Singular Markov Research Articles

Co-design of distributed dynamic event-triggered scheme and extended dissipative consensus control for singular Markov jumping multi-agent systems under periodic Denial-of-Service jamming attacks

This paper introduces a distributed dynamic event-triggered (DDET) controller meticulously crafted to achieve resilient consensus control in singular Markov jumping multi-agent systems (SMJMAs) even in the face of periodic Denial-of-Service (DoS) jamming attacks. With a dual focus on optimizing network resource utilization and fortifying against cyber threats, we propose a distributed dynamic event-triggered scheme (DDETS) grounded in the principles of sampled data consensus. In the presence of cyber attacks, we demonstrate the transformation of the original consensus control challenge within the singular multi-agent system into a robust stability control problem, centering around a singular switching error system governed by the DoS attack signal. Acknowledging the disturbances that typify real-world scenarios, this paper establishes criteria for attaining exponential stability and stochastic admissibility within the singular Markov jumping switching error system under the extended dissipative performance index. Furthermore, we present a hybrid design for the consensus controller and DDETS, delineated through a set of solvable linear matrix inequalities (LMIs). Finally, a comprehensive array of numerical examples meticulously illustrates the compelling effectiveness and unequivocal superiority of our proposed methodology.

Finite-time Stabilization for Singular Markov Jump Systems with Generally Uncertain Transition Rates

Finite-time Stabilization for Singular Markov Jump Systems with Generally Uncertain Transition Rates

Hidden Markov model‐based ℋ∞ control for singular Markov jump systems under denial of service attacks

AbstractThis work investigates the control problem of discrete‐time singular Markov jump systems against denial of service attacks, in which the Markov state information is seen as restricted access. To solve this situation, a hidden Markov model is introduced. The main objective is to construct a controller with the help of hidden Markov model such that the stochastically admissible of the closed‐loop singular Markov jump systems with limited access mode information can be guaranteed under denial of service attacks. To produce the needed hidden Markov model‐based controller, a matrix contract transformation approach is developed. At the end, a numerical example and a tunnel diode circuit are presented to demonstrate the effectiveness and benefit of the design technique described in this research.

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.

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.

Dynamic PDC and HMM-based asynchronous output feedback strict dissipative control for nonlinear singular incomplete jumping systems with actuator saturation

This paper investigates the asynchronous output feedback strict dissipative control for nonlinear singular incomplete jumping systems with actuator saturation via dynamic parallel distributed compensation technique and hidden Markov model mechanism. Dynamic parallel distributed compensation technique is used to design the asynchronous fuzzy dynamic output feedback controller and hidden Markov model is employed to describe the asynchronous phenomenon between the singular Markov jump system modes and the dynamic output feedback controller modes. Novel conditions of stochastic admissibility and strict dissipativity for the fuzzy closed-loop singular Markov jump systems are derived based on singular value decomposition technique and improved L-K functional. The asynchronous dynamic output feedback controller gains are developed in terms of linear matrix inequalities and the minimization optimization scheme is proposed by established ellipsoid. Single-link robot arm simulation results illustrate the practicability and effectiveness of the proposed methods.

Resilient and event-triggered control of singular Markov jump systems against cyber attacks

This paper is concerned with the H ∞ resilient and event-triggered control of singular Markov jump systems against deception attacks. The deception attacks are modelled as a random bounded signal which is governed by a Bernoulli distributed random variable. The event-triggered scheme is adopted to achieve a trade-off between system performance and network resources. Based on the technique of stochastic Lyapunov–Krasovskii functionals and linear matrix inequalities, efficient criteria are developed such that the closed-loop system is stochastically admissible with a certain H ∞ performance under deception attacks. Then, the co-design of resilient controller gains and event-triggered rules is provided in terms of a group of feasible LMIs. Finally, two examples are employed to verify the validity of our design.

Event-triggered finite-time state estimation for discrete singular Markovian systems with quantization

The problem of finite-time state estimation is discussed for discrete singular Markov jump network systems (DSMNSs) based on event-triggered (ET) quantization control strategy. According to the ET network communication and quantization control schemes, an augmented DSMNS model with time-delays is first constructed. Employing stochastic Lyapunov functional and introducing relaxation matrix variables, sufficient conditions are established for the DSMNS to be singularly stochastic finite-time bounded. Besides, the ET gain matrices and ET quantized feedback controllers are co-designed by decoupling matrix variable parameters so that the augmented DSMNS is singularly stochastic finite-time bounded with a specified performance index. Eventually, the effectiveness of the proposed scheme is verified and evaluated by a numerical simulation.

Asynchronous Event-Triggered Output-Feedback Control of Singular Markov Jump Systems.

