Search

In this article, the problem of the asynchronous fault detection (FD) observer design is discussed for 2-D Markov jump systems (MJSs) expressed by a Roesser model. In general, the FD observer cannot work synchronously with the system, that is, the mode of the observer varies with the mode of the system in line with some conditional transitional probabilities. For dealing with this difficult point, a hidden Markov model (HMM) is employed. Then, combining the $H_{\infty }$ attenuation index and $H_{\_{}}$ increscent index, a multiobjective solution to the FD problem is formed. In terms of linear matrix inequality technology, sufficient conditions are gained to guarantee the existence of the asynchronous FD. Simultaneously, an asynchronous FD algorithm is generated to acquire the optimal performance indices. Finally, a numerical example concerned with the Darboux equation is demonstrated to exhibit the soundness of the developed approach. [ABSTRACT FROM AUTHOR]

This article addresses the design issue of fuzzy asynchronous fault detection filter (FAFDF) for a class of nonlinear Markov jump systems by an event-triggered (ET) scheme. The ET scheme can be applied to cut down the transmission times from the system to FAFDF. It is assumed that the system modes cannot be obtained synchronously by the filter, and instead, there is a detector that can measure the estimated modes of the system. The asynchronous phenomenon between the system and the filter is characterized via a hidden Markov model with partly accessible mode detection probabilities. Applying the Lyapunov function methods, sufficient conditions for the presence of FAFDF are obtained. Finally, an application of a wheeled mobile manipulator with hybrid joints is employed to clarify that the devised FAFDF can detect the faults without any incorrect alarm. [ABSTRACT FROM AUTHOR]

Based on the interval type-2 fuzzy (IT2F) approach, this article investigates the fault detection filter design problem for a class of nonhomogeneous higher level Markov jump systems with uncertain transition probabilities. Considering that the mode information of the system cannot be obtained synchronously by the filter, the hidden Markov model can be seen as a detector to handle this asynchronous problem, and the parameter uncertainty can be processed by the IT2F approach with the lower and upper membership functions. Then, the asynchronous IT2F filter is designed to deal with the fault detection problem. Furthermore, the Gaussian transition probability density function is introduced to describe the uncertainty transition probabilities of the system and the filter. Based on the Lyapunov theory, the existence of the designed asynchronous IT2F filter and the dissipativity of the filter error system can be well ensured. In this article, the simulation study on a quarter-car suspension system verifies that the designed asynchronous IT2F filter can detect faults without error alarms. [ABSTRACT FROM AUTHOR]

This article focuses on the finite-time asynchronous output feedback control scheme for a class of Markov jump systems subject to external disturbances and nonlinearities. The conic-type nonlinearities hold a constraint condition which locates in a known hyper-sphere with an indefinite center. In addition, the asynchronization phenomenon occurs between the system and the controller, which can be represented by means of a hidden Markov model. A sufficient condition is derived not only to guarantee the finite-time boundedness of the acquired closed-loop systems but also to possess a desired $H_{\infty }$ performance on the basis of Lyapunov functional technique. Finally, the validity and feasibility of the proposed method are demonstrated with a dc-motor experiment. [ABSTRACT FROM AUTHOR]

Despite rapid sensor technology developments, monitoring a biological process using regular sensor measurements is challenging, making the process very difficult to characterize. Designing an optimal estimator is an attractive alternative to soft-sensing for such complicated hybrid systems. In this article, the variational Bayesian learning algorithms are proposed to estimate the continuous fermenters’ actual states. Special attention is given to the random transition probability matrix (TPM), which is a prerequisite to improving estimation performance. Under the assumption of a time-invariant but random TPM, the Dirichlet distribution is utilized to specify the property of TPM. We then estimate it together with the system state and modal state to approximate the conditional posterior joint distribution. Testing the proposed algorithms using the fermenter model shows that the variational Bayesian learning algorithm can satisfactorily estimate conditions and track TPM in high accuracy. [ABSTRACT FROM AUTHOR]

This article study the asynchronous control problem for a class of discrete-time Markovian jumping Lur’e systems (MJLSs) over the finite-time interval. The partial accessibility of system modes with respect to the designed controller is described by a hidden Markov model (HMM). The asynchronous control law consists of two parts, i.e., the states and the nonlinearities involved in the dynamics of the controlled system. By selecting the appropriate Lyapunov functional and applying the modified sector condition, the finite-time stabilization conditions under the control constraints are derived. Finally, the effectiveness of the designed method is verified by an illustrative simulation. [ABSTRACT FROM AUTHOR]

