Non-homogeneous Markov Process Research Articles

Finite-Time Fuzzy Fault-Tolerant Control for Nonlinear Flexible Spacecraft System with Stochastic Actuator Faults

In the quest for unparalleled reliability and robustness within control systems, significant attention has been directed toward mitigating actuator faults in diverse applications, from space vehicles to sophisticated industrial systems. Despite these advances, the prevalent assumption of homogeneous actuator faults remains a stark simplification, failing to encapsulate the stochastic and unpredictable nature of real-world operational environments. The problem of finite-time fault-tolerant control for nonlinear flexible spacecraft systems with actuator faults is addressed in this paper, utilizing the T-S fuzzy framework. In a departure from conventional approaches, actuator failures are modeled as random signals following a nonhomogeneous Markov process, thus comprehensively addressing the issue of timeliness, which has previously been overlooked in the literature. To effectively manage the intricacies introduced by these factors, the nonhomogeneous Markov process is represented as a polytope set. The proposed solution involves the development of a nonhomogeneous matrix transformation, accompanied by the introduction of adaptable parameters. This innovative controller design methodology yields a stability criterion that ensures H∞ performance in a mean-square sense. To empirically substantiate the effectiveness and advantages of the proposed approaches, a numerical example featuring a nonlinear spacecraft system is presented.

Asynchronous dissipative control for nonhomogeneous Markov jump systems with dual Markovian wireless fading channels

This article is devoted to the matter of asynchronous state feedback control for a class of nonhomogeneous Markov jump systems subjected to the dual Markovian wireless fading channel. A key feature here is that dual Markov chain is employed to model the stochastically switching of channel state with nonhomogeneous Markov process, which characterize both the transition of channel mode itself and the dependence on the system mode. Meanwhile, channel state-dependent packet dropout rate is time-varying with different channel mode. In the case of that, existing methods are difficult to deal with, resulting in the degradation of system performance. To this end, hidden Markov model-based asynchronous controller is firstly presented with compensated measurements. Secondly, co-designing with the asynchronous controller, a novel dynamic compensator is constructed to handle the mismatched measurements. Then, since both the Markov process of system and channel are considered, dual mode-dependent Lyapunov functional is constructed to verify the stochastic stability of the augmented system, as well as the strictly dissipative performance, which leads to less conservatism compared to the single mode-dependent one. Finally, a boost converter model driven by pulse-width-modulation is presented to demonstrate the validation of the proposed strategies.

Nonhomogeneous Markov Process Modeling for Software Reliability Assessment

Nonhomogeneous Markov Process Modeling for Software Reliability Assessment

Finite-Time Control of Markov Jump Lur'e Systems With Singular Perturbations

This paper investigates the asynchronous controller design issue for Markov jump Lur'e systems with singular perturbations within a fixed time interval. For broader practical applications, the variation of system modes is regulated by a switched nonhomogeneous Markov process that corresponded to both lower-level nonhomogeneous stochastic jumping and higher-level deterministic switching. By resorting to the hidden nonhomogeneous-Markov model, an asynchronous control law that relies on the detected mode information is proposed. In light of the mode-dependent average dwell time strategy and mode-dependent stochastic system theory, the singularly perturbed parameter-independent conditions are attained to ensure the stochastic finite-time boundedness of the resulting systems. With respect to a linear matrix inequality optimization problem, a solution to the maximum singular perturbation parameter is obtained. Finally, the feasibility and applicability of the devised theoretical results are verified by simulation examples.

Fuzzy-Affine-Model-Based Filtering Design With Memory-Based Dynamic Event-Triggered Protocol

In this article, a novel dynamic event-triggered protocol is constructed to deal with the filtering problem for affine systems presented by Takagi–Sugeno (T–S) fuzzy model. Unlike the traditional fuzzy systems, a unified framework of T–S fuzzy affine systems is formulated, which is more capable of approximation over different operating regions. For achieving desirable performance while saving communication resources, the memory-based dynamic event-triggered protocol is constructed by flexibly exploiting a series of historically triggered packets. The fading channel is time-varying and described as a novel nonhomogeneous Markov process, in which a higher level deterministic switching signal regulates the variation of transition probabilities. By adopting the region-dependent Lyapunov theory, the mean-square exponentially stable, and expected <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance for resulting systems is guaranteed. In the end, an inverted pendulum model is applied to verify the results of the theoretical analysis.

