A NOTE ON THE GENERAL STABILIZATION OF DISCRETE FEEDBACK CONTROL FOR NON-AUTONOMOUS HYBRID NEUTRAL STOCHASTIC SYSTEMS WITH A DELAY

Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.

Bayesian estimation for nonlinear stochastic hybrid systems with state dependent transitions

The Bayesian approach is considered as the most general formulation of the state estimation for dynamic systems. However, most of the existing Bayesian estimators of stochastic hybrid systems only focus on the Markov jump system, few liter- ature is related to the estimation problem of nonlinear stochastic hybrid systems with state dependent transitions. According to this problem, a new methodology which relaxes quite a restrictive as- sumption that the mode transition process must satisfy Markov properties is proposed. In this method, a general approach is presented to model the state dependent transitions, the state and output spaces are discreted into cell space which handles the nonlinearities and computationally intensive problem offline. Then maximum a posterior estimation is obtained by using the Bayesian theory. The efficacy of the estimator is illustrated by a simulated example .

An Uncertainty Analysis Method for Artillery Dynamics with Hybrid Stochastic and Interval Parameters

This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion(PCE).The uncertainty parameters with sufficient information are regarded as stochastic variables,whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge.In this method,the PCE model is constructed through the Galerkin projection method,in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights.Through the sampling in PCE,the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems,without changing their expressions.The yielded PCE model is utilized as a computationally efficient,surrogate model,and the supremum and infimum of the dynamic responses over all time iteration steps can be easily approximated through Monte Carlo simulation and percentile difference.A numerical example and an artillery exterior ballistic dynamics model are used to illustrate the feasibility and efficiency of this approach.The numerical results indicate that the dynamic response bounds obtained by the PCE approach almost match the results of the direct Monte Carlo simulation,but the computational efficiency of the PCE approach is much higher than direct Monte Carlo simulation.Moreover,the proposed method also exhibits fine precision even in high-dimensional uncertainty analysis problems.

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

Recent results on stochastic hybrid dynamical systems

This paper addresses stochastic hybrid systems,particularly switched and impulsive systems.The systems under consideration are linear and non-linear continuous with/without time delay,and with/without external force.The importance of using such systems and the discrepancies between hybrid and non-hybrid systems are presented.The objective of this paper is to survey recent developments on some of the important qualitative properties such as stability,stabilisation,input-to-state stability and state estimation along with the challenges that might arise when taking hybridness into account.These properties are mainly developed by using the direct method of Lyapunov or Lyapunov-Razumikhin if time delay is taken into account.Several examples with simulations are presented to further clarify the results introduced in this paper.

Perturbation analysis of stochastic hybrid systems and applications to resource contention games

We provide an overview of the recently developed general infinitesimal perturbation analysis(IPA)framework for stochastic hybrid systems(SHSs),and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner.We also propose a general scheme for systematically deriving an abstraction of a discrete event system(DES)in the form of an SHS.Then,as an application of the general IPA framework,we study a class of stochastic non-cooperative games termed“resource contention games”modeled through stochastic flow models(SFMs),where two or more players(users)compete for the use of a sharable resource.Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.

Modelling and analysis of hybrid stochastic timed Petri net

In this paper,an interesting Hybrid Stochastic Timed Petri Net(HSTPN)is proposed for a class of hybrid systems.The proposed HSTPN can be adopted to represent hybrid systems with discrete,continuous,conflicting,time-delay and stochastic characteristics simultaneously.The proposed HSTPN outperforms conventional hybrid Petri net models in terms of describing the scalability and immediacy of hybrid systems.Advantages of the HSTPN on describing hybrid system are verified by establishing some equivalent models of HPN and its derived models.

Randomness in the Hybrid Modeling and Simulation of Insulin Secretion Pathways in Pancreatic Islets

Insulin secreted by pancreatic islet ˇ-cells is the principal regulating hormone of glucose metabolism.Disruption of insulin secretion may cause glucose to accumulate in the blood, and result in diabetes mellitus.Although deterministic models of the insulin secretion pathway have been developed, the stochastic aspect of this biological pathway has not been explored. The first step in this direction presented here is a hybrid model of the insulin secretion pathway, in which the delayed rectifying KCchannels are treated as stochastic events. This hybrid model can not only reproduce the oscillation dynamics as the deterministic model does, but can also capture stochastic dynamics that the deterministic model does not. To measure the insulin oscillation system behavior, a probability-based measure is proposed and applied to test the effectiveness of a new remedy.