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deterministic learning from control of nonlinear systems with disturbances

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Progress in Natural Science:Materials International 2009年第8期19卷 1011-1019页

作者： Guopeng Zhou a,b, Cong Wang a, a School of Automation and Center for Control and Optimization, South China University of Technology, Guangzhou 510640, China b College of Mathematics and Statistics, Xianning University, Xianning 437005, China School of Automation and Center for Control and Optimization South China University of Technology Guangzhou 510640 China College of Mathematics and Statistics Xianning University Xianning 437005 China

In this paper, we investigate deterministic learning in environments with disturbances. We will show that for a class of uncertain nonlinear systems with bounded disturbances, by using an appropriately designed adaptive neural controller, the disturbances are attenuated and the system output tracks a periodic orbit in finite time. As radial basis function (RBF) neural networks (NN) are employed, this leads to the satisfaction of a partial persistence of the excitation (PE) condition. By using the uniform complete observability (UCO) technique, it is analyzed that partial estimated NN weights will converge to a neighborhood of zero, with the size of the neighborhood depending on the amplitude of disturbances as well as on the control gains. Locally-accurate approximation of unknown system dynamics can still be achieved in the stable NN control process. The approximation error level is influenced by the amplitude of disturbances. The obtained knowledge of system dynamics can be reused in another control process towards stability and improved performance. Simulation studies are included to demonstrate the effectiveness of the approach.

关键词： deterministic learning Adaptive NN control Disturbance Partial PE condition Uniform complete observability

deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

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控制理论与应用（英文版） 2012年第2期10卷 201-209页

作者： Tao Peng Cong Wang College of Automation Science and Engineering South China University of Technology Guangzhou Guangdong 510640 China

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deter- ministic learning. The plants are distributed parameter systems （DPS） describing homogeneous and isotropic elastic vibrat- ing strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation （ODE）. The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approxi- mately accurate neural network （NN） approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.

关键词： deterministic learning Wave system Completely resonant Finite-dimensional approximation RBF neu-ral networks System dynamics

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Dynamical pattern recognition for univariate time series and its application to an axial compressor

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Control Theory and Technology 2024年第1期22卷 39-55页

作者： Jingtao Hu Weiming Wu Zejian Zhu Cong Wang Center for Intelligent Medical Engineering School of Control Science and TechnologyShandong UniversityJinan250061ShandongChina School of Automation Science and Engineering South China University of TechnologyGuangzhou510641GuangdongChina

In this paper, a learning and recognition approach is proposed for univariate time series composed of output measurements of general nonlinear dynamical systems. Firstly, a class of dynamical systems in the canonical form is derived to describe the univariate time series by introducing coordinate transformation. An observer-based deterministic learning technique is then adopted to achieve dynamical modeling of the associated transformed systems of the training univariate time series, and the modeling results in the form of radial basis function network (RBFN) models are stored in a pattern library. Subsequently, multiple observer-based dynamical estimators containing the RBFN models in the pattern library are constructed for a test univariate time series, and a recognition decision scheme is proposed by the derived recognition indicator. On this basis, more concise recognition conditions are provided, which is beneficial for verifying the recognition results. Finally, simulation studies on the Rossler system and aero-engine stall warning verify the effectiveness of the proposed approach.

关键词： Dynamical pattern recognition deterministic learning Stall warning Radial basis function network Sampled-data observer

Modeling of nonlinear dynamical systems based on deterministic learning and structural stability

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Science China(Information Sciences) 2016年第9期59卷 91-106页

作者： Danfeng CHEN Cong WANG Xunde DONG School of Automation Science and Engineering South China University of Technology Guangdong Key Laboratory of Biomedical Engineering South China University of Technology School of Mathematical Sciences South China University of Technology

Recently, a deterministic learning(DL) theory was proposed for accurate identification of system dynamics for nonlinear dynamical systems. In this paper, we further investigate the problem of modeling or identification of the partial derivative of dynamics for dynamical systems. Firstly, based on the locally accurate identification of the unknown system dynamics via deterministic learning, the modeling of its partial derivative of dynamics along the periodic or periodic-like trajectory is obtained by using the mathematical concept of directional derivative. Then, with accurately identified system dynamics and the partial derivative of dynamics,a C1-norm modeling approach is proposed from the perspective of structural stability, which can be used for quantitatively measuring the topological similarities between different dynamical systems. This provides more incentives for further applications in the classification of dynamical systems and patterns, as well as the prediction of bifurcation and chaos. Simulation studies are included to demonstrate the effectiveness of this modeling approach.

