Simultaneous fault estimation for uncertain Markovian jump systems subjected to actuator degradation

This paper investigates simultaneous estimations of states, system fault, and sensor fault for a class of Markovian jump systems, resorting to the design of a robust observer, in which both the external disturbance and actuator degradation are taken into consideration. The loss‐of‐effectiveness, stuck, and outage fault cases are involved, and the considered Markovian jump system is assumed to possess generally uncertain transition rates, which can generalize the traditional bounded uncertain transition rates and partially unknown transition rates. In particular, an augmented system whose states cover the original states, system fault, and sensor fault is constructed. Then, a novel adaptive observer is presented with time‐varying gain matrices and parameter accommodation being injected to deal with the disturbance and actuator degradation. Finally, a practical example is shown to demonstrate the high efficiency of the proposed method as well as its advantages over some existing results.     

Integrated design of robust fault estimation and fault‐tolerant control against simultaneous actuator and sensor faults

This paper investigates the problems of simultaneous actuator and sensor faults estimation, as well as the fault‐tolerant control scheme for a class of linear continuous‐time systems subject to external disturbances. First, the original system is transformed into a singular form by extending the actuator fault and sensor fault to be parts of the new state. Then, a new estimation technique named non‐fragile proportional‐derivative observer is designed for the singular system to achieve simultaneous estimations of states and faults. With the obtained estimations information, an integrated design of the non‐fragile output feedback fault‐tolerant controller is explored to compensate for the effect of faults by stabilizing the closed‐loop system. Finally, a simulation study on a two‐stage chemical reactor with recycle streams is provided to verify the effectiveness of the proposed approach.     

Fault‐tolerant control of singularly perturbed systems with actuator faults and disturbances

The article proposes several fault‐tolerant control (FTC) laws for singularly perturbed systems (SPS) with actuator faults and disturbances. One of the main challenges in this context is that the fast‐slow decomposition is not available for actuator faults and disturbances. In view of this, some conditions for the asymptotic stability of the closed‐loop dynamics are investigated by amending the composite Lyapunov approach. On top of this, a closed‐form expression of the upper bound of singular perturbation parameter (SPP) is provided. Moreover, we design several SPP‐independent composite FTC laws, which can be applied when this parameter is unknown. Finally, the chattering phenomenon is eliminated by using the continuous approximation technique. We also emphasize that, for linear SPSs, the FTC design can be formulated as a set of linear matrix inequalities, while the SPP upper bound can be obtained by solving a convex optimization problem. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.     

Moment exponential stability analysis of Markovian jump stochastic differential equations with uncertain transition jump rates

This paper is concerned with the moment exponential stability analysis of Markovian jump stochastic differential equations. The equations under consideration are more general, whose transition jump rates matrix Q is not precisely known. Sufficient conditions for testing the stability of such equations are established, and some numerical examples to illustrate the effectiveness of our results are presented.     

Fault‐tolerant adaptive control allocation schemes for overactuated systems

This paper presents a fault‐tolerant adaptive control allocation scheme for overactuated systems subject to loss of effectiveness actuator faults. The main idea is to use an ‘ad hoc’ online parameters estimator, coupled with a control allocation algorithm, in order to perform online control reconfiguration whenever necessary. Time‐windowed and recursive versions of the algorithm are proposed for nonlinear discrete‐time systems and their properties analyzed. Two final examples have been considered to show the effectiveness of the proposed scheme. The first considers a simple linear system with redundant actuators and it is mainly used to exemplify the main properties and potentialities of the scheme. In the second, a realistic marine vessel scenario under propeller and thruster faults is treated in full details. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive fault‐tolerant formation control for quadrotors with actuator faults

In this paper, we investigate the fault‐tolerant formation control of a group of quadrotor aircrafts with a leader. Continuous fault‐tolerant formation control protocol is constructed by using adaptive updating mechanism and boundary layer theory to compensate actuator fault. Results show that the desired formation pattern and trajectory under actuator fault can be achieved using the proposed fault‐tolerant formation control. A simulation is conducted to illustrate the effectiveness of the method.     

