semi-Markov Switching Research Articles

Fuzzy adaptive-event-triggered control for semi-linear parabolic PDE systems with stochastic actuator failures

This paper investigates the fault-tolerant control problem for fuzzy semi-linear parabolic PDE systems with stochastic actuator failures. First, a pointwise measurement-based adaptive-event-triggered control scheme is newly proposed for semi-linear PDE systems to reduce the waste of communication resources. Second, by introducing a more practical semi-Markov jump model describing the random occurring actuator failures, the closed-loop system is exactly represented by a T–S fuzzy PDE model with semi-Markovian switching parameters. Moreover, by constructing a suitable LKF including an improved looped-functional and using some advanced inequalities, sufficient stability conditions with less conservatism are established. Finally, two simulation examples including comparative studies are employed to demonstrate the superiority and effectiveness of the developed method.

SMC for Uncertain Discrete-Time Semi-Markov Switching Systems

This brief is concerned with the mode-dependent sliding mode control (SMC) for uncertain discrete-time semi-Markov switching systems (S-MSSs). The switching is governed by a semi-Markov chain with a discrete-time semi-Markov kernel (SMK). First, a sliding mode surface (SMS) is constructed to be related to the current switching mode. Second, by means of the upper bound of the sojourn time (ST), some feasible conditions are derived to guarantee <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> -error mean square stability for the corresponding S-MSSs. Third, an appropriate SMC law is established to drive the state onto the specified sliding domain. Finally, an F-404 aircraft model validates the proposed control algorithm.

Event-triggered leader-following consensus of multi-agent systems under semi-Markov switching topology with partially unknown rates

An event-triggered leader-following consensus problem for multi-agent systems with nonlinear dynamics was investigated in this study. The interaction topologies among the agents that we considered are randomly switched ones, governed by a semi-Markov process with partially unknown rates. By building the state error model between the leader and followers, the consensus problem is first converted into a stability problem. Moreover, an event-triggered transmission scheme based on sampling data was proposed to reduce communication redundancy. The consensus controller and event-triggered parameters can be designed effectively. By constructing a Lyapunov–Krasovskii functional (LKF) with a triple integral, the sufficient conditions required to guarantee the event-triggered consensus can be reached with respect to the linear matrix inequalities (LMIs). Ultimately, the validity of the theoretical results is demonstrated by a numerical example.

Cluster synchronization in finite/fixed time for semi-Markovian switching T-S fuzzy complex dynamical networks with discontinuous dynamic nodes

&lt;abstract&gt;&lt;p&gt;In this paper, cluster synchronization in finite/fixed time for semi-Markovian switching complex dynamical networks (CDNs) with discontinuous dynamic nodes is studied. Firstly, the global fixed-time convergence principle of nonlinear systems with semi-Markovian switching is developed. Secondly, the novel state-feedback controllers, which include discontinuous factors and integral terms, are designed to achieve the global stochastic finite/fixed-time cluster synchronization. In the framework of Filippov stochastic differential inclusion, the Lyapunov-Krasovskii functional approach, Takagi-Sugeno(T-S) fuzzy theory, stochastic analysis theory, and inequality analysis techniques are applied, and the global stochastic finite/fixed time synchronization conditions are proposed in the form of linear matrix inequalities (LMIs). Moreover, the upper bound of the stochastic settling time is explicitly proposed. In addition, the correlations among the obtained results are interpreted analytically. Finally, two numerical examples are given to illustrate the correctness of the theoretical results.&lt;/p&gt;&lt;/abstract&gt;

Adaptive Event-Triggered Quantized Communication-Based Distributed Estimation Over Sensor Networks With Semi-Markovian Switching Topologies

This paper presents a distributed state estimation method for nonlinear systems over sensor networks with Semi-Markovian switching topologies (S-MSTs). An adaptive event-triggered quantization scheme (AETQS) is developed to reduce the communication and computation burden for bandwidth-constrained sensor networks, where the quantified measurement data is determined by the specific event triggering condition. The filtering network topology evolves over time, which is assumed to be governed by a Semi-Markov chain. Based on the Semi-Markov kernel theory and Lyapunov stability theory, sufficient conditions are obtained to guarantee that the error dynamics has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -error mean square stability and <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, which is given in the form of linear matrix inequalities. Then, the optimal disturbance attenuation level, initial triggering thresholds, and elapsed-time-dependent distributed filter gains can be determined by addressing a convex optimization problem. Finally, two numerical examples are presented to verify the effectiveness of the proposed approach.