Fault detection filtering of nonhomogeneous Markov switching memristive neural networks with output quantization

This paper explores the fault detection filtering problem of Markov switching memristive neural networks with network-induced constraints in the discrete-time domain. The mode changes of memristive neural networks are described by a piecewise nonhomogeneous Markov process, whose transition probabilities are time-varying and governed by a higher-level nonhomogeneous Markov process. A generalized framework of Markov switching memristive neural networks includes the existing neural networks as special cases. In light of the limited communication bandwidth, the quantized measurement and packet dropouts are considered jointly. A mode-dependent fault detection filter is constructed to generate a residual signal and achieve better performance. From the mode-dependent yet time-varying Lyapunov functional, some less conservative sufficient conditions are devised for Markov switching memristive neural networks to ensure the performance level. Eventually, a simulation example is addressed to verify the feasibility of the attained theoretical analysis.

Finite-time optimal control for Markov jump systems with singular perturbation and hard constraints

This study addresses the finite-time optimal control problem for Markov jump systems subject to singular perturbations and hard constraints. The transition probabilities are considered to vary randomly within a finite set, which can be governed by a higher-level nonhomogeneous Markov process. The input signal is quantized dynamically before being passed to the controller, and a generalized framework is formulated based on the quantized control input and actuator faults. The goal is to ensure the finite-time boundedness of Markov jump singularly perturbed systems by designing a controller that satisfies the hard constraints. Then, by adopting a novel Lyapunov functional, the singularly perturbed parameter-independent sufficient conditions are obtained. For the preset finite-time interval, the optimization problem of minimizing the upper bound of the state trajectory is skillfully solved. Finally, a simulation example is presented to verify the effectiveness of the proposed design method.

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.

Improved filtering of interval type-2 fuzzy systems over Gilbert-Elliott channels

This study is concerned with the filtering problem for networked interval type-2 (IT2) fuzzy systems in the presence of a time-varying saturation function. Different from the existing Bernoulli-type/Gilbert-Elliott packet loss over the unreliable medium, a generalized Gilbert-Elliott model is presented to describe the data transmission follows a two-state nonhomogeneous Markov process, whose transition probabilities are time-varying. For the purpose of mitigating the impacts of abnormal information, a novel filter in the presence of saturation function is constructed, in which the saturation level is dynamically updated along with the estimation errors. On the basis of Lyapunov theory, sufficient conditions for finite-time boundedness of IT2 fuzzy systems are devised. In the end, a simulation example is exploited to show the effectiveness of the above-derived results.

Output-Feedback Control for Fuzzy Singularly Perturbed Systems: A Nonhomogeneous Stochastic Communication Protocol Approach.

In this study, the output-feedback control (OFC) strategy design problem is explored for a type of Takagi-Sugeno fuzzy singular perturbed system. To alleviate the communication load and improve the reliability of signal transmission, a novel stochastic communication protocol (SCP) is proposed. In particular, the SCP is scheduled based on a nonhomogeneous Markov chain, where the time-varying transition probability matrix is characterized by a polytope-structure-based set. Different from the existing homogeneous Markov SCP, a nonhomogeneous Markov SCP depicts the data transmission in a more reasonable manner. To detect the actual network mode, a hidden Markov process observer is addressed. By virtue of the hidden Markov model with partly unidentified detection probabilities, an asynchronous OFC law is formulated. By establishing a novel Lyapunov-Krasovskii functional with a singular perturbation parameter and a nonhomogeneous Markov process, a sufficient condition is exploited to guarantee the stochastic stability of the resulting system, and the solution for the asynchronous controller is portrayed. Eventually, the validity of the attained methodology is expressed through a practical example.

Improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems with incomplete transition rates

This paper proposes an improved asynchronous stabilization method for nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition rates via a nonparallel distributed compensation (non-PDC) control scheme. To cover a more realistic situation in the continuous-time MJFS domain, this paper focuses on addressing the following issues differently from previous studies: 1) emergence of a nonhomogeneous Markov process and asynchronous control mode, 2) separation of the Lyapunov matrix from the control gain within stabilization conditions, and 3) relaxation of stabilization conditions subject to multiple time-varying parameters. Specifically, the effects of nonhomogeneity and asynchronism are simultaneously reflected in the stabilization conditions, and separation and relaxation techniques are additionally developed as needed. Finally, the advantages of our method are illustrated through two examples: the first is provided to show the effectiveness of the proposed separation technique, and the second is provided to show that the relaxed stabilization conditions are less conservative than previous results.

An event-triggered round-robin protocol to dynamic output feedback control for nonhomogeneous Markov switching systems

This paper addresses the dynamic output feedback control issue for nonhomogeneous Markov switching systems with an event-triggered round-robin protocol. The transition probability matrix of the nonhomogeneous Markov process is time-varying, which can be characterized by a polytopic structure. To alleviate the communication burden in a shared network, as a first effort, a novel dynamic event-triggered round-robin protocol is forwarded to regulate whether to release the measurements and which ones to release. In light of the dynamic event-triggered round-robin protocol, an asynchronous dynamic output feedback control law is constructed, which reflects the mismatching phenomenon of modes switching between the nonhomogeneous Markov switching systems and the desired controllers. By resorting to a novel Lyapunov functional, sufficient conditions are attained to guarantee the stochastic stability of the augmented dynamic. At last, two examples are addressed to verify the effectiveness and applicability of the theoretic results.

Saturation control for fuzzy markovian switching systems with singularly perturbation and cyber-attacks

This paper is concerned with the issue of saturation control for discrete-time fuzzy Markov switching singularly perturbed systems. To describe the dynamic stochastic jumping behavior of system states, a novel nonhomogeneous Markov process is proposed, whose time-varying transition probabilities are orchestrated by a higher-level deterministic switching signal. Additionally, a novel control law is built by considering the random occurrence of cyber-attacks, and cyber-attacks rates are uncertain. Meanwhile, the saturation mechanism is adopted in designing an asynchronous controller, which is capable of eliminating the impact of cyber-attacks to a certain extent. In the end, two simulation results are provided to verify the effectiveness of the proposed methodology.

Protocol-based filtering for fuzzy Markov affine systems with switching chain

This paper investigates the reduced-order filter design method for fuzzy Markov jump affine systems with dynamic event-triggered protocol and uncertain packet dropouts. Aiming at approximating the nonlinearities with high accuracy and broadening practical application, the fuzzy Markov jump affine systems associated with mode-dependent operating regions are developed. A novel nonhomogeneous Markov process is proposed to describe the generalized stochastic jumping among subsystems, whose time-varying transition probabilities are orchestrated by a higher-level deterministic switching signal. Compared with the conventional Markov process with arbitrary switchings, the average dwell-time strategy is adopted in the novel nonhomogeneous Markov process to improve the dynamic performance. A dynamic event-triggered protocol is provided to alleviate the network transmission burden by elongating the interval between any two consecutive events. Based on the variation of state-space partitions, nonsynchronous reduced-order generalized filters are considered. Under this framework, sufficient criteria are attained to ensure stochastic stability and prescribed l2−l∞ performance for the filtering error systems. Eventually, the theoretical findings are verified by two simulation examples.

Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time

The stochastic process non-homogeneous Markov system in a stochastic environment in continuous time (S-NHMSC) is introduced in the present paper. The ordinary non-homogeneous Markov process is a very special case of an S-NHMSC. I studied the expected population structure of the S-NHMSC, the first central classical problem of finding the conditions under which the asymptotic behavior of the expected population structure exists and the second central problem of finding which expected relative population structures are possible limiting ones, provided that the limiting vector of input probabilities into the population is controlled. Finally, the rate of convergence was studied.

A Markov chain-based model for structural vulnerability assessmentof corrosion-damaged reinforced concrete bridges.

