Xuyang Lou

Exponential stability of genetic regulatory networks with random delays

This paper on global exponential stability in the mean square sense of genetic regulatory networks (GRNs) is motivated by a practical consideration that different genes have different time delays for transcription and translation, and in some cases, each multimer is assigned to a randomly chosen gene promoter site as an activator or inhibitor. One important feature of the obtained results reported here is that the time-varying delays are assumed to be random and their probability distributions are known a priori. By employing the information of the probability distributions of the time delays, we present some stability criteria for the uncertain delayed genetic networks with SUM regulatory logic where each transcription factor acts additively to regulate a gene. The effects of both variation range and distribution probability of the time delays are taken into account in the proposed approach. Another feature of the results is that a novel Lyapunov functional dependence on auxiliary delay parameters is exploited, which renders the results to be potentially less conservative and allows the time-varying delays to be not differentiable. The theoretical findings are illustrated and verified with two examples.

Parameter-dependent robust stability of uncertain neural networks with time-varying delay

Abstract This paper is concerned with the problem of global robust asymptotic stability for delayed neural networks with polytopic parameter uncertainties and time-varying delay. A delay-dependent and parameter-dependent robust stability criterion for the equilibrium of delayed neural networks in the face of polytopic type uncertainties is presented by using a parameter-dependent Lyapunov functional and taking the relationship between the terms in the Leibniz–Newton formula into account. This criterion, expressed as a set of linear matrix inequalities, requires no matrix variable to be fixed for the entire uncertainty polytope, which produces a less conservative stability result.

A novel neural network for solving convex quadratic programming problems subject to equality and inequality constraints

This paper proposes a neural network model for solving convex quadratic programming (CQP) problems, whose equilibrium points coincide with Karush-Kuhn-Tucker (KKT) points of the CQP problem. Using the equality transformation and Fischer-Burmeister (FB) function, we construct the neural network model and present the KKT condition for the CQP problem. In contrast to two existing neural networks for solving such problems, the proposed neural network has fewer variables and neurons, which makes circuit realization easier. Moreover, the proposed neural network is asymptotically stable in the sense of Lyapunov such that it converges to an exact optimal solution of the CQP problem. Simulation results are provided to show the feasibility and efficiency of the proposed network.

Containment control of second-order multi-agent systems with directed topology and time-delays

Purpose – The purpose of this paper is to discuss the impacts of the communication time-delays to the distributed containment control of the second-order multi-agent systems with directed topology. Design/methodology/approach – A basic theoretical analysis is first carried out for the containment control of the second-order multi-agent systems under directed topology without communication time-delay and a sufficient condition is proposed for the achievement of containment control. Based on the above result and frequency-domain analysis method, a sufficient condition is also derived for the achievement of containment control of the second-order multi-agent systems under directed topology with communication time-delays. Finally, simulation results are presented to support the effectiveness of the theoretical results. Findings – For the achievement of containment control of the second-order multi-agent systems under directed topology with communication time-delay, the control gain in the control protocols is...

Generalized predictive control of a class of MIMO models via a projection neural network

The system identification and generalized predictive control of a class of multiple input multiple output models are studied. The generalized predictive control problem with unknown parameters is first addressed by finding a control sequence for control performance as a goal. Then, the unknown parameters of the models are estimated by a new stochastic gradient algorithm providing high estimation accuracy. Third, the generalized predictive control problem is formulated to a quadratic programming problem with linear inequality constraints. Finally, the constrained quadratic programming problem is solved through a generalized projection neural network with simple structure and small number of neurons, while previous projection neural networks have complex structure and require more neurons. Numerical simulations are provided to reinforce our theoretical results.

Observer-based synchronization of networked distributed parameter systems

Synchronization in networks of dynamical systems is of importance in biological, chemical, physical and social systems. This paper investigates an observer-based synchronization scheme for a class of networked distributed parameter systems under an abstract framework. As in reality the system states may not be available and different subsystems (agents) share information through a communication network, we estimate the states based on a distributed observer in the case of partial network connectivity. Then a synchronizing controller combining a state feedback is constructed and the well-posedness of the closed-loop system is examined. Numerical simulations are provided to illustrate the effectiveness of the proposed results.

Global dissipativity of Cohen-Grossberg neural networks with mixed delays

This paper is concerned with global dissipativity of a general class of Cohen-Grossberg neural networks with both discrete time-varying delays and distributed time-varying delays. Based on the Lyapunov method, linear matrix inequality approach and some inequality techniques, some sufficient conditions are presented for checking the global dissipativity for Cohen- Grossberg neural networks with mixed time-varying delays, and characterizing the sets of global dissipativity and global exponentially dissipativity. Finally, some numerical simulations are given to show the effectiveness and feasibility of the results.

Parameter Estimation of a Class of Neural Systems with Limit Cycles

This work addresses parameter estimation of a class of neural systems with limit cycles. An identification model is formulated based on the discretized neural model. To estimate the parameter vector in the identification model, the recursive least-squares and stochastic gradient algorithms including their multi-innovation versions by introducing an innovation vector are proposed. The simulation results of the FitzHugh–Nagumo model indicate that the proposed algorithms perform according to the expected effectiveness.

Feedback control design of crowd evacuation system based on the diffusion model

This paper pertains to the study of feedback control design for the crowd evacuation in the framework of 1D and 2D models, respectively. The models representing crowd dynamics are based on the conservation law of mass with the density and velocity relationship given by a diffusion model. The feedback controllers taking care of control saturation are designed by using the method of feedback linearization for partial differential equations, which can keep the pedestrians evacuating in specific direction and fixed speed. By constructing the corresponding Lyapunov functional, the stability of the closed-loop system under the designed distributed feedback controller is proved. Finally, an example is given to illustrate the results.

Dynamics of neural systems with distributed delays and diffusion

The paper analyzes global exponential stability of reaction-diffusion cellular neural networks with distributed delays. Some sufficient conditions are proposed to guarantee the global exponential stability of the cellular neural networks by exploiting a delay differential inequality. The conditions are formulated as an M-matrix. Different from the method in the literature, without making use of Lyapunov functionals, the method in this paper is simple and effective for the stability analysis of neural networks with delay.