ℋ∞ leader-following consensus of multi-agent systems with channel fading under switching topologies: a semi-Markov kernel approach

This paper focuses on the leader-following consensus problem of discrete-time multi-agent systems subject to channel fading under switching topologies. First, a topology switching-based channel fading model is established to describe the information fading of the communication channel among agents, which also considers the channel fading from leader to follower and from follower to follower. It is more general than models in the existing literature that only consider follower-to-follower fading. For discrete multi-agent systems, the existing literature usually adopts time series or Markov process to characterize topology switching while ignoring the more general semi-Markov process. Based on the advantages and properties of semi-Markov processes, discrete semi-Markov jump processes are adopted to model network topology switching. Then, the semi-Markov kernel approach for handling discrete semi-Markov jumping systems is exploited and some novel sufficient conditions to ensure the leader-following mean square consensus of closed-loop systems are derived. Furthermore, the distributed consensus protocol is proposed by means of the stochastic Lyapunov stability theory so that the underlying systems can achieve ℋ∞ consensus performance index. In addition, the proposed method is extended to the scenario where the semi-Markov kernel of semi-Markov switching topologies is not completely accessible. Finally, a simulation example is given to verify the results proposed in this paper. Compared with the existing literature, the method in this paper is more effective and general.

Security SMC for Networked Fuzzy Singular Systems With Semi-Markov Switching Parameters

In this paper, the issue of security sliding mode control (SMC) is addressed for networked nonlinear singular systems with semi-Markov switching parameters via the Takagi-Sugeno (T-S) fuzzy strategy. The goal is to guarantee a good steady performance of dynamical systems under the framework of deception attacks. First, the common sliding surface is proposed to avoid the potential instability caused by repeated jumps of sliding surface. Then, based on the partly unknown transition rate, sufficient conditions are constructed to realize the stochastic admissibility for the corresponding system. Moreover, a fuzzy security SMC law is designed to drive the state trajectory onto the specified sliding region. Finally, a practical example is shown to validate the proposed algorithm.

Memory-based event-triggered asynchronous control for semi-Markov switching systems

In this paper, the asynchronous control problem is addressed for semi-Markov switching systems with a memory-based event-triggered mechanism. In light of the asynchronous phenomenon between the resulting dynamic modes and the memory controller modes, a more general hidden semi-Markov model is expected. Notably, aiming at decrease the triggering intervals while improving the dynamic performance, a novel mode-dependent memory-based event-triggered mechanism is proposed, whose triggering condition varies with some historic released data. By virtue of the hidden semi-Markov model and historic released data, a memory asynchronous control strategy is skillfully synthesized. By resorting to Lyapunov theory, some criteria are formulated to guarantee the stochastically stable of the resulting dynamic. Eventually, the feasibility of the presented approach is verified by a practical example.

Dissipativity-based synthesis for semi-Markovian systems with simultaneous probabilistic sensors and actuators faults: A modified event-triggered strategy

Aided by a modified event-triggered communication policy (ETCP), this article addresses the dissipativity-based control synthesis problem for semi-Markovian switching systems (SMSSs) with simultaneous multiplicative probabilistic faults on sensors and actuators modules. The resulting model under consideration is more extensive, which covers semi-Markovian switching coefficients, transmission delays, and randomly occurring sensors and actuators faults in a unified systematic analytical framework instead of investigating separately in some existing works. More specifically, the probabilistic faults are assumed to happen on both the sensors and actuators modules simultaneously, and the distortion probability for each sensor and actuator is irrelevant, which can be characterized by multiplicate mutually independent stochastic variables that obeys certain statistical features and probabilistic distribution delineate on the interval [0,✠](✠≥1). To reduce the bandwidth usage, a novel event-triggered strategy is designed. Additionally, in the light of this newly developed ETCP, and considering the effects of the signal transmission delays and multitudinous probabilistic failures, a generalized and more realistic faulty pattern for SMSSs is presented, which is more fit for real applications. Hereby, the principal superiority of the established new type faulty pattern lies in its practicality and generality, which contains some previous faulty models as special scenarios. By constructing an appropriate semi-Markovian Lyapunov functional (SMLF) together with mathematical analysis technique and matrix inequality decoupling operation, sojourn-time-dependent sufficient conditions for determining both the control gain matrices and triggered configuration coefficients are developed and formulated in terms of a group of feasible linear matrix inequalities (LMIs). Eventually, several practical examples are exploited to substantiate the validity and practicability of the developed control design methodology.

