Razumikhin-type theorems on pth moment boundedness of neutral stochastic functional differential equations with Makovian switching

This paper investigates pth moment boundedness of neutral stochastic functional differential equations with Markovian switching (NSFDEsMS) based on Razumikhin technique and comparison principle. And pth moment stability is examined as a special case. Since the stochastic disturbances and neutral delays are incorporated, the considered system becomes more complex. Besides, the coefficients of the estimated upper bound for the diffusion operation associated with the underlying NSFDEsMS also may be chosen to be sign-changing functions instead of constant functions or negative definite functions, as a result, our results can work in general non-autonomous neutral stochastic systems. Finally, two examples are provided to show the effects of the proposed methods.     

The Razumikhin approach on general decay stability for neutral stochastic functional differential equations

The topic of the paper is both the pth moment and almost sure stability on a general decay rate for neutral stochastic functional differential equations, by applying the Razumikhin approach. This concept is extended to neutral stochastic differential delay equations. The results obtained in the paper are more general and they may be specialized on the exponential, polynomial or logarithmic stability. Moreover, some neutral stochastic functional differential equations which are not pth moment or almost surely exponentially stable, could be stable with respect to a certain lower decay rate. In that sense, some nontrivial examples are presented to justify and illustrate the usefulness of the theory. More precisely, one can say anything about both the pth moment and almost sure exponential stability, although the solutions are pth moment and almost surely polynomially or logarithmically stable.     

pth Moment exponential stability of impulsive stochastic functional differential equations with Markovian switching

In this paper, the pth moment exponential stability for a class of impulsive stochastic functional differential equations with Markovian switching is investigated. Based on the Lyapunov function, Dynkin formula and Razumikhin technique with stochastic version as well as stochastic analysis theory, many new sufficient conditions are derived to ensure the pth moment exponential stability of the trivial solution. The obtained results show that stochastic functional differential equations with/without Markovian switching may be pth moment exponentially stabilized by impulses. Moreover, our results generalize and improve some results obtained in the literature. Finally, a numerical example and its simulations are given to illustrate the theoretical results.     

pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs

This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained.     

Discrete Razumikhin-type stability theorems for stochastic discrete-time delay systems

By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined.     

On input-to-state stability of impulsive stochastic systems

This paper is concerned with the input-to-state stability (ISS) of impulsive stochastic systems. First, appropriate concepts of stochastic input-to-state stability (SISS) and pth moment input-to-state stability (p-ISS) for the mentioned systems are introduced. Then, we prove that impulsive stochastic systems possessing SISS-Lyapunov functions are uniformly SISS and p-ISS over a certain class of impulse sequences. As a byproduct, a criterion on the uniform global asymptotic stability in probability for the system in isolation (without inputs) is also derived. Finally, we provide a numerical example to illustrate our results.     

Intermittent control to stationary distribution and exponential stability for hybrid multi-stochastic-weight coupled networks based on aperiodicity

In this paper, the issue about the stationary distribution for hybrid multi-stochastic-weight coupled networks (HMSWCN) via aperiodically intermittent control is investigated. Specially, when stochastic disturbance gets to zero, the exponential stability in pth moment for hybrid multi-weight coupled networks (HMWCN) is considered. Under the framework of the Lyapunov method, M-matrix and Kirchhoff’s Matrix Tree Theorem in the graph theory, several sufficient conditions are derived to guarantee the existence of a stationary distribution and exponential stability. Different from previous work, the existing area of a stationary distribution is not only related to the topological structure of coupled networks, but also aperiodically intermittent control (the rate of control width and control duration). Subsequently, as an application to theoretical results, a class of hybrid multi-stochastic-weight coupled oscillators is studied. Ultimately, numerical examples are carried out to demonstrate the effectiveness of theoretical results and effects of the control schemes.     

