Set-Membership Filtering Approach to Dynamic Event-Triggered Fault Estimation for a Class of Nonlinear Time-Varying Complex Networks

The present study addresses the problem of fault estimation for a specific class of nonlinear time-varying complex networks,utilizing an unknown-input-observer approach within the framework of dynamic event-triggered mechanism(DETM).In order to optimize communication resource utilization,the DETM is employed to determine whether the current measurement data should be transmitted to the estimator or not.To guarantee a satisfactory estimation performance for the fault signal,an unknown-input-observer-based estimator is constructed to decouple the estimation error dynamics from the influence of fault signals.The aim of this paper is to find the suitable estimator parameters under the effects of DETM such that both the state estimates and fault estimates are confined within two sets of closed ellipsoid domains.The techniques of recursive matrix inequality are applied to derive sufficient conditions for the existence of the desired estimator,ensuring that the specified performance requirements are met under certain conditions.Then,the estimator gains are derived by minimizing the ellipsoid domain in the sense of trace and a recursive estimator parameter design algorithm is then provided.Finally,a numerical example is conducted to demonstrate the effectiveness of the designed estimator.

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

This paper studies the asymptotic behavior of solutions for nonlinear RLCnetwoiks which have the following form The function p i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditiolts. Under the assumption that every element value involving voltage source is asymptotically constallt, we establish four creteria for all solutiolls of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited uonliltear circuits.This results generalize those of Brayton and Moser[1,2].

NONLINEAR STABLE ADAPTIVE CONTROL BASED UPON ELMAN NETWORKS

Elman networks' dynamical modeling capability is discussed in this paper firstly.According to Elman networks' unique structure,a weight training algorithm is designed and a nonlinear adaptive controller is constructed.Without the PE presumption,neural networks controller's closed loop properties are studied and the whole Elman networks' passivity is demonstrated.

Fault detection for nonlinear networked control systems based on fuzzy observer

Security and reliability must be focused on control sys- tems firstly, and fault detection and diagnosis （FDD） is the main theory and technology. Now, there are many positive results in FDD for linear networked control systems （LNCSs）, but nonlinear networked control systems （NNCSs） are less involved. Based on the T-S fuzzy-modeling theory, NNCSs are modeled and network random time-delays are changed into the unknown bounded uncertain part without changing its structure. Then a fuzzy state observer is designed and an observer-based fault detection approach for an NNCS is presented. The main results are given and the relative theories are proved in detail. Finally, some simulation results are given and demonstrate the proposed method is effective.

Robust fault detection for a class of nonlinear network control system with communication delay

To investigate a class of nonlinear network control system, a robust fault diagnosis method is presented based on the robust state observer. To access the objective that the designed robust filter is maximally tolerant to disturbances and sensitive to fault, the robustness and stability properties of the fault diagnosis scheme are established rigorously. Using the residual vector, a fault tolerant controller is established in order to guarantee the stability of the closed-loop system, and the controller law can be obtained by solving a set of linear matrix inequalities. Then, some relevant sufficient conditions for the existence of a solution are given by applying Lyapunov stability theory. Finally, a simulation example is performed to show the effectiveness of the proposed approach.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Impulsive controller design for nonlinear networked control systems with time delay and packet dropouts

The globally exponential stability of nonlinear impul- sive networked control systems （NINCS） with time delay and packet dropouts is investigated. By applying Lyapunov function theory, sufficient conditions on the global exponential stability are derived by introducing a comparison system and estimating the corresponding Cauchy matrix. An impulsive controller is explicitly designed to achieve exponential stability and ensure state con- verge with a given decay rate for the system. The Lorenz oscillator system is presented as a numerical example to illustrate the theo- retical results and effectiveness of the proposed controller design procedure.

Optimal Neuro-Control Strategy for Nonlinear Systems With Asymmetric Input Constraints

In this paper,we present an optimal neuro-control scheme for continuous-time(CT)nonlinear systems with asymmetric input constraints.Initially,we introduce a discounted cost function for the CT nonlinear systems in order to handle the asymmetric input constraints.Then,we develop a Hamilton-Jacobi-Bellman equation(HJBE),which arises in the discounted cost optimal control problem.To obtain the optimal neurocontroller,we utilize a critic neural network(CNN)to solve the HJBE under the framework of reinforcement learning.The CNN's weight vector is tuned via the gradient descent approach.Based on the Lyapunov method,we prove that uniform ultimate boundedness of the CNN's weight vector and the closed-loop system is guaranteed.Finally,we verify the effectiveness of the present optimal neuro-control strategy through performing simulations of two examples.

