Generally Uncertain Transition Rates Research Articles

Mode-dependent observer-based secured hybrid-driven reliable control for semi-Markov jump cyber–physical systems with DoS attacks

This study focuses on the issue of secured observer based hybrid-triggered quantized reliable control design for semi-Markov jump cyber–physical systems (S-MJCPSs) with general uncertain transition rates, quantization, actuator faults, denial-of-service (DoS) attacks and disturbances. In particular, a mode-dependent observer is developed to estimate the unmeasurable states of the considered system. Further, to minimize unnecessary data transmissions within the network channel, we have implemented a hybrid-triggered mechanism in which, the swap process between the time-triggered and the event-triggered mechanisms is governed by a Bernoulli distribution. Moreover, an observer-based hybrid-triggered quantized reliable controller is devised by utilizing the state estimation information obtained from the observer, which assists the S-MJCPSs to achieve primary intent of this study. Subsequently, the control input signals are quantized before being transmitted into the actuator due to the limited capacity of the data transmission medium. Concurrently, periodic DoS jamming attacks are taken into consideration, which have a significant impact on control performances. A set of adequate criteria is established in the context of linear matrix inequalities by employing the mode-dependent time-varying piecewise Lyapunov-Krasovskii functional and the integral inequalities, guaranteeing that the undertaken system accomplishes the global exponential stability and meet a specific H∞ performance level. Following that, by means of the deduced adequate criteria, the values of the controller and observer gain are computed. At last, the efficacy and applicability of the derived theoretical findings are demonstrated through two practical examples.

Nonfragile state estimation for semi-Markovian switching CVNs with general uncertain transition rates: An event-triggered scheme

This paper tackles the problem of nonfragile state estimation for semi-Markovian switching complex-valued networks with time-varying delay. The concerned transition rates of the semi-Markov process are uncertain, including both the completely unknown ones and the inaccurately known ones with known bounds. To reduce the communication burden, a particular event-triggered generator is constructed, which depends on the latest available measurement output and a predefined positive threshold. Combining the stochastic analysis method with the Lyapunov stability theory, some less conservative criteria are obtained to ascertain the global asymptotic stability of the estimation error system in the mean-square sense. In addition, by solving some matrix inequalities, the desired nonfragile estimator gains are explicitly designed. Finally, a numerical example with simulations is given to illustrate effectiveness of the established estimation scheme.

A distributed fault estimation method for a class of nonlinear Markov jump systems

This paper investigates the distributed fault estimation problem of a class of nonlinear Markov jump systems. The main goal is to design a distributed observer network to estimate system states and actuator fault simultaneously. For the two cases of completely known and general uncertain transition rates, we first use a virtual intermediate observer technique to remove the observer matching condition, which upgrades the flexibility in the process of design. Next, by using the information of some special neighboring nodes and adopting observability decomposition approach, a novel distributed observer network allowed to be with unobservable nodes is constructed. Then, the mentioned goal is achieved based on the observer network. The proposed method can compensate missing information of unobservable nodes, which solves the estimation problem in the case of partial information loss. Finally, an example is provided to demonstrate the effectiveness of the proposed method.

Mixed dissipative filtering design for uncertain singular Markovian jump time-varying delay systems with nonlinear perturbations and generally uncertain transition rates

This paper studies the dissipative filtering of uncertain singular time-varying delay Markovian jump systems (MJSs) with nonlinear perturbations and generally uncertain transition rates (GUTRs). We focus on the design of a mixed filter, which can include mode-dependent and mode-independent filters in a unified and simple structure. First, a new Lyapunov–Krasovskii functional is proposed through the delay-decomposition approach, and improved Wirtinger-based integral inequalities are used to obtain a sufficient condition to ensure the stochastic admissibility of the considered uncertain nonlinear singular time-varying delay MJSs with dissipative performance. Based on these ingredients, the explicit expression of the desired mixed filter is obtained. Finally, some numerical examples and the filter design of a two-loop circuit network reflect the less conservatism and effectiveness of the method in this article.