Nonlinear H∞ robust control applied to F-16 aircraft with mass uncertainty using control surface inverse algorithm

In this paper, an analytic solution of nonlinear H_∞ robust controller is first proposed and used in a complete six degree-of-freedom nonlinear equations of motion of flight vehicle system with mass and moment inertia uncertainties. A special Lyapunov function with mass and moment inertia uncertainties is considered to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). The HJPDI is solved analytically, resulting in a nonlinear H_∞ robust controller with simple proportional feedback structure. Next, the control surface inverse algorithm (CSIA) is introduced to determine the angles of control surface deflection from the nonlinear H_∞ control command. The ranges of prefilter and loss ratio that guarantee stability and robustness of nonlinear H_∞ flight control system implemented by CSIA are derived. Real aerodynamic data, engine data and actuator system of F-16 aircraft are carried out in numerical simulations to verify the proposed scheme. The results show that the responses still keep good convergence for large initial perturbation and the robust stability with mass and moment inertia uncertainties in the permissible ranges of the prefilter and loss ratio for which this design guarantees stability give same conclusion.     

Multiple-prespecified-dictionary sparse representation for compressive sensing image reconstruction with nonconvex regularization

Multiple-prespecified-dictionary sparse representation (MSR) has shown powerful potential in compressive sensing (CS) image reconstruction, which can exploit more sparse structure and prior knowledge of images for minimization. Due to the popular L₁ regularization can only achieve the suboptimal solution of L₀ regularization, using the nonconvex regularization can often obtain better results in CS reconstruction. This paper proposes a nonconvex adaptive weighted L_p regularization CS framework via MSR strategy. We first proposed a nonconvex MSR based L_p regularization model, then we propose two algorithms for minimizing the resulting nonconvex L_p optimization problem. According to the fact that the sparsity levels of each regularizers are varying with these prespecified-dictionaries, an adaptive scheme is proposed to weight each regularizer for optimization by exploiting the difference of sparsity levels as prior knowledge. Simulated results show that the proposed nonconvex framework can make a significant improvement in CS reconstruction than convex L₁ regularization, and the proposed MSR strategy can also outperforms the traditional nonconvex L_p regularization methodology.     

Stabilization of highly nonlinear hybrid systems driven by Lévy noise and delay feedback control based on discrete-time state observations

There are many hybrid stochastic differential equations (SDEs) in the real-world that don’t satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.     

A test for robust Hurwitz stability of convex combinations of complex polynomials

In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1−λ)p₀(s)+λp₁(s), where λ∈[0,1] and p₀(s) and p₁(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ-polynomials of degrees 2 and 2n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure.     

An adaptive online learning algorithm for distributed convex optimization with coupled constraints over unbalanced directed graphs

This paper investigates a distributed optimization problem over multi-agent networks subject to both local and coupled constraints in a non-stationary environment, where a set of agents aim to cooperatively minimize the sum of locally time-varying cost functions when the communication graphs are time-changing connected and unbalanced. Based on dual decomposition, we propose a distributed online dual push-sum learning algorithm by incorporating the push-sum protocol into dual gradient method. We then show that the regret bound has a sublinear growth of O(T^p) and the constraint violation is also sublinear with order of $O\left(T^{1?p/2}\right),$ where T is the time horizon and 0 < p ≤ 1/2. Finally, simulation experiments on a plug-in electric vehicle charging problem are utilized to verify the performance of the proposed algorithm. The proposed algorithm is adaptive without knowing the total number of iterations T in advance. The convergence results are established on more general unbalanced graphs without the boundedness assumption on dual variables. In addition, more privacy concerns are guaranteed since only dual variables related with coupled constraints are exchanged among agents.     

Intervention of population health management innovation on economy based on cognitive computing

With the emergence of Delta strains in many regions of China, population health issues have aroused great concern in many industries. Therefore, it is necessary to intervene in population health management through a variety of means. This paper establishes an economic intervention model of cognitive computing to evaluate the health of population health management innovation, track the health risks of the population and actively manage the relationship between population health. This paper establishes a health assessment model based on cognitive computing and uses a population health survey to evaluate the physical condition, illness, and life index of 64 citizens in this city before and after the economic intervention. The results of the study show that when economic dynamics test indicators are added to the prediction model of the post-test scores of economic intervention and health status, the explanatory power R² of the cognitive computing model increased by 4.8% and 3.5%, respectively. The score (β=0.36, p <0.001), IPDT ( Inventory of Piaget's Developmental Tas) intervention score (β=0.15, p = 0.025) and migration score (β=0.18, p = 0.012) can significantly predict the post-economic intervention test score (R²=51.2%, p <0.001). The pre-test score on the health status test (β=0.48, p <0.001) and the IPDT intervention score (β=0.25, p = 0.014) can significantly predict the health status post-test score (R²=32.54%, p <0.001).     

