Markovian Jumping Research Articles

Adaptive neural network control for Markov jumping systems against deception attacks

This paper proposes an innovative approach for mitigating the effects of deception attacks in Markov jumping systems by developing an adaptive neural network control strategy. To address the challenge of dual-mode monitoring mechanisms, two independent Markov chains are used to describe the state changes of the system and the intermittent actuator. By employing a mapping technique, these individual chains are amalgamated into a unified joint Markov chain. Additionally, to effectively approximate the unbounded false signals injected by deception attacks, an adaptive neural network technique is skillfully built. A mode monitoring scheme is implemented to design an asynchronous control law that links the mode information between the joint Markov chain and controller with fewer modes. The paper derives sufficient criteria for the mean-square bounded stability of the resulting system based on Lyapunov theories. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method.

Security control of Markovian jump neural networks with stochastic sampling subject to false data injection attacks★ ★This work was supported by the NNSF of China under Grants 61973199, 62003794, 62173214, the Shandong Provincial NSF ZR2020QF050, ZR2021MF003.

The security control of Markovian jumping neural networks (MJNNs) is investigated under false data injection attacks that take place in the shared communication network. Stochastic sampled-data control is employed to research the exponential synchronization of MJNNs under false data injection attacks (FDIAs) since it can alleviate the impact of the FDIAs on the performance of the system by adjusting the sampling periods. A multi-delay error system model is established through the input-delay approach. To reduce the conservatism of the results, a sampling-period-probability-dependent looped Lyapunov functional is constructed. In light of some less conservative integral inequalities, a synchronization criterion is derived, and an algorithm is provided that can be solved for determining the controller gain. Finally, a numerical simulation is presented to confirm the efficiency of the proposed method.

Stochastic Analysis of Control Systems Subject to Communication and Computation Faults

Control theory allows one to design controllers that are robust to external disturbances, model simplification, and modelling inaccuracy. Researchers have investigated whether the robustness carries on to the controller’s digital implementation, mostly looking at how the controller reacts to either communication or computational problems. Communication problems are typically modelled using random variables (i.e., estimating the probability that a fault will occur during a transmission), while computational problems are modelled using deterministic guarantees on the number of deadlines that the control task has to meet. These fault models allow the engineer to both design robust controllers and assess the controllers’ behaviour in the presence of isolated faults. Despite being very relevant for the real-world implementations of control system, the question of what happens when these faults occur simultaneously does not yet have a proper answer. In this paper, we answer this question in the stochastic setting, using the theory of Markov Jump Linear Systems to provide stability contracts with almost sure guarantees of convergence. For linear time-invariant Markov jump linear systems, mean square stability implies almost sure convergence – a property that is central to our investigation. Our research primarily emphasises the validation of this property for closed-loop systems that are subject to packet losses and computational overruns, potentially occurring simultaneously. We apply our method to two case studies from the recent literature and show their robustness to a comprehensive set of faults. We employ closed-loop system simulations to empirically derive performance metrics that elucidate the quality of the controller implementation, such as the system settling time and the integral absolute error.

Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models.

Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach can be employed to jointly sample models and coefficients, but the effective design of the trans-dimensional jumps of RJMCMC can be challenging, making it hard to implement. Alternatively, the marginal likelihood can be derived conditional on latent variables using a data-augmentation scheme (e.g., Pólya-gamma data augmentation for logistic regression) or using other estimation methods. However, suitable data-augmentation schemes are not available for every generalised linear model and survival model, and estimating the marginal likelihood using a Laplace approximation or a correlated pseudo-marginal method can be computationally expensive. In this paper, three main contributions are presented. Firstly, we present an extended Point-wise implementation of Adaptive Random Neighbourhood Informed proposal (PARNI) to efficiently sample models directly from the marginal posterior distributions of generalised linear models and survival models. Secondly, in light of the recently proposed approximate Laplace approximation, we describe an efficient and accurate estimation method for marginal likelihood that involves adaptive parameters. Additionally, we describe a new method to adapt the algorithmic tuning parameters of the PARNI proposal by replacing Rao-Blackwellised estimates with the combination of a warm-start estimate and the ergodic average. We present numerous numerical results from simulated data and eight high-dimensional genetic mapping data-sets to showcase the efficiency of the novel PARNI proposal compared with the baseline add-delete-swap proposal.

