Markovian Jumping Research Articles

Adaptive Fuzzy Asynchronous Control for Nonhomogeneous Markov Jump Power Systems Under Hybrid Attacks

This article investigates the adaptive fuzzy asynchronous control problem for discrete-time nonhomogeneous Markov jump power systems under hybrid attacks. A nonhomogeneous Markov process is used to describe the phenomenon of transient failures occurring in power lines and subsequent switching of associated circuit breakers. The corresponding nonhomogeneous hidden Markov model is utilized to detect the jump modes of power systems. Both deception attack and denial-of-service attack are analyzed simultaneously owing to the vulnerability of power systems. With detected modes and fuzzy logic systems, an adaptive fuzzy asynchronous control strategy is proposed. Using the mode-dependent Lyapunov function, the existence conditions of the desired controller law are obtained such that the closed-loop power systems are bounded stable in the mean-square sense. Finally, the usefulness of the developed control strategy is demonstrated by a numerical example.

Adaptive Sliding Mode Security Control for Stochastic Markov Jump Cyber-Physical Nonlinear Systems Subject to Actuator Failures and Randomly Occurring Injection Attacks

This article investigates the issue of security control for stochastic Markov jump cyber-physical systems (SMJCPS) against actuator failures (AF), randomly occurring injection attacks (ROIA), and inaccessible states by virtue of state estimator-based adaptive sliding mode control (SMC) strategy. The knowledge of the states is generated with an estimator not requesting any input information from which a novel switching surface of linear type (SSL) is established. Then, an adaptive SMC input is developed to ensure the attainability of the SSL in limited steps, almost surely under stochastic noise, unknown ROIA, and potential AF. In the light of the arrival of the SSL and stochastic stability theory, a new stochastically stable criterion for the target SMJCPS operating on the defined SSL is deducted in the occurrence of AF, ROIA, and more generally uncertain transition rates. At last, a simulation study is performed, in which the raised control scheme is realized and certified by a tunnel diode circuit model.

Event-Triggered Control for Markov Jump Systems Subject to Mismatched Modes and Strict Dissipativity.

In order to save network resources of discrete-time Markov jump systems, an event-triggered control framework is employed in this article. The threshold parameter in the event-triggered mechanism is designed as a diagonal matrix in which all elements can be adjusted according to system performance requirements. The hidden Markov model is introduced to characterize the asynchronization between the controller and controlled system. The effect of randomly occurring gain fluctuations is taken into account during the controller design. For the purpose of guaranteeing that the closed-loop system is stochastically stable and satisfies the strictly (D₁,D₂,D₃)-ɣ-dissipative performance, sufficient conditions are constructed by employing the Lyapunov function and stochastic analysis. After linearization, the proposed controller gains are obtained by solving the linear matrix inequalities. Ultimately, a practical example of the dc motor device is used to illustrate the effectiveness of the proposed new design technique.

Adaptive Neural State Estimation of Markov Jump Systems Under Scheduling Protocols and Probabilistic Deception Attacks.

The neural-network (NN)-based state estimation issue of Markov jump systems (MJSs) subject to communication protocols and deception attacks is addressed in this article. For relieving communication burden and preventing possible data collisions, two types of scheduling protocols, namely: 1) the Round-Robin (RR) protocol and 2) weighted try-once-discard (WTOD) protocol, are applied, respectively, to coordinate the transmission sequence. In addition, considering that the communication channel may suffer from mode-dependent probabilistic deception attacks, a hidden Markov-like model is proposed to characterize the relationship between the malicious signal and system mode. Then, a novel adaptive neural state estimator is presented to reconstruct the system states. By taking the influence of deception attacks into performance analysis, sufficient conditions under two different scheduling protocols are derived, respectively, so as to ensure the ultimately boundedness of the estimate error. In the end, simulation results testify the correctness of the adaptive neural estimator design method proposed in this article.

Finite-Time H∞ Control for Time-Delay Markovian Jump Systems with Partially Unknown Transition Rate via General Controllers

This paper deals with the problems of finite-time boundedness (FTB) and H∞ FTB for time-delay Markovian jump systems with a partially unknown transition rate. First of all, sufficient conditions are provided, ensuring the FTB and H∞ FTB of systems given by linear matrix inequalities (LMIs). A new type of partially delay-dependent controller (PDDC) is designed so that the resulting closed-loop systems are finite-time bounded and satisfy a given H∞ disturbance attenuation level. The PDDC contains both non-time-delay and time-delay states, though not happening at the same time, which is related to the probability distribution of the Bernoulli variable. Furthermore, the PDDC is extended to two other cases; one does not contain the Bernoulli variable, and the other experiences a disordering phenomenon. Finally, three numerical examples are used to show the effectiveness of the proposed approaches.