Event-triggered non-fragile H∞ fault detection for discrete time-delayed nonlinear systems with channel fadings

In this paper, the event-triggered non-fragile H_∞ fault detection filter is designed for a class of discrete-time nonlinear systems subject to time-varying delays and channel fadings. The Lth Rice fading model is utilized to reflect the actual received measurement signals, and its channel coefficients own arbitrary probability density functions on interval [0,1]. The event-based filter is constructed to reduce unnecessary data transmissions in the communication channel, which only updates the measurement signal to the filter when the prespecified “event” is triggered. Multiplicative gain variations are utilized to describe the phenomenon of parameter variations in actual implementation of the filter. Based on Lyapunov stability theory, stochastic analysis technology along with linear matrix inequalities (LMIs) skills, sufficient conditions for the existence of the non-fragile fault detection filter are obtained which make the filtering error system stochastically stable and satisfy the H_∞ constraint. The gains of the filter can be calculated out by solving the feasible solution to a certain LMI. A simulation example is given to show the effectiveness of the proposed method.     

A simple design method for the cosine-modulated filter banks using weighted constrained least square technique

This paper presents a simple and efficient design method for cosine-modulated filter banks with prescribed stopband attenuation, passband ripple, and channel overlap. The method casts the design problem as a linear minimization of filter coefficients such that their value at ω=π/2M is 0.707, which results in a simpler, more direct design procedure. The weighted constrained least squares technique is exploited for designing the prototype filter for cosine modulation (CM) filter banks. Several design examples are included to show the increased efficiency and flexibility of the proposed method over the exiting methods. An application of the proposed method is considered in the area of sub-band coding of the ECG and speech signals.     

Further stability results for random nonlinear systems with stochastic impulses

In this paper, the global asymptotic stability in probability and the exponential stability in $m$th moment are investigated for random nonlinear systems with stochastic impulses, whose occurrence is determined by a Poisson process. The stochastic disturbances in the impulsive random nonlinear systems are driven by second-order processes, which have bounded mean power. Firstly, the improved Lyapunov approaches for the global asymptotic stability in probability and the exponential stability in $m$th moment are established for impulsive random nonlinear systems based on the uniformly asymptotically stable function. Secondly, the improved results are further extended to the impulsive random nonlinear systems with Markovian switching. Finally, two examples are provided to verify the feasibility and effectiveness of the obtained results.     

Stabilizing region of PDμ controller for fractional order system with general interval uncertainties and an interval delay

This paper concentrates on computing the stabilizing region of PD^μ controller for fractional order system with general interval uncertainties and an interval delay. The stabilizing region means the complete/approximate set of PD^μ controllers that stabilize the given closed-loop control system. General interval uncertainties refer to both coefficients and orders of the fractional system suffer from interval uncertainties. Interval delay indicates that the delay also vary in a specified interval.Firstly, a method is presented to calculate the stabilizing region for general interval fractional system with an interval time-constant delay. Based on a novel mapping function and the concept of critical controller parameters, the stabilizing region can be determined numerically. Secondly, the stabilizing region computation problem for general interval fractional system with an interval time-varyingdelay is considered. By applying a revised small-gain theorem, the stabilizing region can be calculated like the time-constant delay case. Thirdly, two alternative methods are proposed to improve the computational efficiency of stabilizing region calculation. Both methods can reduce the number of polynomials which are used to determine the stabilizing region. Examples are followed to illustrate the proposed results.     

Target-synchronization of the distributed wireless sensor networks under the same sleeping–awaking method

Based on the conflict and crosstalk avoidance mechanism (CCAM), we propose a sleeping–awaking method for wireless sensor networks (WSNs) in which the maximal degree node (MDN) and all its neighbors run sleep or wake simultaneously while other nodes run the CCAM. This method is said to be the same sleeping–awaking method (SSAM). The SSAM is motivated by the congestion and collision problems of cliques, MDN and its neighbor set in the communicating graph of the WSN. In this communication way, the related protocol about the SSAM is provided accordingly. Under the designed protocol, we get a Markovian switching WSN with both white noise disturbance and multiple time-varying delays. Based on the theory of exponential stability in pth moment, we show that the protocol ensures the WSNs to keep in synchronization with the target function. A numerical example shows that the WSN can keep its target-synchronization even with large time delays.