Closed-form periodic solutions for piecewise-linear vibrating systems

In this paper, the global robust point dissipativity of an uncertain neural networks model with mixed time-varying delays is investigated, based on Lyapunov theory and inequality techniques. First, the concept of global robust point dissipativity is introduced. Next, some sufficient conditions are given for checking the global robust point dissipativity and the global exponential robust dissipativity of the uncertain neural networks model. Finally, illustrated examples are given to show the effectiveness of our results.     

Non-fragile extended dissipative state estimation for delayed discrete-time neural networks: application to quadruple tank process model

Nonlinear Dynamics - This paper deals with the non-fragile state estimator design to study the robust extended dissipativity criterion for a class of discrete-time neural networks (DNNs) involving...     

Dissipativity of a class of cellular neural networks with proportional delays

In this paper, the problem of dissipativity is investigated for cellular neural networks with proportional delays. Without assuming monotonicity, differentiability, and boundedness of activation functions, two new delay-independent criteria for checking the dissipativity of the addressed neural networks are established by using inner product properties and matrix theory. Two examples and their simulation results are given to show the effectiveness and less conservatism of the proposed criteria.     

Dissipativity analysis of stochastic neural networks with time delays

This paper is concerned with the dissipativity problem of stochastic neural networks with time delay. A new stochastic integral inequality is first proposed. By utilizing the delay partitioning technique combined with the stochastic integral inequalities, some sufficient conditions ensuring mean-square exponential stability and dissipativity are derived. Some special cases are also considered. All the given results in this paper are not only dependent upon the time delay, but also upon the number of delay partitions. Finally, some numerical examples are provided to illustrate the effectiveness and improvement of the proposed criteria.     

Exponential synchronization of Markovian jumping complex dynamical networks with randomly occurring parameter uncertainties

This paper investigates the mean-square exponential synchronization problem of complex dynamical networks with Markovian jumping and randomly occurring parameter uncertainties. The considered Markovian transition rates are assumed to be partially unknown. The parameter uncertainties are considered to be random occurrence and norm-bounded, and the randomly occurring parameter uncertainties obey certain Bernoulli-distributed white noise sequences. Based on the Lyapunov method and stochastic analysis, by designing mode-dependent feedback controller, some sufficient conditions are presented to ensure the mean-square exponential synchronization of Markovian jumping complex dynamical networks with partly unknown transition rates and randomly occurring parameter uncertainties. Numerical examples are given to demonstrate the validity of the theoretical results.     

Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties

In this paper, we investigate the problem of robust state estimator design for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time varying delays and randomly occurring uncertainties. By introducing a new discretized Lyapunov–Krasovskii functional together with a free-weighting matrix technique, first we derive a set of sufficient conditions for the existence of global asymptotic state estimator for the discrete-time GRN model with time delays satisfying both the lower and the upper bound of the interval time-varying delay. Further, the obtained results are extended to deal the robust state estimator design for the discrete-time GRN model in the presence of randomly occurring uncertainties which obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The proposed criterions are established in terms of linear matrix inequalities (LMIs) which can be easily solved via Matlab LMI toolbox. Finally, the robust state estimator design has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained theory.     

Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation

Nonlinear Dynamics - This paper investigates the problem of delay-dependent dissipativity for a class of Markovian jump neural networks with a time-varying delay. A generalized integral inequality...     

State estimation for switched discrete-time stochastic BAM neural networks with time varying delay

This paper focuses the issue of state estimation for a class of switched discrete-time stochastic bidirectional associative memory (BAM) neural networks with time varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the error state system to be robustly exponentially stable. By employing average dwell time approach together with piecewise Lyapunov functional technique, a set of sufficient conditions is derived with respect to all admissible uncertainties, to guarantee the existence of the desired state estimator for the uncertain switched discrete-time BAM delayed neural networks. Specifically, we derive sufficient conditions to achieve robust state estimation with the characterization of complex effects of time delays, parameter uncertainties, and stochastic perturbations. In particular, the parameter uncertainties are assumed to be time varying and unknown, but norm bounded. It should be mentioned that our estimation results are delay dependent, which depend on not only the upper bounds of time delay, but also their lower bounds. More precisely, the desired estimator matrix gain is obtained in terms of the solution of the derived LMIs. Finally, numerical examples with a simulation result are given to illustrate the effectiveness and applicability of the obtained results.     

Finite-time synchronization control for uncertain Markov jump neural networks with input constraints

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.     

Robust synchronization of uncertain chaotic neural networks with randomly occurring uncertainties and non-fragile output coupling delayed feedback controllers

This paper deals with the synchronization control problem for the uncertain chaotic neural networks with randomly occurring uncertainties and randomly occurring control gain fluctuations. By introducing an improved Lyapunov–Krasovskii functional and employing reciprocally convex approach, a delay-dependent non-fragile output feedback controller is designed to achieve synchronization with the help of a drive–response system and the linear matrix inequality approach. Finally, numerical results and its simulations are given to show the effectiveness of the derived results.     

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

The robust observer problem is considered in this paper for a class of discrete-time neural networks with Markovian jumping parameters and mode-dependent time delays which are in both discrete-time form and finite distributed form. The neural network switches from one mode to another controlled by a Markov chain with known transition probability. Time-delays considered in this paper are mode-dependent which may reflect a more realistic version of the neural network. By using the Lyapunov functional method and the techniques of linear matrix inequalities (LMIs), sufficient conditions are established in terms of LMIs that ensure the existence of the robust observer. The obtained conditions are easy to be verified via the LMI toolbox. An example is presented to show the effectiveness of the obtained results.     