Advances on modeling and control of semi-Markovian switching systems: A Survey

In the past decades, semi-Markovian switching systems (S-MSSs) have received significant research attention in the systems and control community. S-MSSs, a special yet unique kind of stochastic switching systems, can be used to model and characterize a broad range of applications including modern communication technology, fault tolerant control, and DNA analysis. Different from Markovian switching systems, the transition rate in S-MSSs is jump-time dependent, which enables the capability of better capturing the practical behavior and modeling the physical systems, and meanwhile brings numerous challenges to the analysis and synthesis. The aim of this paper is to provide a comprehensive overview on recent theoretical development and advances of modeling, stability analysis, and control synthesis for S-MSSs. Researcher methodologies and results for S-MSSs on filter design, sliding mode control, finite-time control, and event-triggered control are systematically analyzed and summarized. Finally, some promising research directions and challenges for S-MSSs are presented.

BASF Catalysts to double capacity at Chennai plant

In the past decades, semi-Markovian switching systems (S-MSSs) have received significant research attention in the systems and control community. S-MSSs, a special yet unique kind of stochastic switching systems, can be used to model and characterize a broad range of applications including modern communication technology, fault tolerant control, and DNA analysis. Different from Markovian switching systems, the transition rate in S-MSSs is jump-time dependent, which enables the capability of better capturing the practical behavior and modeling the physical systems, and meanwhile brings numerous challenges to the analysis and synthesis. The aim of this paper is to provide a comprehensive overview on recent theoretical development and advances of modeling, stability analysis, and control synthesis for S-MSSs. Researcher methodologies and results for S-MSSs on filter design, sliding mode control, finite-time control, and event-triggered control are systematically analyzed and summarized. Finally, some promising research directions and challenges for S-MSSs are presented.

Event-triggered synchronization for semi-Markov jump complex dynamic networks with time-varying delay

This paper investigates the event-triggered synchronization of complex dynamic networks (CDNs) with semi-Markov switching and time-varying delay. First, by proposing auxiliary vectors with a few nonorthogonal polynomials, two slack-matrix-based integral inequalities are formulated, which encompass some existing ones as special cases. Second, a triple-integral-based delay-product-type (TIDPT) Lyapunov-Krasovskii functional (LKF) is formulated, which fully utilizes the information of time delay. After designing a controller via the event- triggered scheme, some sufficient conditions are proposed to achieve the global stochastic synchronization by utilizing the reciprocally convex matrix inequality (RCMI) and the founded inequalities to evaluate the derivative of the established LKF. A numerical example is employed to show the effectiveness and practicability of the proposed method.

State estimation for semi-Markovian switching CVNNs with quantization effects and linear fractional uncertainties

This paper is concerned with the robust state estimation problem for semi-Markovian switching complex-valued neural networks with quantization effects (QEs). The uncertain parameters are described by the linear fractional uncertainties (LFUs). To enhance the channel utilization and save the communication resources, the measured output is quantized before transmission by a logarithmic quantizer. The purpose of the problem under consideration is to design a full-order state estimator to estimate the complex-valued neuron states. Based on the Lyapunov stability theory, stochastic analysis method, and some improved integral inequalities, sufficient conditions are first derived to guarantee the estimation error system to be globally asymptotically stable in the mean square. Then, the desired state estimator can be directly designed after solving a set of matrix inequalities, which is robust against the LFUs and the QEs. In the end of the paper, one numerical example is provided to illustrate the feasibility and effectiveness of the proposed estimation design scheme.

Finite-Time Event-Triggered Control for Semi-Markovian Switching Cyber-Physical Systems With FDI Attacks and Applications

This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks. Compared with the traditional time-triggered mechanism, the proposed event-triggered scheme (ETS) can effectively avoid network resource waste. Considering the network-induced delay in the modeling, a closed-loop system model with time delay is established in the unified framework. By the use of a mode-dependent piecewise Lyapunov-Krasovskii functional (LKF), stochastic finite-time stability (SFTS) criteria are established for the resultant closed-loop system. Then, some solvability conditions are established for the desired finite-time controller in light of a linear matrix inequality framework. Finally, an application example of vertical take-off and landing helicopter model (VTOLHM) is provided to demonstrate the effectiveness of the theoretical findings.

Containment Control of Semi-Markovian Multiagent Systems With Switching Topologies

This article is concerned with the problem of the containment control with respect to continuous-time semi-Markovian multiagent systems with semi-Markovian switching topologies. Two kinds of classical control schemes, which are dynamic containment control and static containment control schemes, are utilized to address the proposed synthesis problem. Based on the linear matrix inequality (LMI) method, the dynamic containment controller and static containment controller are designed to plunge into the studied semi-Markovian multiagent systems, respectively. Moreover, the random switching topologies with the semi-Markovian process, the partly unknown transition rates, and the generally uncertain transition rates are taken into account, which can be applicable to more practical situations. Finally, the simulation results are provided to illustrate the effectiveness of the proposed theoretical results.