关键词： system modeling system identification deterministic learning nonlinear dynamics structural sta bility topological equivalence

Electrocardiogram(ECG) pattern modeling and recognition via deterministic learning

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Control Theory and Technology 2014年第4期12卷 333-344页

作者： Xunde DONG Cong WANG Junmin HU Shanxing OU School of Automation Science and Engineering South China University of Technology Department of Radiology General Hospital of Guangzhou Military Command

A method for electrocardiogram （ECG） pattern modeling and recognition via deterministic learning theory is presented in this paper. Instead of recognizing ECG signals beat-to-beat, each ECG signal which contains a number of heartbeats is recognized. The method is based entirely on the temporal features （i.e., the dynamics） of ECG patterns, which contains complete information of ECG patterns. A dynamical model is employed to demonstrate the method, which is capable of generating synthetic ECG signals. Based on the dynamical model, the method is shown in the following two phases： the identification （training） phase and the recognition （test） phase. In the identification phase, the dynamics of ECG patterns is accurately modeled and expressed as constant RBF neural weights through the deterministic learning. In the recognition phase, the modeling results are used for ECG pattern recognition. The main feature of the proposed method is that the dynamics of ECG patterns is accurately modeled and is used for ECG pattern recognition. Experimental studies using the Physikalisch-Technische Bundesanstalt （PTB） database are included to demonstrate the effectiveness of the approach.

关键词： ECG Pattern recognition deterministic learning Dynamics Temporal features

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Fault detection for nonlinear discrete-time systems via deterministic learning

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Control Theory and Technology 2016年第2期14卷 159-175页

作者： Junmin HU School of Automation Science and Engineering South China University of Technology Guangzhou Guangdong 510640 China Guangdong Key Laboratory of Biomedical Engineering Guangzhou Guangdong 510640 China

Recently, an approach for the rapid detection of small oscillation faults based on deterministic learning theory was proposed for continuous-time systems. In this paper, a fault detection scheme is proposed for a class of nonlinear discrete-time systems via deterministic learning. By using a discrete-time extension of deterministic learning algorithm, the general fault functions （i.e., the internal dynamics） underlying normal and fault modes of nonlinear discrete-time systems are locally-accurately approximated by discrete-time dynamical radial basis function （RBF） networks. Then, a bank of estimators with the obtained knowledge of system dynamics embedded is constructed, and a set of residuals are obtained and used to measure the differences between the dynamics of the monitored system and the dynamics of the trained systems. A fault detection decision scheme is presented according to the smallest residual principle, i.e., the occurrence of a fault can be detected in a discrete-time setting by comparing the magnitude of residuals. The fault detectability analysis is carried out and the upper bound of detection time is derived. A simulation example is given to illustrate the effectiveness of the proposed scheme.

关键词： Fault detection nonlinear discrete-time systems deterministic learning neural networks locally accurate modeling

Design and performance analysis of deterministic learning of sampled-data nonlinear systems

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Science China(Information Sciences) 2014年第3期57卷 204-221页

作者： YUAN ChengZhi WANG Cong College of Automation and the Center for Control and Optimization South China University of Technology

In this paper,we extend the deterministic learning theory to sampled-data nonlinear systems.Based on the Euler approximate model,the adaptive neural network identifier with a normalized learning algorithm is proposed.It is proven that by properly setting the sampling period,the overall system can be guaranteed to be stable and partial neural network weights can exponentially converge to their optimal values under the satisfaction of the partial persistent excitation(PE)condition.Consequently,locally accurate learning of the nonlinear dynamics can be achieved,and the knowledge can be represented by using constant-weight neural networks.Furthermore,we present a performance analysis for the learning algorithm by developing explicit bounds on the learning rate and accuracy.Several factors that influence learning,including the PE level,the learning gain,and the sampling period,are investigated.Simulation studies are included to demonstrate the efectiveness of the approach.

关键词： neural network identification deterministic learning persistent excitation sampled-data systems radial basis function networks(RBFNs)

deterministic learning Control of Disturbed Brunovsky Systems

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Deterministic Learning Control of Disturbed Brunovsky System...

deterministic learning Based Compass Biped Robot Control

第二十七届中国控制会议

作者： Zhou Guopeng1,2,Wang Cong1,Zhao Min3 1.School of Automation,South China University of Technology Guangzhou 510641,P.R.China 2.Mathematics Department,Xianning College,Xianning HuBei 437005,P.R.China 3.School of Electronic and Information Engineering,South China University of Technology Guangzhou,510641,P.R.China

deterministic learning control was investigated recently.Due to the existence of time varying disturbances,learning capability may be influenced.In this paper,deterministic learning theory is analyzed in environments with disturbances.With an appropriately designed neural adaptive controller,the disturbances are attenuated and partial Persistent Excitation（PE） condition for the radial basis neural network（RBF NN） is satisfied.By imposing uniform complete observability（UCO） technique,the tracking error and the neural weight estimate error exponentially converge to a neighborhood of zero in finite time and the size of the neighborhood relies not only on the amplitude of disturbances but also on the control gains.After the learning process,the estimated neural weights are stored in RBF NN and a constant neural controller can be implemented.The simulation shows the effectiveness of this scheme.

关键词： deterministic learning Disturbance Partial persistent excitation Uniform complete observability Radial basis function neural network

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Deterministic Learning Based Compass Biped Robot Control