Synchronization of Generally Uncertain Markovian Inertial Neural Networks With Random Connection Weight Strengths and Image Encryption Application.

This article focuses on the synchronization problem of delayed inertial neural networks (INNs) with generally uncertain Markovian jumping and their applications in image encryption. The random connection weight strengths and generally uncertain Markovian are discussed in the INNs model. Compared with most existing INNs models that have constant connection weight strengths, our model is more practical because connection weight strengths of INNs may randomly vary due to the external and internal environment and human factor. The delay-range-dependent synchronization conditions (DRDSCs) could be obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, two examples are shown to demonstrate the effectiveness of the proposed results.

Asynchronous Event-Triggered-Based Control for Stochastic Networked Markovian Jump Systems With FDI Attacks

In this article, a new asynchronous event-triggered-based output-feedback control method is proposed for a special type of networked Markovian jump systems susceptible to network delays and attacks. A novel controller is designed to make allowances for four cases that are common in practical situations: 1) a network delay; 2) false data injection (FDI) attacks; 3) asynchrony between system modes and controller modes; and 4) an event-triggered scheme. First, to avoid traditional assumptions about system delays, a novel Lyapunov function is proposed, based on which a new stability theory is formulated to guarantee exponential stability. Second, an FDI attack is represented as a stochastic process, which can be dealt with properly by the designed controller. Third, a new delay-based event-triggered scheme is brought into the controller design to reduce the network bandwidth consumption and save the network transmission resources. Then, an asynchronous controller is engineered with the aid of a hidden-Markov model, which can extend the application scope of the proposed method. Note that we put the above four factors into one framework, which implies a co-design of an anti-attack controller and an event-triggered scheme is developed. Finally, an operational amplifier circuit is simulated to verify the feasibility and superiority of the designed controller.

Co-Design of Adaptive Event-Triggered Mechanism and Asynchronous H∞ Control for 2-D Markov Jump Systems via Genetic Algorithm.

This article concerns the co-design scheme of the adaptive event-triggered mechanism (AETM) and asynchronous H∞ control for two-dimensional (2-D) Markov jump systems. First, we introduce a hidden Markov model with the observation that the asynchronous phenomenon is inevitable between the plant mode and the controller mode. Besides, for economizing the communication times, an innovative 2-D AETM is constructed, which can dynamically regulate the event-triggered thresholds to strive for better system performance. Then, by utilizing the 2-D Lyapunov stability theory, nonlinear matrix inequalities are built to ensure the asymptotic mean-square stability with an H∞ performance for the closed-loop 2-D system. To avoid introducing any conservatism when handling the above nonlinear matrix inequalities, a binary-based genetic algorithm (BGA) is exploited to treat some variables as known, such that derive some directly solvable linear matrix inequalities. Finally, a simulation example is provided to verify the effectiveness of the proposed 2-D AETM-based asynchronous controller strategy with a BGA.

Event-Triggered Quantized Stabilization of Markov Jump Systems under Deception Attacks

This paper focuses on the event-triggered quantized control for Markov jump systems with deception attacks. First, we design an event-triggered scheme relying on dwell time and end instants of attacks. It can limit the number of switches within the triggered intervals and the lower bound of triggered instants. Second, the quantization rules and the increasing/decreasing rate of Lyapunov function are obtained for different cases. Next, combined with the increasing/decreasing rate, the lower bound of triggered instants, and the probability of switches occurring, the upper bound of Lyapunov function at the triggered instants is provided. On this basis, sufficient conditions ensuring the exponential convergence in the mean sense of the closed-loop system are given. Finally, atwo-tank system is provided to verify the effectiveness of the proposed stability analysis framework for Markov jump systems.