This study focused on the asynchronous event-triggered output-feedback controller design problem for discrete-time singular Markov jump systems (MJSs). A hidden Markov model (HMM) was employed to estimate the system mode, which cannot always be ideally detected in practice. Because the full state is also difficult to obtain in practical scenarios, an output-feedback control scheme was used. In addition, an HMM-based event-triggered mechanism was also employed in the design of the controller to reduce the communication burden of the networked system. Sufficient conditions for the stochastic admissibility of a closed-loop singular MJS with a prescribed H∞ performance index were established using the Lyapunov functional technique. Finally, design procedures for an asynchronous event-triggered controller were summarized as a linear-matrix-inequality-based optimization algorithm. Two examples were considered to verify the effectiveness of the asynchronous event-triggered output-feedback controller design method.

Reachable Set Control for Discrete-Time Takagi–Sugeno Fuzzy Singular Markov Jump System

This article investigates the problem of reachable set control for a class of discrete-time Takagi-Sugeno fuzzy singular Markov jump systems (T-S FSMJSs) with time-varying delay and disturbance for the first time. By designing the state feedback and output feedback controllers, and based on the Lyapunov functional, two new sufficient conditions for the reachable set control are established. The state feedback and output feedback controller gains are obtained by optimizing the iterative algorithm. Then, all the state trajectories of the closed-loop T-S FSMJSs are contained by the intersection of ellipsoids. In the end, two examples with practical application background are presented to show the validity and usability of the proposed methods.

Improved aperiodic sampled-data control for singular Markov jump systems under incomplete transition descriptions

This paper studies the aperiodic sampled-data control problem of singular Markov jump systems under uncertain and unknown transition rates. First, taking into account the system information from x(tk) to x(tk+1), a novel two-sided looped mode-dependent Lyapunov–Krasovskii function (LKF) is constructed, which provides more freedom to test the feasibility of the LMI condition in the criterion. Based on this LKF and an improved integral inequality, a stochastic admissibility condition is given by linear matrix inequalities (LMIs), which is less conservative. Then, by using a lemma of equivalent set, a controller algorithm without equality constraint is proposed by LMIs to ensure the stability of the system. Finally, several examples are provided to verify the validity of the main results.

Finite‐time exponentially extended dissipative filtering for singular time‐delay Markov jump systems with quantized outputs based on hidden Markov mode

AbstractThis article investigates finite‐time exponentially extended dissipative filtering for singular Markov jump systems with time‐varying delays and quantized outputs. The filter and quantizer are both mode‐dependent and their modes are asynchronous with the system modes, which are described by hidden Markov model. A more general performance index named as finite‐time exponentially extended dissipativity is employed to make the concept of extended dissipativity in infinite‐time domain suitable for the finite‐time case. With the aid of a series of novel and effective schemes, sufficient conditions are established to guarantee that the filtering error dynamics are finite‐time stochastically bounded with the exponentially extended dissipative performance. An asynchronous filter is successfully designed by solving a set of linear matrices inequalities. Finally, numerical examples are given to demonstrate the effectiveness of proposed methods.

Asynchronous sliding mode control of continuous-time singular markov jump systems with time-varying delay under event-triggered strategy

This paper is mainly to design an asynchronous sliding mode controller for singular Markov jump systems (SMJSs) under event-triggered strategy (ETS). A sampling-based ETS is introduced, which can not only save resources but also avoid Zeno behavior. Hidden Markov model (HMM) is used to describe the phenomenon that the system mode is not synchronized with the controller mode. A novel delay-dependent sliding mode surface is constructed. Then, an asynchronous sliding mode control (SMC) law is obtained by utilizing the ETS, which guarantees the reachability of the closed-loop system. A stochastic admissibility with H∞ performance criterion is established for SMJSs by linear matrix inequality. Finally, effectiveness of the theoretical approach is demonstrated through two examples.

Lagrangian Stochastic Model for the Motions of Magnetic Footpoints on the Solar Wind Source Surface and the Path Lengths of Boundary-driven Interplanetary Magnetic Field Lines

In this work, we extend Leighton’s diffusion model describing the turbulent mixing of magnetic footpoints on the solar wind source surface. The present Lagrangian stochastic model is based on the spherical Ornstein–Uhlenbeck process with drift that is controlled by the rotation frequency Ω of the Sun, the Lagrangian integral timescale τ L, and the root-mean-square footpoint velocity V rms. The Lagrangian velocity and the positions of magnetic footpoints on the solar wind source surface are obtained from the solutions of a set of stochastic differential equations, which are solved numerically. The spherical diffusion model of Leighton is recovered in the singular Markov limit when the Lagrangian integral timescale tends to zero while keeping the footpoint diffusivity finite. In contrast to the magnetic field lines driven by standard Brownian processes on the solar wind source surface, the interplanetary magnetic field lines are smooth differentiable functions with finite path lengths in our model. The path lengths of the boundary-driven interplanetary magnetic field lines and their probability distributions at 1 au are computed numerically, and their dependency with respect to the controlling parameters is investigated. The path-length distributions are shown to develop a significant skewness as the width of the distributions increases.

