robustness and accuracy of trajectory tracking under varying conditions. The integrated simulation results from CarSim/Simulink demonstrate high accuracy in road adhesion coefficient estimation for trajectory tracking control, with tracking errors consistently remaining below 0.1 across different road adhesion conditions. For example, the road adhesion coefficient estimation error for the docking surface is 0.5%, and for the split road surface, it is 0.75%, indicating the approach’s applicability across a wide range of road conditions. Notably, when the wind speed reaches level-five intensity and a shelter-type vehicle is used as a test case, the proposed controller significantly outperforms the controller that does not consider wind effects. Under both high and low adhesion conditions, the controller reduces the yaw angle by approximately 15% and 30%, respectively, and the yaw rate by approximately 25% and 20%. These results provide strong evidence for the effectiveness of the proposed trajectory tracking controller in enhancing the stability and control performance of unmanned vehicles.

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Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm

Cited by 3 publications

References 15 publications

GA-BP neural network modeling for project portfolio risk prediction

GA-BP neural network modeling for project portfolio risk prediction

Convergence analysis of the weighted state space search algorithm for recurrent neural networks

Analyzing the Impact of Wind on Trajectory Tracking for Unmanned Vehicles Based on Road Adhesion Coefficient Estimation

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