Observer-Based Finite-Time Fuzzy H∞ Control for Markovian Jump Systems with Time-Delay and Multiplicative Noises

Observer-Based Finite-Time Fuzzy H∞ Control for Markovian Jump Systems with Time-Delay and Multiplicative Noises

Stochastic Sampled-Data Exponential Synchronization of Markovian Jump Neural Networks With Time-Varying Delays.

In this article, the exponential synchronization of Markovian jump neural networks (MJNNs) with time-varying delays is investigated via stochastic sampling and looped-functional (LF) approach. For simplicity, it is assumed that there exist two sampling periods, which satisfies the Bernoulli distribution. To model the synchronization error system, two random variables that, respectively, describe the location of the input delays and the sampling periods are introduced. In order to reduce the conservativeness, a time-dependent looped-functional (TDLF) is designed, which takes full advantage of the available information of the sampling pattern. The Gronwall-Bellman inequalities and the discrete-time Lyapunov stability theory are utilized jointly to analyze the mean-square exponential stability of the error system. A less conservative exponential synchronization criterion is derived, based on which a mode-independent stochastic sampled-data controller (SSDC) is designed. Finally, the effectiveness of the proposed control strategy is demonstrated by a numerical example.

Asynchronous Sampled-Data Controller Design for Switched Markov Jump Systems and Its Applications

This article is dedicated to design asynchronous aperiodic sampled-data controller for a class of Markov jump systems with switching transition rate. The sampling controller corresponding switching transition rate matrix mode is not synchronized with the system corresponding switching transition rate matrix mode due to the possible switching of the transfer rate matrix in the sampling interval. With the help of T–S fuzzy models, the state-space representation of the system is turned into a fuzzy Itô stochastic switched Markov jump systems. By constructing novel Lyapunov functionals, mean square exponential stability criteria, and dissipativity criteria are presented. Furthermore, an asynchronous aperiodic sampled-data controller is designed for fuzzy Itô stochastic Markov jump systems. At last, by fuzzing the nonlinear tunnel diode circuit model and nonlinear mass-spring-damper mechanical model, the effectiveness and lower conservativeness of the proposed method are illustrated.

Event-Triggered and Self-Triggered L∞ Control for Markov Jump Stochastic Nonlinear Systems Under DoS Attacks.

This article investigates event-triggered and self-triggered L∞ control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve L∞ performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

Memory-based adaptive event-triggered secure control of Markovian jumping neural networks suffering from deception attacks

Memory-based adaptive event-triggered secure control of Markovian jumping neural networks suffering from deception attacks

Global h-synchronization of stochastic delayed high-order inertial neural networks subject to Markovian jump parameters

As a first exploration, this paper proposed the second-order response system (SORS) method to study the global h-synchronization (SGhS) for high-order stochastic delayed inertial neural networks subject to Markovian jumping parameters. Different from previous studies, this paper avoids reducing the order of the original drive system via substitution of variables, and directly gives the corresponding SORS. In the following, under the framework of the SORS method, a regulation function dependent Lyapunov–Krasovskii functional (RFD–LKF) is designed to realize that the considered dynamics are globally mean square h-synchronous. Particularly worth mentioning is that the method proposed in this paper can greatly reduce the amount of calculation and control cost. Ultimately, via a typical example, the superiority and validity of the derived h-synchronous criterion can be well demonstrated.

Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates

This paper deals with the model reference tracking control problem of linear systems based on the observer for Markov jump systems with unknown transition rates. The main contributions are as follows: Firstly, we designed a descriptor observer for a given model by the matrix transformation. Then, a tracking control law composed of a feedforward compensator and feedback control law was designed by calculating variations based on the designed observer. The feedback part can stabilize the system. The feedforward part is the complete parametric feedforward tracking compensator. The two parts can be solved separately, and a controller that can make the system stable is proposed under the condition that transition rates are partially unknown through the Lyapunov stability theory. The feedforward parametric solution is given by the generalized Sylvester equation. The algorithm and criteria are proved by several examples and compared with the existing conclusions.

$$H_{\infty }$$ Secure Consensus of Two-Time-Scale Markov Jump Multi-agent Systems with Partially Unknown Transition Rates Against Hybrid Cyber-Attacks

$$H_{\infty }$$ Secure Consensus of Two-Time-Scale Markov Jump Multi-agent Systems with Partially Unknown Transition Rates Against Hybrid Cyber-Attacks

Energy-to-Peak Static Output Control for Continuous-Time Hidden Markov Jump Linear Systems

We study the L2 — L∞ static output feedback control, also known as energy-to-peak control, for continuous-time Markov jump systems in a context of partial observation of the Markov chain. We consider that the controller has only access to an observed process related to the Markov chain of the plant by means of an exponential hidden Markov model. Sufficient conditions for the design of output feedback controllers satisfying an upper bound on the L2—L∞ ratio are given in terms of Linear Matrix Inequalities (LMIs). Based on this result a coordinate descent algorithm is presented to reduce the L2—L∞ upper bound ratio, starting from a feasible solution for the LMIs restrictions. The paper is conclude with a numerical example to illustrate the results.