Neural network-based adaptive output feedback formation control for multi-agent systems

This paper investigates the problem of output feedback formation tracking control for second-order multi-agent systems under an undirected connected graph and in the presence of dynamic uncertainties and bounded external disturbances. Two state tracking error measures (i.e., absolute and relative state tracking errors) are considered for each individual agent in the formation, and linear reduced-order observers are constructed based on the lumped state tracking errors which include absolute and relative state tracking errors. Chebyshev neural networks are used to approximate unknown nonlinear function in the agent dynamics on-line, and the implementation of the basis functions of Chebyshev neural networks depends only on the desired signals. The smooth projection algorithm is applied to guarantee that the estimated parameters remain in some known bounded sets. Numerical simulations are presented to illustrate the performance of the proposed controller.     

A fuzzy wavelet neural network-based approach to hypersonic flight vehicle direct nonaffine hybrid control

A direct nonaffine hybrid control methodology is proposed for a generic hypersonic flight models based on fuzzy wavelet neural networks (FWNNs). The addressed strategy extends the previous indirect nonaffine control approaches stemming from simplified models of affine formulations. To cope with nonaffine effects on control design, analytically invertible models are constructed and then novel hybrid controllers are developed directly using nonaffine models. Furthermore, by employing FWNNs to devise adaptive terms, inversion errors are canceled via fuzzy neural approximations. In addition, robust terms are designed to achieve larger stable region in comparison with earlier work using Lyapunov synthesis. Finally, numerical simulation results from a hypersonic flight vehicle model are given to clarify the efficiency of the proposed direct nonaffine control scheme in the presence of parametric uncertainties.     

Robust control of wheel slip in anti-lock brake system of automobiles

In this paper, performances of two model-free control systems including Fuzzy Logic Control (FLC) and Neural Predictive Control (NPC) on tracking performance of wheel-slip in Anti-lock Braking System (ABS) are compared. As an accurate and control oriented model, a half vehicle model is developed to generate extensive simulation data of the braking system. Brake system identification is preformed through a Perceptron neural networks model of brake system which is trained with offline data by Gradient Descent Back Propagation (GDBP) algorithm. In order to reduce the time cost of the calculations and improving the robustness of closed loop control system, an online Perceptron neural network adaptively generates the optimum control actions. By a comparative simulation analysis it is shown that the NPC system has a better tracking performance, shorter stopping time and distance than the FLC controllers. The robustness of the proposed control systems are evaluated under ±25 % uncertainty. It is shown that the NPC system is more robust against both exogenous disturbances and modeling uncertainties than the FLC system.     

Passivity analysis of stochastic time-delay neural networks

Passivity analysis of stochastic neural networks with time-varying delays and parametric uncertainties is investigated in this paper. Passivity of stochastic neural networks is defined. Both delay-independent and delay-dependent stochastic passivity conditions are presented in terms of linear matrix inequalities (LMIs). The results are established by using the Lyapunov–Krasovskii functional method. In order to derive the delay-dependent passivity criterion, some free-weighting matrices are introduced. The effectiveness of the method is illustrated by numerical examples.     

Decentralized adaptive neural network control for mechanical systems with dead-zone input

We propose a decentralized adaptive robust controller for trajectory tracking of mechanical systems with dead-zone input in this paper. The considered mechanical systems are with high-order interconnections and unknown non-symmetric nonlinear input. In each local controller, the neural network control is introduced to estimate the uncertainties and disturbances, meanwhile the siding mode control and adaptive technical are designed to compensate for the approximation errors. A nonlinear function is chosen to deal with the interconnections. Following, the stability and robustness are verified by using Lyapunov stability theorem. Finally, simulations are provided to support the theoretical results     

Global exponential estimates for uncertain Markovian jump neural networks with reaction-diffusion terms

In this paper, the robust global exponential estimating problem is investigated for Markovian jumping reaction-diffusion delayed neural networks with polytopic uncertainties under Dirichlet boundary conditions. The information on transition rates of the Markov process is assumed to be partially known. By introducing a new inequality, some diffusion-dependent exponential stability criteria are derived in terms of relaxed linear matrix inequalities. Those criteria depend on decay rate, which may be freely selected in a range according to practical situations, rather than required to satisfy a transcendental equation. Estimates of the decay rate and the decay coefficient are presented by solving these established linear matrix inequalities. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.     

Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

In this paper, the global robust exponential stability of interval neural networks with delays and inverse Hölder neuron activation functions is considered. By using linear matrix inequality (LMI) techniques and Brouwer degree properties, the existence and uniqueness of the equilibrium point are proved. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established. A numerical example is provided to demonstrate the validity of the theoretical results.     

Passivity analysis of uncertain neural networks with mixed time-varying delays

This paper addresses the passivity problem for uncertain neural networks with both discrete and distributed time-varying delays. It is assumed that the parameter uncertainties are norm-bounded. By construction of an augmented Lyapunov–Krasovskii functional and utilization of zero equalities, improved passivity criteria for the networks are derived in terms of linear matrix inequalities (LMIs) via new approaches. Through three numerical examples, the effectiveness to enhance the feasible region of the proposed criteria is demonstrated.     

Adaptive sliding mode control of dynamic system using RBF neural network

This paper presents a robust adaptive sliding mode control strategy using radial basis function (RBF) neural network (NN) for a class of time varying system in the presence of model uncertainties and external disturbance. Adaptive RBF neural network controller that can learn the unknown upper bound of model uncertainties and external disturbances is incorporated into the adaptive sliding mode control system in the same Lyapunov framework. The proposed adaptive sliding mode controller can on line update the estimates of system dynamics. The asymptotical stability of the closed-loop system, the convergence of the neural network weight-updating process, and the boundedness of the neural network weight estimation errors can be strictly guaranteed. Numerical simulation for a MEMS triaxial angular velocity sensor is investigated to verify the effectiveness of the proposed adaptive RBF sliding mode control scheme.