Markovian Jump Systems Research Articles

Design of Event-Triggered Asynchronous Sliding Mode Controller for Markov Jump Systems Based on Dynamic Output Feedback

Design of Event-Triggered Asynchronous Sliding Mode Controller for Markov Jump Systems Based on Dynamic Output Feedback

Adaptive neural‐based asynchronous control for nonhomogeneous Markov jumping systems with dead zones

Adaptive neural‐based asynchronous control for nonhomogeneous Markov jumping systems with dead zones

A Double Sensitive Fault Detection Filter for Positive Markovian Jump Systems with A Hybrid Event-Triggered Mechanism

A Double Sensitive Fault Detection Filter for Positive Markovian Jump Systems with A Hybrid Event-Triggered Mechanism

Asynchronous Sliding Mode Control of Networked Markov Jump Systems via an Asynchronous Observer Approach Based on a Dynamic Event Trigger

This paper explores the utilization of sliding mode control, which relies on an asynchronous observer, for Markov jump systems subject to external disturbances. Firstly, given that the system’s mode is not directly measurable and could potentially differ from the observer’s and controller’s mode, the paper constructs an asynchronous observer employing a hidden Markov model. Secondly, a sliding surface is designed to correspond with the asynchronous observer. Moreover, a multi-parameter event-triggered mechanism is incorporated into the observer design to alleviate bandwidth strain. Thirdly, by applying the integrated sliding mode control law, we ensure that the system state trajectories will reach the sliding surface within a finite time. Fourthly, the achievement of H∞ stability is realized by making use of the Lyapunov function. Lastly, a practical-oriented example is presented to illustrate the efficiency of the established method.

A Dynamic Event-Triggered Secure Monitoring and Control for a Class of Discrete-Time Markovian Jump Systems: A Plug-and-Play Architecture

A Dynamic Event-Triggered Secure Monitoring and Control for a Class of Discrete-Time Markovian Jump Systems: A Plug-and-Play Architecture

Event-Based Asynchronous H∞ Control for Nonhomogeneous Markov Jump Systems With Imperfect Transition Probabilities.

The event-based H∞ control problem is investigated for a class of nonhomogeneous Markov jump systems (MJSs) with partially unknown transition probabilities (TPs). The MJS is characterized by a piecewise nonhomogeneous Markovian chain, where the switching of the system TP matrix is governed by a higher-level chain. A hidden Markov model (HMM) is employed to observe the system mode, which cannot always be correctly detected in practice. Under this framework, the partially unknown TPs existing in both higher-level TPs (HTPs) and conditional TPs (CTPs) are taken into account for practical consideration. Additionally, an observed-mode-dependent event-triggered mechanism (ETM) is employed to design an asynchronous controller, which is expected to alleviate the burden of the communication network. Evidently, the considered scenario is fairly general and covers some special cases. With the above consideration, sufficient conditions are established to guarantee stochastic stability of the resulting closed-loop system with a prescribed H∞ performance. Finally, two examples are presented to demonstrate the effectiveness and applicability of the proposed method.

Memory-Based Event-Triggered Control of Markov Jump Systems Under Hybrid Cyber Attacks: A Switching-Like Adaptive Law

Memory-Based Event-Triggered Control of Markov Jump Systems Under Hybrid Cyber Attacks: A Switching-Like Adaptive Law

Hybrid-triggered H∞ control for Markov jump systems with quantizations and hybrid attacks

The hybrid-triggered quantized H∞ control problem is investigated for discrete-time Markov jump systems (MJSs) under hybrid cyber attacks. A novel hybrid-triggered mechanism obeying Bernoulli distribution between the time-triggered mechanism and the adaptive event-triggered mechanism is introduced. The triggered condition considers the average value between current measured output and latest triggered output to avoid the unnecessary triggered data released. Meanwhile, a quantizer is adopted to optimize the data transmission rate and an observer-based controller is designed to resist the impact of deception attacks and aperiodic DoS attacks on the system. Utilizing Lyapunov stability theory and iterative methods, sufficient conditions are obtained to ensure that the closed-loop MJSs are asymptotically mean-square stable with H∞ performance. Then, an algorithm for gain matrices and triggered matrices is given. Finally, the effectiveness and availability of the proposed method are verified by a numerical example and a DC motor model.

Asynchronous sliding‐mode control for two‐dimensional nonlinear Markov jump systems with time‐varying delays

AbstractBased on the Roesser model, the asynchronous sliding‐mode control (SMC) problem for two‐dimensional (2‐D) Markov jump systems (MJSs) with time‐varying delays is studied in this article. Since the controller mode cannot always access the system mode, the asynchronous phenomenon between the system mode and the controller mode will be described by the hidden Markov model (HMM). First, under the framework of HMM, the asynchronous 2D‐SMC law is designed based on 2‐D sliding surface function to ensure closed‐loop 2‐D discrete MJSs asymptotic mean square stability and the reachability of sliding regions around specific sliding surfaces. Second, an algorithm for deducing the law of 2‐D asynchronous SMC is presented. Finally, a numerical example is given to verify the effective of the results.

Finite‐time H∞ filtering for Markov jump systems with partially unknown transition rates

SummaryThe thesis studies a stochastic finite‐time bounded (SFTB) filter design method for time‐varying delay Markov jump systems (MJSs) with partially unknown transition rates. First, a Lyapunov–Krasovskii functional with triple integral is built, the free weight matrix is added for lowering the conservatism. And the condition of SFTB of the error system is analyzed. Then, according to linear matrix inequalities (LMIs), a new filter design method is presented. Moreover, the dimension of the filter obtained is free, and the filter ensures that the error system is SFTB. Finally, the validity and effectiveness of the conclusion of this paper are demonstrated by simulation examples.