The deterioration and cracking of reinforced concrete (RC) bridges due to the chloride-induced corrosion of steel reinforcement is an inherently time-dependent stochastic phenomenon. In the current practice of bridge management systems, however, the determination of the condition states of deteriorated bridges is highly dependent on the opinion of experienced inspectors. Taking such complexity into account, the current paper presents a new stochastic predictive methodology using a non-homogeneous Markov process, which directly relates the visual inspection data (corrosion rate and crack widths) to the structural vulnerability of deteriorated concrete bridges. This methodology predicts the future condition of corrosion-induced damage (concrete cracking) by linking structural vulnerability analysis and a discrete-time Markov chain model. The application of the proposed methodology is demonstrated through a case-study corrosion-damaged RC bridge pier.This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

Event-based asynchronous dissipative filtering for fuzzy nonhomogeneous Markov switching systems with variable packet dropouts

This work concerns the event-based asynchronous filtering problem for T-S fuzzy nonhomogeneous Markov switching systems with variable packet dropouts. The discrete-time nonhomogeneous Markov process is adopted to depict mode switching among subsystems, in which the time-varying transition probabilities are characterized by a polytope structure. The variable packet dropouts are developed to describe the randomly occurring packet dropouts, where the arriving rate remains variable and uncertain. Aiming to save the limited network bandwidth, event-triggered strategy and quantization scheme are presented. By establishing the fuzzy-rule-dependent Lyapunov functional and applying a hidden Markov model policy, sufficient criteria are gained and asynchronous filters are designed by solving linear matrix inequalities (LMIs). Finally, the applicability of the proposed filtering strategy is verified by an inverted pendulum model.

Fuzzy-Model-Based Control for Singularly Perturbed Systems With Nonhomogeneous Markov Switching: A Dropout Compensation Strategy

This article addresses the asynchronous control for singularly perturbed systems with nonhomogeneous Markov switching approximated by T–S fuzzy models. The transition probabilities of the nonhomogeneous Markov process are supposed to be time-varying and distinguished by of a polytopic set. As distinct from some reported works, to abate the effect of missing packets in unreliable communication network, a novel dropout compensation strategy is constructed, where the packet arriving rate is assumed to be uncertain. Meanwhile, to describe the asynchronizations of the dropout compensation strategy and the controller, the hidden Markov models are absorbed. By resorting to the fuzzy-rule-dependent and the parameter-dependent Lyapunov–Krasovskii functional, novel sufficient conditions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance are formulated and the fuzzy-based asynchronous controller gains are realized. Finally, to testify the efficiency and applicability of the proposed results, a numerical example and practical tunnel diode circuit system are provided.

Asynchronous filtering for nonhomogeneous Markov jumping systems with deception attacks

This paper deals with the problem of asynchronous filtering for nonhomogeneous Markov jumping systems with deception attacks. To describe the nonhomogeneous Markov process, the polytopic-structure-based transition probabilities (TPs) are introduced. Note that TPs are characterized by time-varying property, which cover the time independent TPs as a special case. Added by a hidden Markov model, the asynchronous phenomenon among the original plant, the quantizer and the filter is revealed. By establishing the Lyapunov functional, a sufficient condition with mean square exponentially stable is acquired. Benefit from the matrix inequality decoupling method, the asynchronous filters with less conservative are achieved. Finally, two examples are presented to show the validity of the obtained strategy.

An opportunistic maintenance strategy for offshore wind turbine system considering optimal maintenance intervals of subsystems

Operation and maintenance (O&M) costs account for a large proportion of the total costs for offshore wind energy. Performing a reasonable maintenance strategy is an effective approach to reduce O&M costs and gain more profits. In this paper, an opportunistic maintenance strategy for offshore wind turbine systems considering maintenance intervals of each subsystem is proposed to minimize the total maintenance cost. First, a Non-homogeneous Continuous-Time Markov Process based state transition model is established to study degradation process of subsystems. The influence of maintenance time schedule on the maintenance cost is studied to obtain the optimal maintenance intervals of each subsystems. Then, an opportunistic maintenance model considering economic dependencies between multiple subsystems is proposed to optimize the maintenance strategy by combining maintenance activities of individual subsystems to a grouping maintenance activity. A numerical example is used to indicate the significant effectiveness of the maintenance model. The result shows that the total maintenance cost of an offshore wind turbine system will be reduced by adopting the opportunistic maintenance strategy when compared with conventional preventive maintenance strategy.