Mixed [formula omitted] and passive exponential synchronization for singular Markov jump neural networks based on hybrid event trigger scheme

This article considers the driving-response-based exponential synchronization issue for delayed singular Markov jump neural networks by virtue of hybrid event triggering strategy. By employing singular value decomposition method, the regularity and impulse-freeness of synchronization error system are obtained. Under the framework of hybrid event-triggered scheme, the novel exponential admissibility conditions, mixed H∞ and passive performance are acquired by establishing improved Lyapunov–Krasovskill functional and dealing with nonlinear neuron activation function. Furthermore, the desired synchronization state feedback controller is designed by virtue of linear matrix inequalities. Finally, a numerical example and an analog resistance-capacitance network circuit are used to verify the effectiveness and practicability of the method.

Fuzzy-model-based ℋ∞ filtering for discrete-time singular Markov jump nonlinear systems against hybrid attacks

This paper investigates the H ∞ filtering problem for a class of discrete-time singular Markov jump nonlinear systems against hybrid attacks via a fuzzy-model-based method, in which the hybrid attacks contain deception attacks and denial of service attacks. Two random variables subject to the Bernoulli distribution are used to describe whether the hybrid attacks are encountered during the measurement output of the original system being transmitted to the filter. By using linear matrix inequality technology and Lyapunov stability theory, some sufficient conditions are given to guarantee the considered systems are stochastically admissible and meet H ∞ performance index γ. The design approach of the secure filter and a specific form to acquire the expected secure filter gains are obtained, respectively. Finally, to demonstrate the effectiveness of the proposed approach, both a numerical example and a practical example are provided.

ℋ∞ filtering for discrete‐time hidden singular Markov jump systems subject to partially known probability information under DoS attacks

SummaryThis paper concentrates on the problem of asynchronous filtering for singular Markov jump systems under DoS attacks, in which the unknown probability information cases are considered. To better describe cyber security problem, DoS attacks are considered as encountered randomly and modeled by a set of stochastic variables obeying Bernoulli distribution. Besides, hidden Markov model with partially known probability information is proposed to handle the cases that the Markov state information of the system is restrictedly accessed, and the transition probability information and observation probability information can not be directly obtained. A set of criteria are derived to analyze the regularity, causality, and stochastic stability for the filtering error system with an performance index. Furthermore, an asynchronous filter design method is proposed to against DoS attacks. Finally, a numerical example and a practical example modeled by a DC motor are given to demonstrate the effectiveness of the proposed method.

Finite-Time Static Output-Feedback H∞ Control for Discrete-Time Singular Markov Jump Systems Based on Event-Triggered Scheme

The problem of finite-time static output feedback H∞ control for a class of discrete-time singular Markov jump systems is studied in this paper. With the consideration of network transmission delay and event-triggered schemes, a closed-loop model of a discrete-time singular Markov jump system is established under the static output feedback control law, and the corresponding sufficient condition is given to guarantee this system will be regular, causal, finite-time bounded and satisfy the given H∞ performance. Based on the matrix decomposition algorithm, the output feedback controller can be reduced to a feasible solution of a set of strict matrix inequalities. A numerical example is presented to show the effectiveness of the presented method.

Output Reachable Set Synthesis of Event-Triggered Control for Singular Markov Jump Systems Under Multiple Cyber-Attacks

This paper investigates the asynchronous event-triggered state-feedback control for discrete-time nonlinear singular Markov jump systems subject to reachable set bounding and stochastic cyber-attacks. An event-triggered mechanism is introduced to regulate data transmission and save network resources. While this mechanism brings advantages, it also causes that the mode information of the system and the controller are not synchronized. On the other hand, network communication has brought convenience to signal transmission, and it has also resulted in the network channel being in an open and unreliable environment, which is vulnerable to cyber-attacks. In order to solve these problems, the secure asynchronous controller is designed to effectively resist the influence of attacks. In addition, by using the reachable set analysis approach, the constructed controller ensures that the estimation error is within the boundary of the ellipsoid, and the existence conditions of the required controller are given by solving the linear matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.

H∞ Asynchronous Deconvolution Fuzzy Filter Design for Nonlinear Singular Markov Jump Systems with Time-Varying Delays

H∞ Asynchronous Deconvolution Fuzzy Filter Design for Nonlinear Singular Markov Jump Systems with Time-Varying Delays