Jumping Parameters Research Articles

Almost surely asymptotic synchronization for stochastic neural networks of neutral type with Markovian jumping parameters

SummaryThis paper studies the problem of the almost surely asymptotic synchronization for a class of stochastic neural networks of neutral type with both Markovian jumping parameters and mixed time delays. Based on the stochastic analysis theory, LaSalle‐type invariance principle, and delayed state‐feedback control technique, some novel delay‐dependent sufficient criteria to guarantee the almost surely asymptotic synchronization are given. These criteria are expressed as the linear matrix inequalities, which can be easily checked by MATLAB LMI Control Toolbox. Finally, four numerical examples and their simulations are provided to illustrate the effectiveness of the proposed method.

Horse phenotyping based on video image analysis of jumping performance for conservation breeding.

BackgroundMany horse breeds in the world are reserved as genetic resources; however, their characteristics seem to be insufficiently clarified, especially in terms of horse performance. Two jumping ability evaluation methods have been used to compare different types of performance breeds and on this basis their applicability for precision phenotyping has been determined.MethodsJumping data of 186 young Polish Warmblood stallions (27 with an endangered status) bred for sport and multipurpose use was collected during their performance tests organised under identical environmental conditions following the same guidelines. Jumping data consisted of objective measurements of free jumping parameters and the marks for jumping. Video recordings of 514 jumps (73 records for 27 stallions with an endangered status) were collected using a digital Panasonic AG-EZ 35 camera (25 fr/sec). Filming was recorded during a free jumping test in the line on a doublebarre obstacle (100–120 cm × 100 cm). Spatial and temporal variables of the jump were measured. The analysis of variance was performed (SAS, General Linear Model and Mixed procedures) using the statistical model, which included the random effect of the horse and fixed effects of the year of test, breeding status, height of jump and the successive number of the jump for objective kinematic data. The fixed effects of the year of test and breeding status were included in the model for subjective performance test data.ResultsPerformance marks for free jumping were lower in the endangered group of stallions in the trainers’ opinion (p ≤ 0.05), while no statistically significant differences were found in the judges’ opinions. Statistically significant differences in jumping variables were measured for the bascule points—the elevations of the withers and croup were higher in the endangered group (p ≤ 0.001) and the take-off time was prolonged (p ≤ 0.05), which explained the subjective evaluation.DiscussionThe use of objective evaluation methods provides important information for practice, as phenotypic differences between horses may be unclear in the subjective evaluation. The objective evaluation should be used to characterise the performance potential of different breeds, because the information from the evaluators might not be consistent. Such characteristics should be recorded at least for every new population.

Acute Effect of Mini-Trampoline Jumping on Vertical Jump and Balance Performance

Jumping and balance are necessary skills for most athletes, and mini-trampoline training has been shown to improve them. Little is known about the acute effect of mini-trampoline jumping on jump performance and dynamic balance. Objectives: The purpose of this study is to investigate the effect of 6 maximal jumps on a mini-trampoline on countermovement vertical jump (CMVJ) variables and on balance parameters. Methods: Twenty one recreationally trained individuals participated in three testing sessions and were either allocated to a control group (N=10) or a trampoline group (N=11). All the participants performed a dynamic warm up prior to their assessments. Baseline CMVJ and balance assessments were measured. For the jump performance tests, the control group rested for 30s, and the trampoline group performed 6 maximal CMVJs on a mini-trampoline. Immediately following the trampoline jumps or the rest period, participants performed three jump trials. The jumping protocol was repeated every minute up to 5 minutes and balance was reassessed immediately after only. Results: There was no significant interaction of time by group and no group effects in all the jumping parameters, however, there was a significant increase in jump height (p <0.001) post-condition, and a significant decrease in peak power (p= 0.01) at the 4th minute for both groups. There was no significant interaction of time by condition, no time effect and no group effect (p>0.05) on the balance variables. Conclusion: These results do not support our hypothesis and show that trampoline jumping does not improve jump and balance performance acutely.