Hidden Markov Model-Based Control for Cooperative Output Regulation of Heterogeneous Multi-Agent Systems under Switching Network Topology

This paper investigates the problem of stochastically cooperative output regulation of heterogeneous multi-agent systems (MASs) subject to hidden Markov jumps using observer-based distributed control. In order to address a more realistic situation than prior studies, this paper focuses on the following issues: (1) asynchronous phenomena in the system mode’s transmission to the controller; (2) the impact of system mode switching on network topology; and (3) the emergence of coupled terms between the mode-dependent Lyapunov matrix and the control gain in control design conditions. Specifically, to reduce the complexity arising from the asynchronous controller-side mode, the leader–state observer is developed so that the solution pair of regulator equations can be integrated into the observer. Furthermore, a linear decoupling method is proposed to handle the emergence of the aforementioned coupled terms; this provides sufficient LMI conditions to achieve stochastically cooperative output regulation for heterogeneous MASs. Finally, the validity of the proposed method is shown through two illustrative examples.

A New Approach to Fault Estimation of Discrete-Time Markov Jump Fuzzy Systems with Iterative Current Observers

A New Approach to Fault Estimation of Discrete-Time Markov Jump Fuzzy Systems with Iterative Current Observers

Mode-Dependent Adaptive Event-Triggered Control for Stabilization of Markovian Memristor-Based Reaction-Diffusion Neural Networks.

This article focuses on the design of a mode- dependent adaptive event-triggered control (AETC) scheme for the stabilization of Markovian memristor-based reaction-diffusion neural networks (RDNNs). Different from the existing works with completely known transition probabilities, partly unknown transition probabilities (PUTPs) are considered here. The switching conditions and values of memristive connection weights are all correlated with Markovian jumping. A mode-dependent AETC scheme is newly proposed, in which different adaptive event-triggered mechanisms will be applied for different Markovian jumping modes and memristor switching modes. For each given mode, the corresponding event-triggered mechanism can efficiently reduce the number of transmission signals by adaptively adjusting the threshold. Thus, the mode-dependent AETC scheme can effectively save the limited network communication resources for the considered system. Based on the proposed control scheme, a new stabilization criterion is set up for Markovian memristor-based RDNNs with PUTPs. Meanwhile, a memristor-dependent AETC scheme is devised for memristor-based RDNNs. Finally, simulation results are presented to verify the effectiveness and superiority of the analysis results.

Dissipativity-Based Consensus Tracking Control of Nonlinear Multiagent Systems With Generally Uncertain Markovian Switching Topologies and Event-Triggered Strategy.

This article focuses on the dissipativity-based consensus tracking control (DBCTC) problems of time-varying delayed leader-following nonlinear multiagent systems (LFNMASs) with the event-triggered transmission strategy. The switching topologies of the LFNMASs are subject to the uncertain and partially unknown generally Markovian jumping process. The control inputs of the following agents are updated according to the proposed event-triggered transmission strategy, which could reduce the communication burden. Based on the event-triggered transmission condition and distributed consensus protocol, some dissipativity-based criteria obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII) are proposed to guarantee the LFNMAS consensus. The validity of the main results is verified by two simulation examples.

Asynchronous Output Regulation Control for Continuous-Time Markovian Jump Systems with Colored-Noise

Asynchronous Output Regulation Control for Continuous-Time Markovian Jump Systems with Colored-Noise

Regulation of Uncertain Markov Jump Linear Systems With Application on Automotive Powertrain Control

Modeling and control of dynamic systems that experience abrupt changes are challenging and fundamental tasks in applications of different areas of engineering. Among these, control synthesis for autonomous heavy-duty vehicles has the potential to highly benefit transportation systems. That said, we propose a robust recursive regulator for discrete-time Markov jump linear systems with polytopic uncertain data. We assume the uncertainties affect the state-space parameters as well as the transition probability matrix. We formulate an optimization problem using the penalty function method and design a recursive solution, whereby we attain the robust state feedback gains. We impose no restrictions on how fast the uncertainties can change between two consecutive iterations. Conditions for convergence and mean-square stability are well defined in terms of Riccati recursive equations. We also set up a procedure for powertrain polytopic model identification based on CAN bus data of an autonomous heavy-duty ground vehicle. We provide two numerical examples to verify the effectiveness of the robust recursive regulator. Moreover, in a third example, we validate the obtained powertrain model on a trajectory tracking problem and compute acceleration and braking inputs using the robust regulator.