Finite-time H ∞ control for stochastic Markovian jump systems with time-varying delay and generally uncertain transition rates

This paper considers the finite-time control problem for Markovian jump systems (MJSs) with time-varying delay and generally uncertain transition rates (GUTRs). Based on Lyapunov-Krasovskii functionals and free-weight matrices, some sufficient conditions for finite-time boundedness and finite-time boundedness of MJSs are derived in the presence of external disturbances and It-type stochastic disturbances. A state feedback controller is proposed to achieve finite-time boundedness performance. By applying linear matrix inequalities (LMIs), the parameterisation of the controller is converted to a convex optimisation problem. Finally, a practical example demonstrates the effectiveness of the proposed method.

Dissipativity of the stochastic Markovian switching CVNNs with randomly occurring uncertainties and general uncertain transition rates

The robust dissipativity problem is analysed in this article for the Markovian switching complex-valued neural networks perturbed by stochastic noises, where the transition rates of the Markovian switching are uncertain which comprise two categories: completely unknown or unknown but with known upper/lower bounds. The randomly occurring system uncertainties are governed by certain mutually independent Bernoulli-distributed white sequences, which might reflect more realistic dynamical behaviours of the switching network. Based on the generalised It's formula in complex form as well as certain stochastic analysis methods, several mode-dependent dissipativity/passivity criteria are obtained in terms of complex matrix inequalities. Finally, illustrative examples are provided to demonstrate feasibility of the derived results.

Event‐triggered stabilization for continuous‐time saturating Markov jump systems with generally uncertain transition rates

AbstractThis paper is concerned with the stabilization for continuous‐time saturating Markov jump system with generally uncertain transition rates (GUTRs) under event‐triggered strategy. In the GUTRs model, the transition rate could be unknown or only its estimated value and estimated error bound are known. In practical systems, actuator saturation commonly exists, which may lead to instability. Event‐triggered strategy is introduced in Markov jump systems to save communication resources. A stochastic stabilization condition is derived for the underlying system considering event‐triggered control and the lower bound of the inter‐event time interval is calculated to avoid Zeno behavior. To obtain the biggest domain of attraction, an optimization algorithm is formulated. Finally, numerical examples are provided to illustrate the application of the given results.

Fuzzy Control of Uncertain Positive Markov Jump Fuzzy Systems With Input Constraint.

This article considers the stochastic stability of uncertain positive Markov jump fuzzy systems (PMJFSs). The uncertainties consist of partially unknown membership functions and generally uncertain transition rates (GUTRs). In the GUTR model, each transition rate (TR) is completely unknown or only its estimate value is known. The coexistence of the partially unknown membership functions and GUTRs makes the control problem difficult to handle. Based on the T-S fuzzy scheme, a switching-type controller with input constraint which parallels as the structure of the uncertain fuzzy model is applied to ensure the positivity and stochastic stability of such systems. A linear decoupling strategy is proposed to tackle the coupling problems when designing the controller and further derives the desired controller parameters. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

Robust Observer Based Fault-tolerant Control for One-sided Lipschitz Markovian Jump Systems with General Uncertain Transition Rates

This paper presents an integrated design of adaptive sliding mode observer and fault-tolerant control for a class of one-sided Lipschitz Markovian jump systems with general uncertain transition rates. In the design process, an adaptive sliding mode observer is first constructed to estimate the states of the original system without knowing any information of the unknown input. Then a fault-tolerant control strategy is therefore proposed to stabilize the closed-loop system against the unknown input. Sufficient conditions of the existences of the designed observer and controller are deduced in the forms of linear matrix inequalities. In the end, several examples are given to illustrate the effectiveness and make some comparisons with other results.

