Markovian Jumping Research Articles

Synchronization Analysis for Stochastic T-S Fuzzy Complex Networks with Markovian Jumping Parameters and Mixed Time-Varying Delays via Impulsive Control

In this paper, we propose and explore the synchronization examination for fuzzy stochastic complex networks’ Markovian jumping parameters portrayed by Takagi-Sugeno (T-S) fuzzy model with mixed time-varying coupling delays via impulsive control. The hybrid coupling includes time-varying discrete and distributed delays. Based on appropriate Lyapunov–Krasovskii functional (LKF) approach, Newton–Leibniz formula, and Jensen’s inequality, the stochastic examination systems and Kronecker product to create delay-dependent synchronization criteria that guarantee stochastically synchronous of the proposed T-S fuzzy stochastic complex networks with mixed time-varying delays. Adequate conditions for the synchronization criteria for the frameworks are established in terms of linear matrix inequalities (LMIs). At long last, numerical examples and simulations are given to demonstrate the correctness of the hypothetical outcomes.

Infinite horizon LQ Nash Games for SDEs with infinite jumps

AbstractIn this paper, we consider infinite horizon linear‐quadratic (LQ) Nash games for stochastic differential equations (SDEs) with infinite Markovian jumps and (x,u,v)‐dependent noise. An indefinite stochastic LQ result is first derived for the considered system. Then, under the condition of strong detectability, a necessary and sufficient condition for the existence of a Nash equilibrium is put forward in terms of the solvability of a countably infinite set of coupled generalized algebraic Riccati equations (ICGAREs). Moreover, the mixed H2/H∞ control is investigated by Nash game approach as an important application. At last, we present an iterative algorithm to solve the ICGAREs, and a numerical simulation is given to illustrate its efficiency.

Passivity Analysis of Markov Jumping Delayed Reaction-Diffusion Neural Networks under Different Boundary Conditions

This work analyzes the passivity for a set of Markov jumping reaction-diffusion neural networks limited by time-varying delays under Dirichlet and Neumann boundary conditions, respectively, in which Markov jumping is used to describe the variations among system parameters. To overcome some difficulties originated from partial differential terms, the Lyapunov–Krasovskii functional that introduces a new integral term is proposed and some inequality techniques are also adopted to obtain the delay-dependent stability conditions in terms of linear matrix inequalities, which ensures that the designed neural networks satisfy the specified performance of passivity. Finally, the advantages and effectiveness of the obtained results are verified via displaying two illustrated examples.

Extended Dissipative Control for Markovian Jump Time-Delayed Systems with Bounded Disturbances

In this work, the result of reachable set bounding and extended dissipative control synthesis of the Markovian jump time-delayed system is studied subject to stochastic actuator failures and partially known transition probabilities. Specifically, a novel actuator fault model is designed, in which the actuator fault matrix satisfies a certain probabilistic condition. Under the construction of an appropriate Lyapunov–Krasovskii functional (LKF), as well as reciprocal convex approach, Jensen’s integral inequality, and reachable set lemma, delay-dependent sufficient criteria are obtained in terms of linear matrix inequalities (LMIs) for finding an ellipsoid to bound the reachable sets of the Markovian jump time-delayed system with bounded disturbances. Finally, two numerical examples are provided to validate the effectiveness of the proposed strategy.

Target State and Markovian Jump Ionospheric Height Bias Estimation for OTHR Tracking Systems

Ionospheric heights provided by ionosondes are vital for over-the-horizon radar (OTHR) target tracking. However, biases contained in the provided ionospheric heights definitely cause degradation of the tracking performance. This paper is concerned with the joint estimation problem of the target state and the ionospheric height bias for OTHR target tracking subject to multipath and cluttered measurements. A Markovian jump ionospheric height bias model is presented by simultaneously considering the intermittent and abrupt ionosphere changes. Meanwhile, a set of stochastic variables are adopted to depict association uncertainties among measurements, clutters, and propagation modes so that association is embedded in the resultant measurement model with random coefficients. Through such modeling transformation from association uncertainties to parameter randomness, the coupling processing of data association and state estimate is equivalent to pure state estimate subject to stochastic parameters. Furthermore, an optimal linear joint estimator containing causality constraints is developed in the minimum mean-squared error sense, and further extended to the case of nonlinear measurement model via iterative optimization. A target tracking example with four resolvable propagation modes illustrates the effectiveness of the proposed estimation scheme.