Observer-based control of uncertain nonlinear Markovian jump systems with time-varying delay and actuator failures via sliding mode technique

This paper focuses on the discussion of asynchronous sliding mode control (SMC) design for uncertain Markovian jump systems (MJSs) in which nonlinearities, time-varying delays, and actuator failures are considered. At first, the study establishes an asynchronous observer and correspondingly constructs a sliding mode switching function in which the controller gain operates asynchronously with the original system. Then the observer-based SMC law is designed through Lyapunov stability theory to achieve reachability of the specified sliding surface, resulting in mean-square stability of the closed-loop system. In addition, we extend the aforementioned findings to a more practical case where the conditional probability is only partially known. Eventually, numerical examples and tunnel-diode-circuit examples are provided to demonstrate the merits of the summarized results.

Asynchronous Control of 2-D Markov Jump Roesser Systems With Nonideal Transition Probabilities.

This article intends to study the asynchronous control problem for 2-D Markov jump systems (MJSs) with nonideal transition probabilities (TPs) under the Roesser model. Two practical considerations motivate the current work. First, considering that the system mode cannot always be observed accurately, a hidden Markov model (HMM) is adopted to describe the relationship between the mismatched modes. Second, considering that the TPs information related to the Markov process and the observation process is difficult to obtain, the nonideal TPs (unknown or uncertain) are simultaneously considered on the two processes. Under the considerations, several new sufficient conditions are developed for concerned closed-loop 2-D MJSs with nonideal TPs, by which the asymptotic mean square stability is ensured with an H∞ performance index. A nonconservative separation strategy is utilized to decouple the system mode TPs and the observation TPs to facilitate the analysis of nonideal TPs. An unified LMI-based condition is finally developed for the concerned closed-loop 2-D MJSs with/without nonideal TPs, showing more satisfactory conservatism than that in the literature. In the end, we present two examples to validate the superiority of the proposed design method.

Imitation-Based Reinforcement Learning for Markov Jump Systems and Its Application

Imitation-Based Reinforcement Learning for Markov Jump Systems and Its Application

Reachable Set Estimation for Neutral Markovian Jump Systems with Time-varying Delay and Distributed Delay

Reachable Set Estimation for Neutral Markovian Jump Systems with Time-varying Delay and Distributed Delay

Stabilization of Takagi–Sugeno fuzzy Hidden Markov Jump Systems with memory sampled-data control

The stability of Takagi–Sugeno fuzzy hidden Markovian jump systems by employing a memory sampled-data control (SDC) scheme that includes a constant signal transmission delay is investigated. The asynchronous situation between the system plant and the controller is represented using the hidden Markov model. The stability of the provided model is ensured by implication of the fuzzy time-scheduled Lyapunov functional (LF), and the sufficient conditions are derived in the form of linear matrix inequalities (LMIs). This simplifies the utilization and generalization of the analysis results, as they exhibit convexity in the subsystem matrix. Additionally, it diminishes the influence of external disturbances by employing the H∞ norm bound. To acquire the required time-dependent memory SDC, it is necessary to solve this set of LMIs. The efficacy and feasibility of the proposed method is established by attaining stability for a chaotic Lorenz system using the T–S fuzzy Hidden Markov Jump Systems with Memory SDC.

Adaptive fixed-time fault-tolerant tracking control for rotary steerable drilling tool systems

In this paper, the problem of adaptive fixed-time fault-tolerant tracking control is investigated for rotary steerable drilling tool systems (RSDTSs). Markov jump system (MJS) is used to describe the RSDTS with varying parameters which are induced by the changing environment. By employing the smooth projection operator technique, adaptive laws are established to estimate the faults. Based on the fault compensation strategy, a new adaptive fixed-time fault-tolerant tracking control scheme is proposed to ensure that the RSDTS is globally stochastically practically fixed-time stable. In addition, to reduce the computational burden in the backstepping framework, the derivatives of the virtual control are directly derived using command filters. Finally, the experiment performed on the rotary steerable drilling tool systems prototype is exploited to demonstrate the feasibility and effectiveness of the proposed method.

L1-gain control for 2D delayed positive continuous Markov jumping systems

This study is focused on analyzing the L1-stochastic internal stability and the design of an L1-gain controller for two-dimensional (2D) continuous positive Markov jumping systems (PMJSs) with constraints on the inputs and states. An algorithm is developed to explicitly determine the state feedback control law with the optional L1-gain performance. First, by constructing a co-positive stochastic Lyapunov function for the positive system and establishing the equation for the Markov states' mathematical expectation, several sufficient and necessary conditions for L1-stochastic internal stability are derived. This analysis indicates that 2D PMJSs with directional delays are influenced by sizes of the system matrices and magnitude of delays, and transition matrix. Second, a method for calculating the L1-gain is formulated utilizing linear programming (LP), thus, an L1-gain controller is designed to guarantee that the closed-loop system is positive and L1-stochastically internally stable, while achieving optimal L1-gain performance. Two numerical and practical examples are considered, and the influence of delays and transition probability matrices on the L1-gain is specified to validate the preceding theoretical findings.

Asynchronous Event-Triggered Control for Polynomial Fuzzy-Model-Based Markov Jump Systems With Complex Transition Probabilities

Asynchronous Event-Triggered Control for Polynomial Fuzzy-Model-Based Markov Jump Systems With Complex Transition Probabilities

Finite-Time Stabilization of Uncertain Markovian Jump Systems: An Adaptive Gain-Scheduling Control Method

Finite-Time Stabilization of Uncertain Markovian Jump Systems: An Adaptive Gain-Scheduling Control Method

Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying delay driven by fractional Brownian motion

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov–Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the pth moment exponential stability conditions are derived by utilizing the generalized fractional Itoˆ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results.