Composite anti-disturbance resilient control for Markovian jump nonlinear systems with general uncertain transition rate

In this paper, the issue of disturbance observer based resilient control is addressed for Markovian jump nonlinear systems with multiple disturbances and general uncertain transition rates. The disturbances are divided into two parts: one has a bounded $H_2$ norm, and the other is given by an exogenous system. The general uncertain transition rate matrix is composed of unknown elements and uncertain ones. The uncertain transition rate only has a known approximate range. First, the disturbance described by the exogenous system is estimated by a disturbance observer, and its estimation is used for the controller as feedforward compensation. Subsequently, by using the resilient control method, a composite anti-disturbance resilient controller is constructed to guarantee stochastic stability with $L_2-L_\infty$ performance of the closed-loop systems. Subsequently, the Lyapunov stability method and linear matrix inequality technique are applied to obtain the controller gain. Finally, an application example is provided to illustrate the effectiveness of the proposed approach.

Finite-Time Stochastic $H_\infty$ Control for Singular Markovian Jump Systems With $(x,v)$ -Dependent Noise and Generally Uncertain Transition Rates

This paper is concerned with the problems of finite-time stochastic $H_\infty $ control for singular Ito Markovian jump systems with $(x,v)$ -dependent noise and generally uncertain transition rates (GUTRs). Based on two equivalent sets, a new criterion, ensuring the considered systems with completely known TRs to be finite-time stochastically bounded with $H_\infty $ performance, is first established, which is less conservative than the existing one. Then, the obtained results are extended to the case of GUTRs. To overcome the nonlinear difficulty resulting in the Young inequality for designing a convex controller, an approach called the association of free variables and slack variables are used. The state feedback controller and observer-based controller are respectively designed such that the corresponding closed-loop systems with GUTRs are finite-time stochastically bounded while achieving $H_\infty $ performance. Finally, the numerical examples are addressed to illustrate the effectiveness and efficiency of our obtained results.

Simultaneous Fault Detection and Control for Markovian Jump Systems with General Uncertain Transition Rates

This paper investigates the simultaneous control and fault detection of Markovian jump systems with general transition rates allowed to be unknown and known with uncertainties. By introducing slack matrices, a new approach is developed to conquer the nonlinearity induced by unknown and uncertain transition rates. Then, sufficient conditions are presented to ensure the stochastic stability of the resultant closed-loop system and meet the robust and detection performance indices. Finally, an example is given to illustrate the effectiveness of the proposed theoretical results.

Stability of Markovian jump stochastic parabolic Itô equations with generally uncertain transition rates

In this paper, the stability problem for delayed Markovian jump stochastic parabolic Ito^ equations (DMJSPIEs) subject to generally uncertain transition rates (GUTRs) is investigated via Lyapunov-Krasovskii functional and linear matrix inequality (LMI) method. In the model discussed, we suppose that only part of the transition rates of the jumping process are known, namely, some factors have been already available, some elements have been simply known with lower and upper bounds, and the rest of elements may have no useful information. Lastly, the applicability and effectiveness of the obtained results are illustrated through an example.

Delay-dependent H∞ filtering for singular Markov jump systems with Wiener process and generally uncertain transition rates

This paper is devoted to the investigation of the delay-dependent filtering problem for a class of continuous-time singular Markov jump systems with Wiener process and generally uncertain transition rates (GUTRs). In the GUTR stochastic singular model under consideration, based on an auxiliary vector function, by employing an integral inequality and some appropriate free-weighting matrices, the delay-dependent sufficient conditions are derived, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, impulse-free and stochastically stable, but also satisfies a prescribed performance for all time-varying delays no larger than a given upper bound. Furthermore, the solvability conditions of the filtering problem are deduced in terms of a new type of candidate Lyapunov–Krasovskii function and a set of matrix inequalities. Finally, simulation examples are performed to validate the proposed method in this paper.

Robust fault estimation and fault-tolerant control for Markovian jump systems with general uncertain transition rates

This paper is concerned with the problems on simultaneous actuator and sensor fault estimation as well as the fault-tolerant control for a class of Markovian jump systems subjected to faults and disturbances. Firstly, the original system is converted into a descriptor system by extending the sensor faults as auxiliary states. Secondly, an adaptive observer is designed for the descriptor system, in which the actuator faults are adjusted by the designed adaptive law. Based on the estimations of the actuator faults, a fault-tolerant control strategy is therefore proposed to stabilize the closed-loop system against actuator faults, sensor faults and disturbances. Sufficient conditions for the existence of the observer and controller are derived in accordance with linear matrix inequalities. Finally, some practical examples are delivered to illustrate the validation and effectiveness of the proposed method.