In the present study, a temporal difference (TD) learning algorithm is proposed to solve the H∞ optimal control problem for semi‐Markov jump linear systems (S‐MJLSs). The proposed scheme is TP‐free so that it can be applied in cases without pre‐known transition probabilities of embedded Markov chain. Coupled algebraic Riccati equations (CAREs) implied with the analytical solution of control gains are derived by utilizing a S‐MJLS augmented with maximum sojourn time, which contributes to develop the TD learning algorithm. It is proved that for sufficiently rich enough jumping modes and jumping numbers observed online, the value function in TD algorithm converges to CAREs solutions. Finally, an example is carried out to evaluate the learning capability of TD algorithm and the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the sliding mode control (SMC) via finite-time stabilization (FTS) for a class of conic-type nonlinear semi-Markovian jumping systems (SMJSs). Comparing with the classical Markovian jumping systems, the transition rates of SMJSs are related to the random sojourn-time $g$. Based on this, a suitable SMC law for driving the state trajectories to the designed sliding surface within a finite-time interval is given. Then, the FTS over reaching phase and sliding motion phase is further proved to guarantee the FTS of the whole SMJSs. Finally, the effectiveness of the proposed method is demonstrated by a time-delayed Chua’s circuit simulation. [ABSTRACT FROM AUTHOR]

To solve the problem of high‐order moment Gaussian distribution (HGD) noise in state estimation, a fusion filter for Markov jump linear systems (MJLSs) with high‐order moment information obtained from sensor data is designed. To obtain high‐order moment information, the multi‐sensor MJLS is converted to a single‐mode system composed of high‐order moment components by using a cumulant generating function. Next, a filter design based on Bayesian theory is established to achieve state estimation with a high‐order moment information form according to the transformed single‐mode deterministic system. Subsequently, a high‐order moment fusion technique based on entropy theory is proposed to obtain a more accurate estimation result of the state by using the high‐order moment information obtained from various sensors. Comparing the first‐ and second‐order moment information obtained by traditional Gaussian distribution, the HGD introduces higher‐order moment information and makes the fusion process more reasonable. In this way, a more precise and reasonable performance of the state estimation is achieved, depending on the sensor fusion technique. To confirm the effectiveness and advantages of the proposed method, a numerical simulation example is provided with various fusion methods. Thus, the performance of the proposed fusion filter design is verified. [ABSTRACT FROM AUTHOR]

Considering that state distribution obeys a generalized Gaussian distribution, it cannot be accurately estimated using only the mean error criterion or mean square error criterion. Therefore, this brief addresses the high-order moment filter design problem for Markov jump systems in the finite frequency domain. An estimation method is applied by transforming the original stochastic system into a high-order component form via the cumulant generating function. Then, the generalized Kalman–Yakubovic–Popov lemma can be used in filter design, by considering finite frequency characteristics. Sufficient conditions for the existence of a high-order moment filter with the required finite frequency performance are established. Finally, a simulation example is presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The finite‐time stabilisation for a class of time‐delayed Markovian jumping systems with conic nonlinearities is studied. The authors aim to design a suitable control law to stabilise the closed‐loop system during a specified finite time. An appropriate Lyapunov–Krasovskii functional method is given to ensure the existence of finite‐time stabilisation controller and the relevant sufficient conditions have been formulated in the form of linear matrix inequalities. Finally, a simulation example is given to show the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

Under the framework of derandomisation approach, the state feedback control issues for both continuous-time and discrete-time Markov jump linear systems (MJLSs) are investigated to meet multiple performance objectives over multiple frequency ranges. Because of the stochastic jumping among different modes, the generalised Kalman-Yakubovic-Popov lemma-based finite-frequency controller design approach cannot be directly applied to MJLSs. To overcome this limitation, a derandomisation approach is established by transforming the original stochastic multiple modes systems to deterministic ones. Then the multiple frequency controllers for both discrete-time and continuous-time MJLSs are designed to guarantee the multiple performances of the closed-loop systems. To verify the effectiveness of the developed algorithms, examples are presented, where the performance requirements include specifications in low-frequency and high-frequency ranges, respectively. [ABSTRACT FROM AUTHOR]

