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.

Adaptive Neural Network-Based Control for a Class of Nonlinear Pure-Feedback Systems With Time-Varying Full State Constraints

Abstract--In this paper, an adaptive neural network （NN） control approach is proposed for nonlinear pure-feedback sys- tems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions （BLFs） with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closed- loop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach. Index TermsmAdaptive control, neural networks （NNs）, non- linear pure-feedback systems, time-varying constraints.

Adaptive Variable Structure Control of MIMO Nonlinear Systems with Time-varying Delays and Unknown Dead-zones

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output （MIMO） nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncer- tainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.

ABSOLUTE STABILITY OF TIME-VARYING NONLINEAR CONTROL SYSTEM

In this paper the authors study two classes of time-varying nonlinear control systems. A few sufficient conditions of absolute stability of these systems were obtained by means of classical analysis and the analogue of the variation of constants formula of nonlinear systems. Moreover, they gave some sufficient conditions of absolute stability in Hurwitz angle for these systems.

Exponential stability for networked control systems based on the model of nonlinear discrete-time system with time-varying delay

An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criteria of exponential stability are obtained based on norm inequality methods. A numerical example is given todemonstrate that those criteria are useful to analyzing the stability of nonlinear NCSs.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom(DOF)nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics,including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Nonlinear System Identification with Unknown Piecewise Time-Varying Delay

Identification of nonlinear systems with unknown piecewise time-varying delay is concerned in this paper.Multiple auto regressive exogenous(ARX) models are identified at different process operating points,and the complete dynamics of the nonlinear system is represented by using a combination of a normalized exponential function as the probability density function with each of the local models.The parameters of the local ARX models and the exponential functions as well as the unknown piecewise time-varying delays are estimated simultaneously under the framework of the expectation maximization(EM) algorithm.A simulation example is applied to demonstrating the proposed identification method.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

TECHNICAL STABILITY OF NONLINEAR TIME-VARYING SYSTEMS WITH SMALL PARAMETERS

Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.

Robust Stability Criteria for Neutral Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.

Dynamics of a Nonautonomous Plant Disease Model with General Nonlinear Incidence Rate and Time-Varying Impulse

In this paper, for controlling the spread of plant diseases, a nonautonomous SEIS (Susceptible → Exposed → Infectious → Susceptible) epidemic model with a general nonlinear incidence rate and time-varying impulsive control strategy is proposed and investigated. This novel model could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Using the method of small amplitude perturbation, the sufficient conditions under which guarantee the globally attractive of the disease-free periodic solution and the permanence of the disease are obtained, that is, the disease dies out if R12>1.

A Comparative Study of Nonlinear Time-Varying Process Modeling Techniques: Application to Chemical Reactor

This paper proposes the design and a comparative study of two nonlinear systems modeling techniques. These two approaches are developed to address a class of nonlinear systems with time-varying parameter. The first is a Radial Basis Function (RBF) neural networks and the second is a Multi Layer Perceptron (MLP). The MLP model consists of an input layer, an output layer and usually one or more hidden layers. However, training MLP network based on back propagation learning is computationally expensive. In this paper, an RBF network is called. The parameters of the RBF model are optimized by two methods: the Gradient Descent (GD) method and Genetic Algorithms (GA). However, the MLP model is optimized by the Gradient Descent method. The performance of both models are evaluated first by using a numerical simulation and second by handling a chemical process known as the Continuous Stirred Tank Reactor CSTR. It has been shown that in both validation operations the results were successful. The optimized RBF model by Genetic Algorithms gave the best results.

Optimal Control of Nonlinear Systems Using Experience Inference Human-Behavior Learning

Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior learning is proposed to solve the migration problem of optimal controllers applied to real-world nonlinear systems.The approach is inspired in the complementary properties that exhibits the hippocampus,the neocortex,and the striatum learning systems located in the brain.The hippocampus defines a physics informed reference model of the realworld nonlinear system for experience inference and the neocortex is the adaptive dynamic programming(ADP)or reinforcement learning(RL)algorithm that ensures optimal performance of the reference model.This optimal performance is inferred to the real-world nonlinear system by means of an adaptive neocortex/striatum control policy that forces the nonlinear system to behave as the reference model.Stability and convergence of the proposed approach is analyzed using Lyapunov stability theory.Simulation studies are carried out to verify the approach.

Asymmetric time-varying integral barrier Lyapunov function based adaptive optimal control for nonlinear systems with dynamic state constraints

This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints.An asymmetric time-varying integral barrier Lyapunov function(ATIBLF)based integral reinforcement learning(IRL)control algorithm with an actor–critic structure is first proposed.The ATIBLF items are appropriately arranged in every step of the optimized backstepping control design to ensure that the dynamic full-state constraints are never violated.Thus,optimal virtual/actual control in every backstepping subsystem is decomposed with ATIBLF items and also with an adaptive optimized item.Meanwhile,neural networks are used to approximate the gradient value functions.According to the Lyapunov stability theorem,the boundedness of all signals of the closed-loop system is proved,and the proposed control scheme ensures that the system states are within predefined compact sets.Finally,the effectiveness of the proposed control approach is validated by simulations.

Command filtered integrated estimation guidance and control for strapdown missiles with circular field of view

In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier Lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The Lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.

Stability of nonlinearly-perturbed systems with time varying delay using LMIs

This paper studies delay dependent robust stability and the stabilization problem of nonlinear perturbed systems with time varying delay. A new set of sufficient conditions for the stability of open as well as close loop systems are obtained in the sense of Lyapunov-Krasovskii. To reduce the conservatism, the work exploits the idea of splitting the delay interval into multiple equal regions so that less information on the time delay can be imposed to derive the results. The derived criterion not only improves the upper bounds of the time delay but also does not require the derivative of the delay to be known at prior. Easily testable sufficient criteria are presented in terms of linear matrix inequalities. It is shown that the derived conditions are very less conservative while comparing the maximum allowable upper bound of delay with the existing results in literature.

Translational - torsional coupled model based nonlinear dynamic analysis of an NGW planetary gear train

This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.

Delay-dependent criteria for the robust stability of systems with time-varying delay

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach. Keywords Delay-dependent criteria - Robust stability - Time-varying structured uncertainties - Nonlinear perturbations - Linear matrix inequality This work was supported by the Doctor Subject Foundation of China (No. 2000053303).

Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations

This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.