Co-Design of Adaptive Event Generator and Asynchronous Fault Detection Filter for Markov Jump Systems via Genetic Algorithm.

This article investigates the co-design problem of adaptive event-triggered schemes (AETSs) and asynchronous fault detection filter (AFDF) for nonhomogeneous higher-level Markov jump systems, involving the hidden Markov model (HMM), higher-level Markov chain (MC), and conic-type nonlinearities. The transformation of the system transition probability can be reflected by the designed higher-level MC. An HMM with another conditional transition probability is applied to detect higher-level Markov processes and make the system be more practical. In order to balance the utilization of network resources and system performance, a novel AETS is proposed and used in the construction of the AFDF. By the Lyapunov theory, sufficient conditions are given to ensure the existences of the AETS and AFDF. It is not only an appropriate tradeoff between the utilization of network resources and system performance, but also reduces the conservatism. Finally, a numerical example is given to detect the faults effectively by the co-designed AFDF.

Analysis of Markovian Jump Stochastic Cohen–Grossberg BAM Neural Networks with Time Delays for Exponential Input-to-State Stability

Analysis of Markovian Jump Stochastic Cohen–Grossberg BAM Neural Networks with Time Delays for Exponential Input-to-State Stability

Finite/fixed‐time synchronization of nonidentical chaotic delayed neural networks with Markovian jump and uncertainties via sliding mode control

AbstractThis article investigates the finite/fixed‐time synchronization problem of Markovian jumping delayed chaotic recurrent neural networks with uncertainties by employing sliding mode control method. In order to cope with Markovian jump and parameter uncertainties, sliding model control is used for its strong robustness and insensitivity character to external disturbances and parameter variations. Above all, two simplified sliding mode surfaces are constructed. Following that, matching controllers are constructed to guarantee the finite/fixed‐time reachability of sliding mode surfaces. Additionally, the dynamics of the sliding mode surfaces can be achieved in a finite/fixed‐time. Based on the Lyapunov stability theory, some sufficient conditions are proposed to guarantee the finite/fixed‐time synchronization. Compared with the conclusions of the existing literature, this article generalizes the corresponding results to Markovian jump, parameter uncertainties, and nonidentical systems. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

Tracking Control Design for Markov Jump Systems With Time-varying Delay and External Disturbances

Tracking Control Design for Markov Jump Systems With Time-varying Delay and External Disturbances

Optimal Control and Stabilization for Discrete-time Markov Jump Systems With Indefinite Weight Costs and Multi-channel Multiplicative Noises

Optimal Control and Stabilization for Discrete-time Markov Jump Systems With Indefinite Weight Costs and Multi-channel Multiplicative Noises

Adaptive Event-Triggered Asynchronous Fault Detection for Nonlinear Markov Jump Systems With Its Application: A Zonotopic Residual Evaluation Approach

In this paper, the event-triggered asynchronous fault detection (FD) problem is investigated for a class of nonlinear Markov jump systems (NMJSs) via zonotopic residual evaluation (ZRE). An adaptive event-triggered scheme (AETS) is utilized to reduce the redundant data releasing frequency such that both communication resources and network bandwidth can be saved as much as possible. The hidden Markov model (HMM) with generally hybrid probabilities is introduced into the FD framework to fully characterize the asynchronization phenomenon between the plant and the FD filter as well as the event generator and to address both the general transition and mode detection information issues simultaneously. By applying the double variables-based decoupling principle and variable substitution principle, a co-design criterion of optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}/H_{\infty }$</tex-math></inline-formula> asynchronous reduced-order FD filter and AETS is derived fully considering accessible mode information, such that the generated residual signal is sensitive to system faults while being robust to amplitude-bounded exogenous disturbances and measurement noise. Furthermore, a novel ZRE strategy with dynamic thresholds is developed for FD in NMJSs. Finally, an application of automotive electronic throttle body is used to illustrate the effectiveness of the proposed approach.