Near-optimal control for a singularly perturbed linear stochastic singular system with Markovian jumping parameters

In this paper, we investigate the near-optimal control for a singularly perturbed linear stochastic singular system with Markovian jumping parameters. Firstly, we warrant the given system has an impulse-free solution. Secondly, by means of the singular value decomposition, the existence of solution are obtained for the singularly perturbed stochastic generalized coupled differential Riccati equation and establish an existence of solution to parameter-independent system for the stochastic generalized coupled differential Riccati equation. As an application, we apply the existence results to consider the near-optimal control of singularly perturbed linear stochastic singular system with Markovian jumping parameters, and obtain the desired explicit representation of the optimal controllers for the optimal control problem with the finite horizon.

Stochastic stability analysis for neutral-type Markov jump neural networks with additive time-varying delays via a new reciprocally convex combination inequality

ABSTRACTThis paper investigates the stochastic stability problem for a class of neutral-type Markov jump neural networks with additive time-varying delays. Firstly, to derive a tighter lower bound of the reciprocally convex quadratic terms, a new reciprocally convex combination inequality is established by using parameters transformation approach. Secondly, by fully considering the peculiarity of various time-varying delays and Markov jumping parameters, an eligible stochastic Lyapunov–Krasovskii functional is constructed. Then, by employing the new reciprocally convex combination inequality and other analytical techniques, some novel stability criteria are provided in the forms of linear matrix inequalities. Finally, four illustrated examples are given to verify the effectiveness and feasibility of the proposed methods.

Stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi‐Markovian jumping parameters via novel free matrix–based integral inequality

SummaryThis paper investigates the issues of stochastic stability and extended dissipativity analysis for uncertain neutral systems with semi‐Markovian jumping parameters. A new criterion about the stochastic stability and extended dissipativity of uncertain neutral systems with semi‐Markovian jumping parameters is obtained based on the new Lyapunov‐Krasovskii functionals together with the introduced novel free matrix–based integral inequality. The major contribution of this study is that the stochastic stability and extended dissipativity concept for uncertain neutral systems with semi‐Markovian jumping parameters can be developed to simultaneously analyze the solutions of the L2 − L∞ performance, H∞ action, passivity behavior, and dissipativity by selecting different weighting matrices. Finally, several interesting numerical examples are provided to show the effectiveness and less conservatism of the proposed method.

Robust H∞ synchronization of Markov jump stochastic uncertain neural networks with decentralized event-triggered mechanism

This study examines the problem of robust H∞ synchronization of Markov jump stochastic neural networks with mixed time varying delays and decentralized event triggered scheme. We present a decentralized event-triggered scheme, which utilize only locally available information, for determining the moment in time of communication from the sensors to the significant controller. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By formulating a suitable Lyapunov–Krasovskii functional(LKF) and by using Newton–Leibniz formulation, utilizing free weighting matrix method, the sufficient conditions under which the proposed neural network is stochastic stable. Moreover, these stability criteria are expressed in terms of linear matrix inequalities (LMIs), which can be efficiently solved via the standard numerical packages. The effectiveness of the proposed results is illustrated by numerical examples.

Reliable sampled data control for Stabilization of non-linear multi-agent system with mixed delay and Markovian jumping parameters

Reliable sampled data control for Stabilization of non-linear multi-agent system with mixed delay and Markovian jumping parameters

Linear Matrix Inequality Approach to Stochastic Stabilization of Networked Control System with Markovian Jumping Parameters

This paper is concerned with the stochastic stabilization problem for a class of networked control system (NCS) with destabilizing transmission factors. By introducing the effective sampling instant to model random time delays and successive packet dropouts as two independent Markov chains, NCS is modeled as a discrete-time Markovian jump linear system with mixed integrated Markovian jumping parameters. In this way, a novel framework to analyze the stochastic stabilization problem of NCS is provided. The necessary and sufficient conditions for the stochastic stabilization of the NCS are obtained by the Lyapunov method and the state-feedback controller gain that depends on the delay modes is obtained in terms of the linear matrix inequalities (LMIs) formulation via the Schur complement theory. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Weighted Multiple Neural Network Boundary Control for a Flexible Manipulator With Uncertain Parameters

This paper addresses the angle tracking and vibration suppression for a flexible manipulator with uncertain parameters. Based on the partial differential equation (PDE) model, a unified framework of weighted multiple neural network boundary control (WMNNBC) is proposed to deal with the jumping parameters, in which neural networks are designed as the local boundary controllers to suppress vibrations. A novel proportion-derivative-like machine learning algorithm is developed to guarantee the learning convergence. Besides, the weighting algorithm is used to fuse multiple local neural network controllers to generate the appropriate global control signals with the variations of plant parameters. The stability of the overall closed-loop system is proved by the virtual equivalent system (VES) theory. The simulations are implemented to illustrate the feasibility and control performance of the proposed WMNNBC strategy.

Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching

In this paper, we are concerned with the stability analysis of stochastic nonlinear systems with delayed impulses and Markovian switching. Different from the previous literature, the impulses in this paper depend on delays and the jumping parameters are described by a continuous-time Markov chain with a finite-state space. Several novel stability criteria are obtained by using a stochastic Lyapunov function method and the Razumikhin technique. To be less conservative, the Razumikhin condition imposed on the coefficient of the estimated upper bound for the Lyapunov function's time-derivative is improved from a constant to a function, which can be either positive or negative. Finally, we use two examples and their simulations to verify the validity of the theory results.

New stochastic synchronisation condition of neutral-type Markovian chaotic neural networks under impulsive perturbations

This paper investigates the globally stochastic synchronisation problem for a class of neutral-type chaotic neural networks with Markovian jumping parameters under impulsive perturbations in mean square. By virtue of drive-response concept and time-delay feedback control techniques, by using the Lyapunov functional method, vector Wirtinger-type inequality, a novel reciprocal convex lemma and the free-weight matrix method, a novel sufficient condition is derived to ensure the asymptotic synchronisation of two identical Markovian jumping chaotic delayed neural networks with impulsive perturbation. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via MATLAB software. Finally, a numerical example with simulations is provided to illustrate the effectiveness of the presented synchronisation scheme.

Iterative Learning Control Design of Switched Systems With Markovian Jump Parameters via Fuzzy Approach

In this paper, based on Takagi-Sugeno (T-S) approach the work is concerned with the iterative learning control (ILC) problem for a class of switched systems with data packet dropouts. The designed scheme is described by a class of Markovian switching systems with transition probabilities which are time-variant in a network environment. The links of network communications between controller-to-actuator (C/A) and sensor-to-controller (S/C) are unreliable. In terms of the construction of two-dimensional (2D) T-S model, a novel composite strategy of 2D fuzzy iterative learning output feedback control is proposed. The sufficient conditions on stochastic stability are obtained by the 2D Lyapunov stability theory. Furthermore, the dynamics of the closed-loop are guaranteed to be stochastically stable and the desired $H_{\infty }$ performance is also provided. The solutions of the ILC controller are derived by the application of the cone complementarity linearisation (CCL) procedure. Finally, a numerical simulation is illustrated to show the validity of the design.

Stochastic stability criterion of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump

In this paper, the stochastic stability problem for a class of neutral-type neural networks with additive time-varying delay and uncertain semi-Markov jump is discussed. The uncertainty of semi-Markov jump refers to that the partial information on transition rates are incompletely known. Firstly, an extended reciprocally convex combination inequality with less conservative is provided. Secondly, by constructing an eligible stochastic Lyapunov–Krasovskii functional with considering more information about various time delays, uncertain semi-Markov jumping parameters, some stability criterions are derived via utilizing the improved inequality together with some integral inequalities. Finally, the validity and feasibility of the proposed method are demonstrated by two numerical examples.

Fuzzy-Model-Based Nonfragile Control for Nonlinear Singularly Perturbed Systems With Semi-Markov Jump Parameters

This paper is concerned with the fuzzy-model-based nonfragile control problem for discrete-time nonlinear singularly perturbed systems with stochastic jumping parameters. The stochastic parameters are generated from the semi-Markov process. The memory property of the transition probabilities among subsystems is fully considered in the investigated systems. Consequently, the restriction that the transition probabilities are memoryless in widely used discrete-time Markov jump model can be removed. Based on the T-S fuzzy model approach and semi-Markov kernel concept, several criteria ensuring $\delta$ -error mean square stability of the underlying closed-loop system are established. With the help of those criteria, the designed procedures which could well deal with the fragility problem in the implementation of the proposed fuzzy-model-based controller are presented. A technique is developed to estimate the permissible maximum value of singularly perturbed parameter for discrete-time nonlinear semi-Markov jump singularly perturbed systems. Finally, the validity of the established theoretical results is illustrated by a numerical example and a modified tunnel diode circuit model.