A stochastic finite frequency consensus protocol for directed networks with Markov jump topologies and external disturbances is proposed in this paper. By introducing the frequency band information into consensus control design, the disagreement dynamics of interconnected networks asymptotically converge to zero with an improved level of disturbance attenuation in the specific frequency band. In addition, the new model transformation approach is presented by exploring certain features of Laplacian matrix in real Jordan form, which leads to more generality of the designed protocol. A numerical example validates the potential of the developed results. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the problems of finite-time stability and stabilization for continuous-time switching Markov jump systems with uncertain transition rates are investigated, where some elements in the transition rate matrix are not known precisely, but their bounds are known or completely unknown. The main results are achieved by piecewise integrating the Markov processes and allowing the stochastic multiple Lyapunov function to increase at every switching instant with a limited switching rate such that the state trajectories are kept within the prescribed bound in a short time interval. Finally, two examples illustrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This study is devoted to the finite‐time consensus control for directed networks with stochastic Markov jump topologies and external disturbances. The purpose of the study is to design a control protocol to ensure that the disagreement dynamics of interconnected networks stay in a given bound over a finite‐time interval rather than asymptotically converge to zero in infinite settling time. Through utilisation of certain features of Laplacian matrix in real Jordan form, sufficient conditions for the existence of finite‐time consensus protocol is derived by allowing Lyapunov function to increase in a fixed‐time interval. Finite‐time convergence result for stochastic consensus problem is validated via a simulation study. [ABSTRACT FROM AUTHOR]

This paper solves the observer-based finite-time stabilization problem for discrete-time non-homogeneous jump linear systems with time-delays and norm-bounded exogenous disturbance. The exact value of transition probabilities (TPs) is not available, and the known information is the measured Gaussian probability density function of TPs. For the case that the states are not measurable, an observer-based control scheme is adopted to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop systems. Numerical examples are given to verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This study considers the problem of finite‐time H∞ control for a class of discrete‐time time‐delay Markov jump linear systems governed by deterministic switches. By allowing the stochastic Lyapunov function to increase at every switching instant with a limited increase rate, new results on the stochastic finite‐time boundness with given H∞ disturbance attenuation level are derived. Moreover, the coupling relationship among time‐delay, average dwell time and given finite‐time horizon of the underlying system is obtained through an average dwell‐time constraint. Finally, one example is given to demonstrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

SUMMARY This paper investigates the state estimation problem for a class of Markov jump systems with unknown transition probabilities (TPs). Considering more general cases where the TPs are unknown, but the distribution of TPs can be approximated by Gaussian process, we use the Gaussian transition PDF to describe the random distribution characteristics of TPs. With the proposed PDF description, the corresponding Markov jump systems can cover the systems with precisely known and partially known TPs as two special cases. A discretization method is firstly developed to obtain the expectation of TPs from the Gaussian PDF. Then, an H ∞ filter is designed such that the closed-loop systems are stochastically stable and the estimation error satisfies a given noise attenuation level. Finally, a numerical example is worked out to illustrate the effectiveness of the theoretical results.Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The problems of finite‐time analysis and design for a class of Markov jump systems with Gaussian transition probabilities (TPs) are investigated in this study. Gaussian TP density function is introduced to quantise the stochastic uncertain information of TPs. Mode‐dependent and variation‐dependent controller is designed to make the resulting closed‐loop systems finite‐time bounded and finite‐time stabilisable for all admissible unknown external disturbances and random uncertain TPs. It is shown that the approach proposed in the paper dealing with TPs outperforms available ones in literature to date, which is also confirmed by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of observer-based finite-time stabilization for a class of extended Markov jump systems with norm-bounded uncertainties and external disturbances. The stochastic character under consideration is governed by a finite-state Markov process, but with only partial information on the transition jump rates. Based on the finite-time stability analysis, sufficient conditions for the existence of the observer-based controller are derived via a linear matrix inequality approach such that the closed-loop system trajectory stays within a prescribed bound in a fixed time interval. When these conditions are satisfied, the designed observer-based controller gain matrices can be obtained by solving a convex optimization problem. Simulation results demonstrate the effectiveness of the approaches proposed in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]

This article proposes a new design approach for robust finite-time H∞ control of a class of Markov jump systems with partially known information on the transition jump rates. The system under consideration involves norm-bounded parameter uncertainties and external disturbance. The problems of robust finite-time boundedness and finite-time stabilisation of the underlying systems are considered. Then, a H∞ state feedback controller is designed. Sufficient conditions that consider only the known bounds on the transition jump rates are developed in the form of linear matrix inequalities. A numerical example is included to show the usefulness of the theoretic results obtained. [ABSTRACT FROM AUTHOR]