Responses of stochastic dynamical systems by the generalized cell mapping method with deep learning

Yue, Xiaole; Cui, Suping; Pei, Bin; Xu, Yong

doi:10.1016/j.ijnonlinmec.2022.104190

Cited by 10 publications

(1 citation statement)

References 45 publications

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“…With regards to the nonlinear systems, GCM and its improved algorithms have been used in many fields such as fuzzy control, optimum trajectory planning in robotic systems, optimal control of populations, and semiactive control, among others [22][23][24]. Moreover, extensive efforts have been devoted to explore pursuit-evasion problems in the so-called differential games [25].…”

Section: Introductionmentioning

confidence: 99%

Pattern-Moving-Modelling and Analysis Based on Clustered Generalized Cell Mapping for a Class of Complex Systems

Li,

Xu,

2024

Processes

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Considering a class of complex nonlinear systems whose dynamics are mostly governed by statistical regulations, the pattern-moving theory was developed to characterise such systems and successfully estimate the outputs or states. However, since the pattern class variable is not computable directly, this study establishes a clustered generalized cell mapping (C-GCM) to reveal system characteristics. C-GCM is a two-stage approach consisting of a pattern-moving-based description and analysis method. First, a density algorithm, named density-based spatial clustering of applications with noise (DBSCAN), is designed to obtain cell space Ω and the corresponding classification guidelines; this algorithm is initiated after the initial pre-image cells, and the total number of entity cells amounts to Ns. Then, the GCM provides several image cells based on a cell mapping function that refers to the multivariate ARMAX model. The global dynamic analysis employing both searching and storing algorithms depend on the attractor, domain of attraction, and periodic cell groups. At last, simulation results of two examples emphasise the practicality as well as efficacy of the technique suggested. The chief aim of this study was to offer a new perspective for a class of complex systems that could inspire research into nonmechanistic principles modelling and application to nonlinear systems.

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Section: Introductionmentioning

confidence: 99%

Pattern-Moving-Modelling and Analysis Based on Clustered Generalized Cell Mapping for a Class of Complex Systems

Li,

Xu,

2024

Processes

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Pattern‐moving‐based dynamic description and optimal control for non‐Newtonian mechanical systems with generalized cell mapping

Li,

Xu,

Zhao

et al. 2024

Can J Chem Eng

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This article focuses on the problem of modelling and control for a non‐Newtonian mechanical system that may be subject to the statistical law instead of the traditional Newtonian principles mechanics. A discrete method, synthesizing the generalized cell mapping (GCM) together with dynamic programming (DP), with inverse search strategy, using pattern moving theory (PMT) framework, was proposed. The basic idea is to describe and control the system's dynamic peculiarity utilizing pattern class variable in ‘pattern moving space’. First, a few prior concepts were reviewed, including PMT, cell mapping, and optimal control for this kind system. Then, we articulated a cross‐mapping method to analyze the system dynamic behaviour, which takes into account the computational and statistical properties of pattern class variable simultaneously. For system optimal control, the improved GCM and cost function were performed to determine the discrete optimal control table (DOCT) in accordance with dynamic programming and inverse search. Finally, simulation results of two cases demonstrate the efficiency and practicality of the proposed approach. The study has resulted in a solution of describing and controlling based on pattern class variable for non‐Newtonian mechanical systems, and its main objective was to give a different perspective in term of research into non mechanistic principles modelling and application of nonlinear systems.

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Parameter identification of dynamical systems based on short-term prediction by the generalized cell mapping method with deep learning

Yue,

Jing,

Liu

et al. 2024

Nonlinear Dyn

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Responses of stochastic dynamical systems by the generalized cell mapping method with deep learning

Cited by 10 publications

References 45 publications

Pattern-Moving-Modelling and Analysis Based on Clustered Generalized Cell Mapping for a Class of Complex Systems

Pattern-Moving-Modelling and Analysis Based on Clustered Generalized Cell Mapping for a Class of Complex Systems

Pattern‐moving‐based dynamic description and optimal control for non‐Newtonian mechanical systems with generalized cell mapping

Parameter identification of dynamical systems based on short-term prediction by the generalized cell mapping method with deep learning

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