Online spatiotemporal modeling for time-varying distributed parameter systems using Kernel-based Multilayer Extreme Learning Machine

2021 ◽  
Author(s):  
ChengJiu Zhu ◽  
HaiDong Yang ◽  
YaJun Fan ◽  
Bi Fan ◽  
KangKang Xu
Keyword(s):  
Extreme Learning Machine ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Spatiotemporal Modeling ◽  
Time Varying ◽  
Learning Machine

scholarly journals State Estimation for a Class of Distributed Parameter Systems with Time-Varying Delay over Mobile Sensor–Actuator Networks with Missing Measurements

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 661
Author(s):  
Huansen Fu ◽  
Baotong Cui ◽  
Bo Zhuang ◽  
Jianzhong Zhang
Keyword(s):  
State Estimation ◽  
Distributed Parameter Systems ◽  
Operator Semigroup ◽  
Distributed Parameter ◽  
Time Varying ◽  
Mobile Sensor ◽  
Missing Measurements ◽  
Time Varying Delay ◽  
Sensor Actuator ◽  
Varying Delay

This work proposes a state estimation strategy over mobile sensor–actuator networks with missing measurements for a class of distributed parameter systems (DPSs) with time-varying delay. Initially, taking advantage of the abstract development equation theory and operator semigroup method, this kind of delayed DPSs described by partial differential equations (PDEs) is derived for evolution equations. Subsequently, the distributed state estimators including consistency component and gain component are designed; the purpose is to estimate the original state distribution of the delayed DPSs with missing measurements. Then, a delay-dependent guidance approach is presented in the form of mobile control forces by constructing an appropriate Lyapunov function candidate. Furthermore, by applying Lyapunov stability theorem, operator semigroup theory, and a stochastic analysis approach, the estimation error systems have been proved asymptotically stable in the mean square sense, which indicates the estimators can approximate the original system states effectively when this kind of DPS has time-delay and the mobile sensors occur missing measurements. Finally, the correctness of control strategy is illustrated by numerical simulation results.

scholarly journals Online Regularized and Kernelized Extreme Learning Machines with Forgetting Mechanism

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinran Zhou ◽  
Zijian Liu ◽  
Congxu Zhu
Keyword(s):  
Extreme Learning Machine ◽  
Feedforward Neural Networks ◽  
Matrix Inversion ◽  
Time Varying ◽  
Extreme Learning Machines ◽  
Learning Machines ◽  
Matrix Expansion ◽  
Learning Machine ◽  
Hidden Layer ◽  
Forgetting Mechanism

To apply the single hidden-layer feedforward neural networks (SLFN) to identify time-varying system, online regularized extreme learning machine (ELM) with forgetting mechanism (FORELM) and online kernelized ELM with forgetting mechanism (FOKELM) are presented in this paper. The FORELM updates the output weights of SLFN recursively by using Sherman-Morrison formula, and it combines advantages of online sequential ELM with forgetting mechanism (FOS-ELM) and regularized online sequential ELM (ReOS-ELM); that is, it can capture the latest properties of identified system by studying a certain number of the newest samples and also can avoid issue of ill-conditioned matrix inversion by regularization. The FOKELM tackles the problem of matrix expansion of kernel based incremental ELM (KB-IELM) by deleting the oldest sample according to the block matrix inverse formula when samples occur continually. The experimental results show that the proposed FORELM and FOKELM have better stability than FOS-ELM and have higher accuracy than ReOS-ELM in nonstationary environments; moreover, FORELM and FOKELM have time efficiencies superiority over dynamic regression extreme learning machine (DR-ELM) under certain conditions.

Delay-Dependent Exponential Stabilization for Linear Distributed Parameter Systems With Time-Varying Delay

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Jun-Wei Wang ◽  
Chang-Yin Sun
Keyword(s):  
Time Delay ◽  
Distributed Parameter Systems ◽  
Dirichlet Boundary Conditions ◽  
Exponential Stabilization ◽  
Distributed Parameter ◽  
Control Input ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper extends the framework of Lyapunov–Krasovskii functional to address the problem of exponential stabilization for a class of linearly distributed parameter systems (DPSs) with continuous differentiable time-varying delay and a spatiotemporal control input, where the system model is described by parabolic partial differential-difference equations (PDdEs) subject to homogeneous Neumann or Dirichlet boundary conditions. By constructing an appropriate Lyapunov–Krasovskii functional candidate and using some inequality techniques (e.g., spatial integral form of Jensen's inequalities and vector-valued Wirtinger's inequalities), some delay-dependent exponential stabilization conditions are derived, and presented in terms of standard linear matrix inequalities (LMIs). These stabilization conditions are applicable to both slow-varying and fast-varying time delay cases. The detailed and rigorous proof of the closed-loop exponential stability is also provided in this paper. Moreover, the main results of this paper are reduced to the constant time delay case and extended to the stochastic time-varying delay case, and also extended to address the problem of exponential stabilization for linear parabolic PDdE systems with a temporal control input. The numerical simulation results of two examples show the effectiveness and merit of the main results.

GAO – Based Identification of Time – Varying Distributed Parameter Systems

2004 ◽  
Vol 37 (19) ◽  
pp. 125-130
Author(s):  
Mariana Georgieva Todorova ◽  
Borko Ganev Boyanov
Keyword(s):  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Time Varying
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