Análisis de la estabilidad de los sistemas lineales con saltos markovianos en tiempo continuo

In this paper analyzed the stability of linear systems with continuous Markovian jumps. Firstly, the conditions for the Markov chain to be homogeneous and the state space is finite are imposed. Then the types of stability are presented, for example quadratic average stability, stochastic stability, exponential stability and almost certain stability. Stability in quadratic mean is analyzed by the real part of the eigenvalues of a certain matrix. Finally, an equation of Lyapunov is presented.

Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control

This paper focuses on the exponential stabilization problem for Markov jump neural networks with Time-varying Delays (TDs). Firstly, we provide a new Free-matrix-based Exponential-type Integral Inequality (FMEII) containing the information of attenuation exponent, which is helpful to reduce the conservativeness of stability criteria. To further save control cost, we introduce a sample-based Adaptive Event-triggered Impulsive Control (AEIC) scheme, in which the trigger threshold is adaptively varied with the sampled state. By fully considering the information about sampled state, TDs, and Markov jump parameters, a suitable Lyapunov–Krasovskii functional is constructed. With the virtue of FMEII and AEIC scheme, some novel stabilization criteria are presented in the form of linear matrix inequalities. At last, two numerical examples are given to show the validity of the obtained results.

An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters

The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings.

Modified Looped Functional for Sampled-Data Control of T–S Fuzzy Markovian Jump Systems

This article investigates the sampled-data control for a class of Takagi-Sugeno (T-S) fuzzy Markovian jump systems via a novel looped functional approach. By refining the fractional delayed state concept, the looped functional is established to include more sampling information of the intervals not only from x(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) to x(t) but also from x(t) to x(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sub> ), which would contribute to a reduction in the conservatism. Then, a sufficient criterion is presented to ensure the stochastic stability of the resulting closed-loop system, based on which the sampled-data controller is further designed for the T-S fuzzy Markovian jump system under the influence of asynchronous premise variables. Finally, the obtained theorems are applied to a numerical example and a practical application to show the effectiveness and superiority of the proposed method.

Stability of stochastic discrete-time piecewise homogeneous Markov jump systems with time delay and impulsive effects

This paper considers the stability of stochastic nonlinear discrete-time impulsive systems with time delay and Markov jumps. The transition probabilities of Markov jumps are finite piecewise homogeneous and the variations in the finite set are contingent on a higher-level transition probability matrix. By Lyapunov functional method and the discrete average impulsive interval approach, several novel stability criteria are obtained, which can loosen the constraint on impulsive intervals and thus reduce the conservativeness compared with previous results that take the upper/lower bound of all impulsive intervals. Also, our results are suitable for both stable impulses and unstable impulses. As illustrations, the obtained results are applied to stochastic impulsive neural networks and stochastic impulsive oscillator model, respectively. The simulations are also presented to support and validate the theoretical results.

Road extraction from remote sensing image based on marked point process with a structure mark library

ABSTRACT This paper proposes a road extraction algorithm based on marked point process (MPP) with a structure mark library. Instead of segments as elements in traditional MPP-based road extraction algorithm, the proposed algorithm uses a library including shapes ‘X,’ ‘Y’, ‘L,’ and ‘–’ to build road network. Elements in the library are defined according to the typical structures in the complex road network and their locations are modelled as random points. Based on that modelling, a local structure model to constrain interactions between the elements is built. On the other hand, a spectral measurement model is built by testing the spectral homogeneity and spectral heterogeneity of pixels covered by road body and non-road body. In this way, by using Bayes theorem, all of the models are integrated together into a road extraction model. To extract the optimal road system based on a maximum posterior probability criteria, the simulated annealing RJMCMC (Reversible Jump Markov Chain Monte Carlo) algorithm with related transfer kernels is designed properly. Remote sensing images covering different road networks are experimented with the proposed algorithm and conventional algorithm, respectively. Compared with the results obtained from both of them, it demonstrates that the proposed algorithm is visually and quantitatively effective for road extraction.

