Markovian Jump Systems Research Articles

The GM-JMNS-CPHD Filtering Algorithm for Nonlinear Systems Based on a Generalized Covariance Intersection.

Some fusion criteria in multisensor and multitarget motion tracking cannot be directly applied to nonlinear motion models, as the fusion accuracy applied in nonlinear systems is relatively low. In response to the above issue, this study proposes a distributed Gaussian mixture cardinality jumping Markov-cardinalized probability hypothesis density (GM-JMNS-CPHD) filter based on a generalized inverse covariance intersection. The state estimation of the JMNS-CPHD filter combines the state evaluation of traditional CPHD filters with the state estimation of jump Markov systems, estimating the target state of multiple motion models without knowing the current motion models. The performances of the generalized covariance intersection (GCI)GCI-GM-JMNS-CPHD and generalized inverse covariance intersection (GICI)GICI-GM-JMNS-CPHD methods are evaluated via simulation results. The simulation results show that, compared with algorithms such as Sensor1, Sensor2, GCI-GM-CPHD, and GICI-GM-CPHD, this algorithm has smaller optimal subpattern assignment (OSPA) errors and a higher fusion accuracy.

The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates

This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for the MJSs with partial knowledge in terms of the transition rates. To reduce the conservativity of the proposed condition, we used a boundary condition related to the bounds of the transition rate with slack variables. Finally, two simulation results are presented to describe the feasibility of the proposed controller.

Collaborative Optimization Design of Event-based Asynchronous Filter for Discrete-time T-S Fuzzy Markov Jump Systems

Collaborative Optimization Design of Event-based Asynchronous Filter for Discrete-time T-S Fuzzy Markov Jump Systems

Event-Triggered Distributed Fusion Estimator for Asynchronous Markov Jump Systems with Correlated Noises and Fading Measurements.

In this study, we investigate event-triggered distributed fusion estimation for asynchronous Markov jump systems subject to correlated noises and fading measurements. The measurement noises are interrelated, and they are simultaneously coupled with the system noise. The sensor samples measurements uniformly, and the sampling rates of the sensors are different. First, the asynchronous system is synchronized at state update points; then, the local filter is obtained. Furthermore, a variance-based event-triggered strategy is introduced between the local estimator and the fusion center to decrease the energy consumption of network communication. Then, a distributed fusion estimation algorithm is proposed using a matrix-weighted fusion criterion. Finally, the effectiveness of the algorithm is verified using computer simulations.

Multiplicative Barrier Certificates for Probabilistic Safety of Markov Jump Systems

This work offers a formal framework for providing safety certificates over discrete-time Markov jump systems (MJSs). Our proposed scheme centers around a new concept of multiplicative barrier certificates (MBCs), enabling us to establish a probabilistic lower bound for the safety property in infinite time horizons within this class of models. In particular, while a summative barrier certificate, as commonly proposed in the relevant literature, may not be available to ensure the safety of MJS models, we introduce an alternative approach in a multiplicative form, as opposed to the conventional “decreasing in mean” formulation. We demonstrate that in scenarios where a summative barrier does not exist, there is potential for the existence of a multiplicative counterpart. We also provide a systematic methodology grounded on the counterexample-guided inductive synthesis (CEGIS) scheme to systematically construct the proposed multiplicative certificates. We showcase the efficacy of our approach through its application in an air traffic management system.

Indefinite Robust Linear Quadratic Optimal Regulator for Discrete-Time Uncertain Singular Markov Jump Systems.

The robust LQ optimal regulator problem for discrete-time uncertain singular Markov jump systems (SMJSs) is solved by introducing a new quadratic cost function established by the penalty function method, which combines the penalty function and the weighting matrices. First, the indefinite robust optimal regulator problem for uncertain SMJSs is transformed into the robust optimal regulator problem with positive definite weighting matrices for uncertain Markov jump systems (MJSs). The transformed robust LQ problem is settled by the robust least-squares method, and the condition of the existence and analytic form of the robust optimal regulator are proposed. On the infinite horizon, the optimal state feedback is obtained, which can guarantee the regularity, causality, and stochastic stability of the corresponding optimal closed-loop system and eliminate the uncertain parameters of the closed-loop system. A numerical example and a practical example of DC motor are used to verify the validity of the conclusions.

Asynchronous Deconvolution Filtering for 2-D Markov Jump Systems With Packet Loss Compensation

Asynchronous Deconvolution Filtering for 2-D Markov Jump Systems With Packet Loss Compensation

Attack-Resistant Sliding Mode Control for Markov Jump Systems With Redundant Channels: A Novel Two-Layer Mapping approach

Attack-Resistant Sliding Mode Control for Markov Jump Systems With Redundant Channels: A Novel Two-Layer Mapping approach

An Inversion-Free Iterative Algorithm With a Scalar Tuning Parameter for Coupled Riccati Matrix Equations Arising in LQ Optimal Control of Markov Jump Systems

An Inversion-Free Iterative Algorithm With a Scalar Tuning Parameter for Coupled Riccati Matrix Equations Arising in LQ Optimal Control of Markov Jump Systems

Event-Triggered Multiasynchronous H∞ Control for Markov Jump Systems With Transmission Delay.