The application of neural networks to comprehensive prediction by seismology prediction method

BP neural networks is used to mid-term earthquake prediction in this paper. Some usual prediction parameters of seismology are used as the import units of neural networks. And the export units of neural networks is called as the character parameter W_0 describing enhancement of seismicity. We applied this method to space scanning of North China. The result shows that the mid-term anomalous zone of W_0-value usually appeared obviously around the future epicenter 1~3 years before earthquake. It is effective to mid-term prediction.

Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are constructed based on its Lax pair.Nonlocal discrete generalized(m,N−m)-fold Darboux transformation is extended and applied to solve this system.As an application of the method,we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized(1,N−1)-fold Darboux transformation,respectively.By using the asymptotic and graphic analysis,structures of one-,two-,three-and four-soliton solutions are shown and discussed graphically.We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures.It is shown that the soliton structures are quite different between discrete local and nonlocal systems.Results given in this paper may be helpful for understanding the electrical signals propagation.

Novel Multisoliton Solutions of Some Soliton Equations

The novel multisoliton solutions for the nonlinear lumped self-dual network equations, Toda lattice and KP equation were obtained by using the Hirota direct method.

ON-LINE STATE PREDICTION OF ENGINES BASED ON FLAT NEURAL NETWORK

A flat neural network is designed for the on line state prediction of engine. To reduce the computational cost of weight matrix, a fast recursive algorithm is derived according to the pseudoinverse formula of a partition matrix. Furthermore, the forgetting factor approach is introduced to improve predictive accuracy and robustness of the model. The experiment results indicate that the improved neural network is of good accuracy and strong robustness in prediction, and can apply for the on line prediction of nonlinear multi input multi output systems like vehicle engines.

A Systematic Design of Emulators for Multivariable Non Square and Nonlinear Systems

In this paper, multimodel and neural emulators are proposed for uncoupled multivariable nonlinear plants with unknown dynamics. The contributions of this paper are to extend the emulators to multivariable non square systems and to propose a systematic method to compute the multimodel synthesis parameters. The effectiveness of the proposed emulators is shown through two simulation examples. The obtained results are very satisfactory, they illustrate the performance of both emulators and show the advantages of the multimodel emulator relatively to the neural one.

NN-based Output Tracking for More General Stochastic Nonlinear Systems with Unknown Control Coefficients

This paper considers the output tracking problem for more general classes of stochastic nonlinear systems with unknown control coefficients and driven by noise of unknown covariance. By utilizing the radial basis function neural network approximation method and backstepping technique, we successfully construct a controller to guarantee the solution process to be bounded in probability.The tracking error signal is 4th-moment semi-globally uniformly ultimately bounded（SGUUB） and can be regulated into a small neighborhood of the origin in probability. A simulation example is given to demonstrate the effectiveness of the control scheme.

Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

In this paper,we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation(QPME).Three variational formulations of this nonlinear PDE are presented:a strong formulation and two weak formulations.For the strong formulation,the solution is directly parameterized with a neural network and optimized by minimizing the PDEresidual.It can be proved that the convergence of the optimization problem guarantees the convergence of the approximate solution in the L^(1)sense.Theweak formulations are derived following(Brenier in Examples of hidden convexity in nonlinear PDEs,2020)which characterizes the very weak solutions of QPME.Specifically speaking,the solutions are represented with intermediate functions who are parameterized with neural networks and are trained to optimize the weak formulations.Extensive numerical tests are further carried out to investigate the pros and cons of each formulation in low and high dimensions.This is an initial exploration made along the line of solving high-dimensional nonlinear PDEs with neural network-based methods,which we hope can provide some useful experience for future investigations.

Performance Comparison of Artificial Neural Network Models for Daily Rainfall Prediction

With an aim to predict rainfall one-day in advance, this paper adopted different neural network models such as feed forward back propagation neural network （BPN）, cascade-forward back propagation neural network （CBPN）, distributed time delay neural network （DTDNN） and nonlinear autoregressive exogenous network （NARX）, and compared their forecasting capabilities. The study deals with two data sets, one containing daily rainfall, temperature and humidity data of Nilgiris and the other containing only daily rainfall data from 14 rain gauge stations located in and around Coonoor （a taluk of Nilgiris）. Based on the performance analysis, NARX network outperformed all the other networks. Though there is no major difference in the performances of BPN, CBPN and DTDNN, yet BPN performed considerably well confirming its prediction capabilities. Levenberg Marquardt proved to be the most effective weight updating technique when compared to different gradient descent approaches. Sensitivity analysis was instrumental in identifying the key predictors.