Formula omitted] estimation for stochastic semi-Markovian switching CVNNs with missing measurements and mode-dependent delays

This article is devoted to the H∞ estimation problem for stochastic semi-Markovian switching complex-valued neural networks subject to incomplete measurement outputs, where the time-varying delay also depends on another semi-Markov process. A sequence of random variables with known statistical property is introduced to depict the missing measurement phenomenon. Based on the generalized Itoˆ’s formula in complex form concerning with the semi-Markovian systems, complex-valued reciprocal convex inequality as well as intensive stochastic analysis method, some mode-dependent sufficient conditions are presented guaranteeing the estimation error system to be exponentially mean-square stable with a prespecified H∞ disturbance attenuation level. In addition, the mode-dependent estimator gain matrices are appropriately designed according to the feasible solutions of certain complex matrix inequalities. In the end, one numerical example is provided to illustrate effectiveness of the theoretical results.

H ∞ containment control with time‐varying delays and communicate noise under semi‐Markov switching topologies

This article focuses on H ∞ containment control and the communication network topologies that are driven by a semi-Markov chain. Moreover, the communication channels between agents exist time-varying delays and noise. Firstly, the authors extend the Markov switching topologies to semi-Markov switching topologies. Because the transition rate of the semi-Markov switching topology is time-varying and depends on the sojourn time, the analysis of containment control under semi-Markov switching topology becomes more challenging. Secondly, a control protocol with time-varying delays is adopted. The error function is derived by the property of graph theory, convex hull and communication noise. Hence, the problem of H ∞ containment control is transformed into the stability problem of the semi-Markov jump system. To avoid the zero initial condition in the traditional H ∞ control approach, a novel performance function is constructed with the initial condition considered. Finally, simulation experiments are provided to verify the effectiveness of the proposed algorithm.

Event-triggered stochastic consensus for networked Lagrangian systems with semi-Markov switching topologies and communication delays

In this paper, the event-triggered stochastic consensus for networked Lagrangian systems with semi-Markov switching topologies and communication delays is considered. An event-triggered sampling control strategy is used to design the distributed stochastic consensus scheme of networked Lagrangian systems for two cases with leader and leaderless. Two delay-dependent consensus criteria are derived in the sense of mean square by use of a suitable Lyapunov-Krasovskii functional and the stochastic delayed Halanay inequality, respectively. A key feature of the developed event-triggered consensus algorithm is to introduce a suitable adjustment parameter on consensus control gains characterizing the effect of both semi-Markov switching topology and communication delay. Finally, a numerical example of four manipulators with two links is presented to illustrate the effectiveness of the developed event-triggered methodology.

Synchronization for Quantized Semi-Markov Switching Neural Networks in a Finite Time.

Finite-time synchronization (FTS) is discussed for delayed semi-Markov switching neural networks (S-MSNNs) with quantized measurement, in which a logarithmic quantizer is employed. The stochastic phenomena of structural and parametrical changes are modeled by a semi-Markov process whose transition rates are time-varying to depend on the sojourn time. Practical systems subject to unpredictable structural changes, such as quadruple-tank process systems, are described by delayed S-MSNNs. A key issue under the consideration is how to design a feedback controller to guarantee the FTS between the master system and the slave system. For this purpose, by using the weak infinitesimal operator, sufficient conditions are constructed to realize FTS of the resulting error system over a finite-time interval. Then, the solvability conditions for the desired finite-time controller can be determined under a linear matrix inequality framework. Finally, the theoretical findings are illustrated by the quadruple-tank process model.

Scaled consensus problem for multi-agent systems with semi-Markov switching topologies: A view from the probability

This paper investigates the stochastic scaled consensus problem for multi-agent systems with semi-Markov switching topologies. Sufficient conditions are established to guarantee the addressed system to realize the scaled consensus with probability one, which means that all agents’ states almost surely reach a dictated proportion. Here, the semi-Markov process concerned is much more general than those utilized in the recent literature, which can be characterized by two important factors: (1) the transition probability matrix, and (2) the polytropical distribution functions of sojourn times. In addition, pinning scaled consensus protocol is designed by employing the pinning control technique, where only the root nodes of the union set of all the topologies are chosen to be pinned, and the final desired state value of the considered system can be realized with probability one. Finally, numerical simulations are provided to illustrate validity of the obtained main results.