In this article, the issue of event-triggered multiasynchronous H∞ control for Markov jump systems with transmission delay is concerned. In order to reduce sampling frequency, multiple event-triggered schemes (ETSs) are introduced. Then hidden Markov model (HMM) is employed to describe multiasynchronous jumps among subsystems, ETSs, and controller. Based on the HMM, the time-delay closed-loop model is constructed. In particular, when triggered data are transmitted over networks, a large transmission delay may cause disorder of transmission data such that the time-delay closed-loop model cannot be developed directly. To overcome this difficulty, a packet loss schedule is presented and the unified time-delay closed-loop system is obtained. By the use of the Lyapunov-Krasovskii functional method, sufficient conditions with the controller design are formulated for guaranteeing the H∞ performance of the time-delay closed-loop system. Finally, the effectiveness of the proposed control strategy is demonstrated by two numerical examples.

Finite-Time Asynchronous Switching Control for Fuzzy Markov Jump Systems by Applying Polynomial Membership Functions

Finite-Time Asynchronous Switching Control for Fuzzy Markov Jump Systems by Applying Polynomial Membership Functions

Reinforcement Learning Control of Double-Layer Markov Jump Systems With PDT-Switched Transition Probabilities

Reinforcement Learning Control of Double-Layer Markov Jump Systems With PDT-Switched Transition Probabilities

Protocol-based Control for Hidden Markov Jump Systems With Incomplete Transition Descriptions Against Injection Attacks

Protocol-based Control for Hidden Markov Jump Systems With Incomplete Transition Descriptions Against Injection Attacks

Markov Jump System Modeling and Control of Inverter-Fed Remote Area Weak Grid via Quantized Sliding Mode

Markov Jump System Modeling and Control of Inverter-Fed Remote Area Weak Grid via Quantized Sliding Mode

Asynchronous Switching Control for Fuzzy Markov Jump Systems With Periodically Varying Delay and Its Application to Electronic Circuits

Asynchronous Switching Control for Fuzzy Markov Jump Systems With Periodically Varying Delay and Its Application to Electronic Circuits

Bumpless Transfer Hybrid Non-Fragile Finite-Time Control for Markovian Jump Systems and Its Application

Bumpless Transfer Hybrid Non-Fragile Finite-Time Control for Markovian Jump Systems and Its Application

Stability Analysis of Delayed Discrete Singular Piecewise Homogeneous Markovian Jump Systems With Unknown Transition Probabilities via Sliding-Mode Approach

Stability Analysis of Delayed Discrete Singular Piecewise Homogeneous Markovian Jump Systems With Unknown Transition Probabilities via Sliding-Mode Approach

Dynamic event-triggered resilient controller design for discrete-time singular Markov jump CPSs under hybrid cyber-attacks

In this article, the hybrid cyber-attacks for singular Markov jump systems (MJSs) are mainly solved by designing the asynchronous mixed H∞ and passive controller. A kind of dynamic event-triggered (ETM) based strategy is adopted to maximize the savings of network bandwidth resources. And the hybrid cyber-attacks including two common attacks, the spoofing attack and the denial of service (DoS) attack are considered, which are assumed to be mutually independent and meet Bernoulli distribution. The singular MJSs under cyber-attacks are converted into the singular Markov jump time-delay systems. Then, the criteria of stochastically stable for the closed-loop singular MJSs meeting the mixed H∞ and passive performance are obtained by linear matrix inequalities (LMIs). And by optimizing the obtained LMIs, the gains of asynchronous resilient controller are further derived, and the weighting matrices of dynamic event-triggered based strategy are also gained. Eventually, the feasibility of the offered way is verified by an industrial example of DC motor control system.

Secure Control of Markovian Jumping Systems Under Deception Attacks: An Attack-Probability-Dependent Adaptive Event-Triggered Mechanism

This article considers the secure control of Markovian jumping systems (MJSs) under stochastic deception attacks that occurred in the communication network. Therein, the stochastic deception attack is described by a Bernoulli random variable. Considering the limited network bandwidth and the impact of deception attacks simultaneously, we propose an attack-probability-dependent adaptive event-trigger mechanism (AETM). It can not only reduce the number of the controller updates, but also adapt to the variation of the system dynamics subject to deception attacks. A mathematical model is established for the closed-loop system under stochastic deception attacks. Then, a time-dependent looped-functional is constructed to reduce the conservatism of stability results. The norm of the system state is estimated, and based on the discrete-time Lyapunov theory, a less conservative stability criterion is derived. Then, an easy-to-implement design algorithm for the controller gain is given so that the exponential stabilization in mean square sense can be realized for Markovian jumping system subject to stochastic deception attacks. Finally, an electrical circuit example is provided to validate the feasibility and superiority of the presented method.

Probabilistic Event-Triggered Policy for Extended Dissipative Finite-Time Control of MJSs under Cyber-Attacks and Actuator Failures

This technical note investigates the problem of extended dissipative finite-time control for Markov jump systems (MJSs) with cyber-attacks and actuator failures. A probabilistic event-triggered mechanism (PETM) is proposed to relieve the communication burden by exploiting both the pattern variation of triggering thresholds and the time-varying characteristic of transmission delays. To characterize the actual control inputs, a stochastic actuator failure model (SAFM) is established using a random variable of any discrete-time distribution over [0,1]. Firstly, based on the PETM and SAFM, static output feedback controllers are devised which may not switch with the system synchronously. Then, novel sufficient conditions with less conservatism are obtained to achieve the extended dissipative finite-time control performance of the closed-loop system under admissible cyber-attacks and actuator failures. Furthermore, controller gains with non-convex constraints are calculated with the aid of a newly proposed lemma. Finally, an application oriented example is provided to verify the effectiveness and superiority of the proposed results.