Sliding Mode Control Against False Data Injection Attacks in DC Microgrid Systems

In this letter, the problem of false data injection (FDI) attacks is investigated for dc microgrid systems, which involves Markovian jumping parameters and Lévy noises. Moreover, an adaptive sliding mode controller is constructed to assure the stability of such dc microgrid systems. First, the dynamical equations of dc microgrid systems are proposed, which consider Lévy noises and Markovian jumping parameters. Meanwhile, the impact of FDI attacks is taken into account in dc microgrid systems. Next, the sliding mode motion dynamic of dc microgrid systems can be attained by designing a sliding mode surface (SMS) in the form of integral. Several sufficient conditions are proposed to guarantee the asymptotic stability for dc microgrid systems. Then, a novel sliding mode control (SMC) law is put forward to drive systems to reach and maintain a given sliding mode surface. In addition, the solution of linear matrix inequalities can determine undetermined parameters in the SMC and SMS. Ultimately, a practical example is demonstrated to prove that the proposed adaptive sliding mode controller can ensure the stability of the dc microgrid system under FDI attacks.

Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control

<abstract><p>We are concerned in this paper with the finite-time synchronization problem for fuzzy bi-directional associative memory neural networks with Markovian switching, discrete-time delay in leakage terms, continuous-time and infinitely distributed delays in transmission terms. After detailed analysis, we come up with an intermittent quantized control for the concerned bi-directional associative memory neural network. By designing an elaborate Lyapunov-Krasovskii functional, we prove under certain additional conditions that the controlled network is stochastically synchronizable in finite time: The $ 1 $st moment of every trajectory of the error network system associated to the concerned controlled network tends to zero as time approaches a finite instant (the settling time) which is given explicitly, and remains to be zero constantly thereupon. In the meantime, we present a numerical example to illustrate that the synchronization control designed in this paper is indeed effective. Since the concerned fuzzy network includes Markovian jumping and several types of delays simultaneously, and it can be synchronized in finite time by our suggested control, as well as the suggested intermittent control is quantized which could reduce significantly the control cost, the theoretical results in this paper are rich in mathematical implication and have wide potential applicability in the real world.</p></abstract>

On the H2 Control of Hidden Markov Jump Linear Systems

This letter studies H2 control of linear systems with parameters driven by a hidden Markov chain, emphasizing a property of invariance of the norm to time shifts in the disturbance signal, which we call H2 time-invariance (H2TI). We show that some systems are not H2TI and that the lack of H2TI may deteriorate the performance of H2 control systems when they are subject to disturbances other than impulses at the time instant k = 0 (as in standard H2 control). This motivates us to propose a new variant of the H2-norm, based on a stochastic process having an impulse at a random time. We develop the formula for computing this new variant and apply the result to an LMI optimization problem. Numerical tests are performed, indicating the superiority of the proposed controller for systems subject to different types of disturbances.

Learning, Control, and Reduction for Markov Jump Systems

Learning, Control, and Reduction for Markov Jump Systems

A Kalman Variational Autoencoder Model assisted by Odometric Clustering for Video Frame Prediction and Anomaly Detection.

The combination of different sensory information to predict upcoming situations is an innate capability of intelligent beings. Consequently, various studies in the Artificial Intelligence field are currently being conducted to transfer this ability to artificial systems. Autonomous vehicles can particularly benefit from the combination of multi-modal information from the different sensors of the agent. This paper proposes a method for video-frame prediction that leverages odometric data. It can then serve as a basis for anomaly detection. A Dynamic Bayesian Network framework is adopted, combined with the use of Deep Learning methods to learn an appropriate latent space. First, a Markov Jump Particle Filter is built over the odometric data. This odometry model comprises a set of clusters. As a second step, the video model is learned. It is composed of a Kalman Variational Autoencoder modified to leverage the odometry clusters for focusing its learning attention on features related to the dynamic tasks that the vehicle is performing. We call the obtained overall model Cluster-Guided Kalman Variational Autoencoder. Evaluation is conducted using data from a car moving in a closed environment [1] and leveraging a part of the University of Alcalá DriveSet dataset [2], where several drivers move in a normal and drowsy way along a secondary road.

带有无限马尔可夫跳跃的离散系统LQ纳什博弈

带有无限马尔可夫跳跃的离散系统LQ纳什博弈