A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems

This paper studies the problems of stability and stabilization of a class of Markovian chaotic systems via fuzzy sampled-data control. Different from some existing results, the Markovian jumping with general uncertain transition rates is considered for such systems. A novel approach, i.e., input-delay-dependent vector approach, is proposed for the first time. Based on this approach, an input-delay-dependent Lyapunov–Krasovskii functional (LKF) with cubic function of input delay is successfully constructed, and the convex combination technique is used with ease to derive stability and stabilization criteria. Compared with some existing stability and stabilization criteria for chaotic systems, our results are not only less conservative but also with reduced calculation complexity. Finally, the superiorities of proposed results are illustrated by two numerical examples.

Formula omitted] performance for neutral-type Markovian switching systems with general uncertain transition rates via sliding mode control method

The paper is devoted to the investigation of observer-based H∞ sliding mode controller design for a class of nonlinear uncertain neutral Markovian switching systems (NUNMSSs) with general uncertain transition rates. In this case, each transition rate can be completely unknown or only its estimate value is known. Firstly, an H∞ non-fragile observer subjected to the general uncertain transition rates of the NUNMSSs is constructed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are founded. Secondly, the state-estimation-based sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite time interval. Thirdly, an asymptotically stochastic stability criterion is established by utilizing a new-type Lyapunov function to guarantee the error system and sliding mode dynamics to be asymptotically stochastic stable with a given disturbance attenuation level. Finally, an example is provided to illustrate the efficiency of the proposed method.

Exponential Stability of Neutral-Type Impulsive Markovian Jump Neural Networks with General Incomplete Transition Rates

This paper is devoted to the investigation of exponential stability of Neutral-type impulsive Markovian jump neural networks with mixed time-varying delays and generally uncertain transition rates (GUTRs). Each transition rate can be completely unknown or only its estimate value is known in this GUTR model. This new uncertain model is more general than the existing ones. By utilizing Lyapunov–Krasovkii functional approach and linear matrix inequality technology, some novel globally exponentially stable results are derived. An example is given to show the effectiveness of the obtained results.

Quantized control for uncertain singular Markovian jump linear systems with general incomplete transition rates

Quantization is indeed a natural way to take into consideration in the control design of the complexity constraints for the controller as well as the communication constraints in the information exchange between the controller and the plant. This paper is devoted to investigating quantized state-feedback control problems for a class of continuous-time uncertain singular Markovian jump linear systems (CUSMJLSs) with generally uncertain transition rates (GUTRs) and input quantization. In this case, each transition rate can be completely unknown or only its estimate value is known. First, input quantization is introduced, then by introducing new matrix inequality conditions, sufficient conditions are formulated for quantized state-feedback control of CSMJLUSs with GUTRs and input quantization. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed results.

Fault‐tolerant control for Markovian jump systems with general uncertain transition rates against simultaneous actuator and sensor faults

SummaryThis paper investigates the problems of simultaneous estimations of actuator faults and sensor faults, as well as fault‐tolerant control schemes for a class of Markovian jump systems with general uncertain transition rates. In a general uncertain transition rate matrix model, transition rate may be completely unknown, or one can only acquire its estimated value, which makes the design much more challenging. First, the original system is transformed into a descriptor one by extending the sensor faults to be parts of state vector. Then, a robust stochastic adaptive observer is designed for the descriptor system with the actuator fault being adjusted by an adaptive law. On the basis of the estimated states as well as estimated actuator and sensor faults, a fault‐tolerant control strategy is proposed to make the resulting closed‐loop system stable in the presence of the actuator fault. Sufficient existence conditions of the observer and controller are derived in terms of linear matrix inequalities. Finally, three practical examples are given to validate the high efficiency of our proposed method. Copyright © 2017 John Wiley & Sons, Ltd.