Fixed-time sliding mode controller design for a class of nonlinear Markovian jumping systems

In this paper, a sliding mode control (SMC) strategy is applied to investigate the fixed-time stabilization (FTS) problems for nonlinear Markovian jumping systems (NMJSs) with nonlinear parts satisfying conic conditions. We aim to design a suitable SMC law to drive the system state trajectories onto the specified sliding mode surfaces (SMS) within a specified fixed-time interval. Then, by using the slack matrix approach, the sufficient conditions are derived to ensure the FTS of MJSs during the reaching phase. An appropriate Lyapunov-Krasovskii functional method is given to guarantee the FTS of the NMJSs during the slidinging motion phase. Finally, the FTS condition of the NMJSs in the whole fixed-time interval is given and proved. The effectiveness of the method is verified by a simulation result related to the Chua’s circuit.

Finite-Time Stability and Stabilization of Discrete-Time Switching Markov Jump Linear System

Switching Markov jump linear system (SMJLS), a special hybrid system, has attracted a lot of studies recently. SMJLS is governed by stochastic and deterministic commutations. This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems. Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided, and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities (LMIs). Finally, numerical examples are given to show the feasibility and effectiveness of the results.

PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps

AbstractA parameter estimation method, called PMCMC in this paper, is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps. There is a closed form solution to term structure of interest rates under Markov regime. However, the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM) in the case of adding jumps. Although the difficulty of parameter estimation greatly prevents from researching models, we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility. The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR. Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.

Reachable set estimation of delayed fuzzy inertial neural networks with Markov jumping parameters

This paper addresses the problem of reachable set estimation for a class of Takagi-Sugeno fuzzy model based Markov jump inertial neural networks with time-varying delay. The objective of this paper is to obtain a compact set bounding all states of the system from some domains under initial conditions, while all the states from other domain are exponential convergence in another compact set. Primarily, on the basis of the Lyapunov-Krasovskii functional (LKF), in which both the upper and lower bounds of time-varying delay as well as the triple-summation term are considered, a novel approach of combining the reciprocally convex combination and weighted summation inequalities is employed to get the less conservative conditions. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

Adaptive Neural Sliding Mode Control of Markov Jump Systems Subject to Malicious Attacks

This article investigates the problem of adaptive neural sliding mode control for Markov jump systems. The transition probabilities of the Markov process are partly unknown. The cyber layer, which is vulnerable to the adversary, is deployed to broadcast the control signal to the actuator. The attacker can inject malicious information to the control signal to deteriorate the system performance. A sliding mode controller is designed to stabilize the system. Then, sufficient conditions that ensure the stability of the closed-loop system are given in the framework of the Lyapunov theory. In the end, two simulation examples are applied to illustrate the effectiveness and feasibility of the proposed methodology.

Composite disturbance rejection control for Markovian Jump systems with external disturbances

This paper concerns the active disturbance rejection of Markovian jump systems (MJSs) by utilizing disturbance observers. The control objective is to improve the control performance of closed-loop MJSs under the influence of the external matched and mismatched disturbances. The disturbance observer is designed to estimate the unknown disturbances, the composite disturbance rejection controllers are organized to compensate the impact of the disturbance. Accordingly, for both the disturbance estimation error systems and closed-loop systems, the stochastic stability analysis problems are also addressed. Finally, two examples are carried out to validate the practicability of the developed control approaches.

Adaptive Event-Triggered $$H_{\infty }$$ Control for Markov Jump Systems with Generally Uncertain Transition Rates

Adaptive Event-Triggered $$H_{\infty }$$ Control for Markov Jump Systems with Generally Uncertain Transition Rates

Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

This note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a necessary condition for the solution of H2/H∞ control are, respectively, offered by four cross-coupled Hamilton–Jacobi equations (HJEs). Besides, numerical examples show the effectiveness of the obtained results.

Stability and stabilization for singularly perturbed systems with Markovian jumps

SummaryThis article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any with positive bound predefined. First, stability conditions expressed ϵi‐free but involving its bound are developed by constructing an ϵi‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.