Kanjian Zhang

On exponential stability of delayed neural networks with a general class of activation functions

Abstract In this Letter, based on globally Lipschitz continuous activation functions, new conditions ensuring existence, uniqueness and global exponential stability of the equilibrium point of delayed neural networks are obtained. The delayed Hopfield network and bidirectional associative memory network are special cases of the network model considered in this Letter. So this work gives some improvements to the previous ones.

Letters: Adaptive neural control for a class of output feedback time delay nonlinear systems

An output feedback control scheme combined with backstepping, radial basis function (RBF) neural networks, and adaptive control is proposed for the stabilization of nonlinear system with input delay and disturbances. A filter and a virtual observer are constructed to substitute the immeasurable system state. By using state transformation, the original system is converted to the system without input delay. Neural networks are employed to estimate the unknown continuous functions. The control scheme ensures that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB).

Policy iteration based feedback control

It is well known that stochastic control systems can be viewed as Markov decision processes (MDPs) with continuous state spaces. In this paper, we propose to apply the policy iteration approach in MDPs to the optimal control problem of stochastic systems. We first provide an optimality equation based on performance potentials and develop a policy iteration procedure. Then we apply policy iteration to the jump linear quadratic problem and obtain the coupled Riccati equations for their optimal solutions. The approach is applicable to linear as well as nonlinear systems and can be implemented on-line on real world systems without identifying all the system structure and parameters.

Simplified exponential stability analysis for recurrent neural networks with discrete and distributed time-varying delays

This paper provides simplified exponential stability criteria for a class of recurrent neural networks (RNNs) with discrete and distributed time-varying delays. The activation functions of the RNNs are assumed to be more general, and the proposed criteria are obtained by only using a integral inequality and are not involved any free-weighting matrices. This feature makes the computational burden largely reduced. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Direct interval forecasting of wind speed using radial basis function neural networks in a multi-objective optimization framework

Point predictions of wind speed can hardly be reliable and accurate when the uncertainty level increases in data. Prediction intervals (PIs) provide a solution to quantify the uncertainty associated with point predictions. In this paper, we adopt radial basis function (RBF) neural networks to perform interval forecasting of the future wind speed. A two-step method is proposed to determine the RBF connection weights in a multi-objective optimization framework. In the first step, the centers of the RBF are determined using the K-means clustering algorithm and the hidden-output weights of the RBF are pre-trained using the least squares algorithm. In the second step, the hidden-output weights are further adjusted by the non-dominated sorting genetic algorithm-II (NSGA-II), which aims at concurrently minimizing the width and maximizing the coverage probability of the constructed intervals. We test the performance of the proposed method on three real data sets, which are collected from different wind farms in China. The experimental results indicate that the proposed method can provide higher quality PIs than the conventional multi-layer perceptron (MLP) based methods.

Adaptive Fuzzy Tracking Control of a Class of Stochastic Nonlinear Systems with Unknown Dead-Zone Input

In this paper, a direct adaptive fuzzy tracking control scheme is presented for a class of stochastic uncertain nonlinear systems with unknown dead-zone input. A direct adaptive fuzzy tracking controller is developed by using the backstepping approach. It is proved that the design scheme ensures that all the error variables are bounded in probability while the mean square tracking error becomes semiglobally uniformly ultimately bounded (SGUUB) in an arbitrarily small area around the origin. Simulation results show the effectiveness of the control scheme.

Impulsive fractional partial differential equations

This paper deals with Cauchy problem for a class of impulsive partial hyperbolic differential equations involving the Caputo derivative. Our first purpose is to show that the formula of solutions in cited papers are incorrect. Next, we reconsider a class of impulsive fractional partial hyperbolic differential equations and introduce a correct formula of solutions for Cauchy problem in R n . Further, some sufficient conditions for existence of the solutions are established by applying fixed point method. At last, we consider the Cauchy problem in a Banach space via the technique of measures of noncompactness and Monchs fixed point theorem. Some examples are given to illustrate our results.

Stabilisation for switched linear systems with time-varying delay and input saturation

This article investigates the stabilisation problems for continuous-time and discrete-time switched systems with time-varying delay and saturated control input. Based on dwell time switching signals and multiple Lyapunov functional method, stabilisation conditions are well obtained in the context of linear matrix inequalities. To estimate attractive regions as large as possible, the feasibility problems are translated into optimisation problems. In addition, the corresponding results are presented for linear time-delay systems and switched delay-free systems, which improve and supplement some existing ones in the literature. Finally, numerical examples and simulations are given to illustrate the effectiveness and values of the proposed results.

Optimal control of switching time in switched stochastic systems with multi-switching times and different costs

ABSTRACT In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.

Robust fuzzy control of nonlinear stochastic delay systems with impulsive effects

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive stochastic systems with time-varying delays is investigated. The nonlinear delay system is represented by the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for mean square exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the applicability of the theoretical results.