Linear state estimation for Markov jump linear system with multi-channel observation delays and packet dropouts

ABSTRACTThis paper is to investigate the linear minimum mean square error estimation for Markovian jump linear system subject to unknown Markov chains, multi-channel mode and observation delays, and packet losses. The reorganisation method is employed to convert the delayed measurement system into an equivalent delay-free one and a new state variable is introduced, by which the original state estimation with transmission delays and data losses is transformed into the new state estimation for the reorganised delay-free system with jumping parameters and multiplicative noises. The new state estimation is derived via the innovation analysis method, and an analytical solution to the estimator is given in terms of a set of generalised Riccati difference equations based on a set of coupled Lyapunov equations. Then the original state estimation will be obtained via the jumping property. Finally, we show that the difference Riccati equations converge to a set of generalised algebraic Riccati equations under appropriate assumptions, which result in an optimal stationary filter.

Passivity-based synchronization of Markovian jump complex dynamical networks with time-varying delays, parameter uncertainties, reaction–diffusion terms, and sampled-data control

The problem of passivity analysis of reaction–diffusion complex dynamical networks with time-varying delays and Markovian jumping parameters is considered in this article. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. Specially, the time varying delays are taken into consideration to describe the sample-data control of the system. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of passivity-based synchronization of complex dynamical networks even in the case of uncertainty and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and reciprocal convex techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is passive. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative example is presented to demonstrate the effectiveness and usefulness of the proposed results.

Finite-time annular domain stability of Itô stochastic impulsive systems with markovian jumping under asynchronous switching

ABSTRACT This study examines the finite time annular domain stability (FTADS) and stabilisation of a class of Itô stochastic impulsive systems with asynchronous switching controller. The asynchronous switching means that the controller switching does not accurately coincide with system switching in delayed time interval. The design of the controller depends on the observed jumping parameters, which cannot be precisely measured in real-time because of switching delay. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. When the subsystem is stable in the synchronous switching interval and unstable in the asynchronous case, a compromise among the average impulsive interval, the upper bound of delay, and the decay/increasing rate of Lyapunov function in the synchronous/asynchronous switching interval respectively is given. By the mode-dependent parameter approach (MDPA) and allowing the increase of the impulses on all the switching times, the extended FTADS criteria for Itô stochastic impulsive systems in generally nonlinear setting are derived first. Then, we focus on the case when the system in both synchronous and asynchronous switching intervals are unstable. By reaching a tradeoff among average impulsive interval, the upper bound of delay, the magnitude of impulses and the difference between the increasing rate of Lyapunov function in the synchronous and asynchronous switching interval, new sufficient conditions for existence of the state feedback controller are also developed by MDPA. In addition, we consider the effect of different impulsive strengths (harmful and beneficial impulses) and obtained less conservative results because the Lyapunov function may be non-decreasing during switching interval. Moreover, we extend the conclusion from nonlinear stochastic impulsive switching systems to linear case. Finally, we present two examples to illustrate the effectiveness of the results obtained in this study.

Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

In this paper, exponential stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to guarantee the mean square exponential stability of the equilibrium point. Then some sufficient conditions for the existence of feedback controller are presented to guarantee that the resulting closed-loop system has mean square exponential stability for the zero exogenous disturbance and satisfies a prescribed H∞ performance level. Numerical simulations are exploited to validate the applicability of developed theoretical results.

H∞ Control for Nonlinear Infinite Markov Jump Systems

In this paper, we discuss the infinite horizon H∞ control problem for a class of nonlinear stochastic systems with state, control, and disturbance dependent noise. The jumping parameters are modelled as an infinite-state Markov chain. Based on the solvability of a set of coupled Hamilton-Jacobi inequalities (HJIs), the exponential mean square H∞ controller for the considered nonlinear stochastic systems is obtained. A numerical example is given to show the effectiveness of the proposed design method.