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovian jump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality (LMI) conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.     

Stability analysis and stabilization of Markovian jump systems with time‐varying delay and uncertain transition information

The paper investigates the problems of stability and stabilization of Markovian jump systems with time‐varying delays and uncertain transition rates matrix. First, the stochastic scaled small‐gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov‐Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method.     

Finite-time dissipative control for semi-Markovian jump systems with time-varying delays and generally uncertain transition rates

In this paper, we mainly address the issue of finite-time stochastic boundedness (FTSB) and finite-time stochastic dissipation for semi-Markovian jump systems (SMJSs) with generally uncertain transition rates (TRs). Firstly, by resorting to linear matrix inequities (LMIs), some sufficient conditions on FTSB for SMJSs with uncertain TRs are introduced, which includes two cases. Then, dissipative control is developed and a state feedback controller is designed to ensure the FTSB of the closed-loop system by solving a series of LMIs. Finally, two examples are used to illustrate the results.     

Static anti‐windup design for a class of Markovian jump systems with partial information on transition rates

This paper investigates the problem of static anti‐windup design for uncertain continuous‐time Markovian jump systems with partially unknown transition rates in the face of actuator saturation. The underlying system is subject to time‐varying and norm‐bounded parameter uncertainties in both the state and input matrices. It is assumed that a set of stabilizing dynamic output‐feedback controllers have been designed for the system in the absence of control saturation. The objective is to design anti‐windup compensation gains for the given controllers such that the system can still be stabilized, irrespective of whether actuator saturation appears or not. To obtain a maximum estimation of the domain of attraction of the resulting closed‐loop system, a convex optimization problem in the linear matrix inequality framework is formulated. Furthermore, the results are extended to the cases of the systems with completely known transition rates and with completely unknown transition rates. Finally, the usefulness of the developed method is demonstrated through simulation examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive fault tolerant control for a class of uncertain fractional‐order systems based on disturbance observer

In this paper, a class of fractional‐order nonlinear systems are considered in the presence of actuator faults. A novel fault tolerant control scheme based on disturbance observer has been presented, where the actuator faults are considered as the system disturbance and can be approximated by the proposed disturbance observer. The developed fault tolerant control guarantees the convergence of the closed‐loop system and the output tracking performance. Finally, a simulation example is presented to verify the effectiveness of the new method.     

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

In this paper, the exponential mean‐square stability of neutral switching Markovian jump systems with generally incomplete transition probabilities is investigated. The model discussed in this paper concludes both deterministic switching signals and Markovian jumping signals. The transition rates of the jumping process are assumed to be partly available, that is, some elements have been exactly known, some have been merely known with lower and upper bounds, and others may have no information to use. Based on the Lyapunov‐Krasovskii functional method, sufficient conditions on the exponential mean‐square stability of the considered system are derived in terms of liner matrix inequalities. A numerical example is provided to show the feasibility and effectiveness of the proposed results.     

Fault estimation for a class of nonlinear Markov jump systems with general uncertain transition rates

This paper addresses the problem of fault estimation for a class of nonlinear Markov jump systems with Lipschitz-type nonlinearities and general transition rates allowed to be uncertain and unknown. First, by introducing a mode-dependent intermediate variable, an intermediate estimator is proposed to estimate faults and state simultaneously. Then, a vertex separator is exploited to develop a sufficient condition for the fault estimator design in terms of linear matrix inequalities. The design guarantees the boundedness in probability of the estimation errors if the derivations of the faults are bounded. Further, it is proved that the proposed approach is less conservative than the traditional methods. Finally, examples are given to show the advantages and effectiveness of the results.     

转移概率一般不确知时滞Markov跳变神经网络的同步

研究了一类具有一般不确知转移概率的时滞Markov跳变神经网络的渐近同步问题.此类系统跳变过程的转移概率完全未知或者仅知道其估计值,因而更具有一般性.通过选择适当的Lyapunov-Krasovskii函数,利用线性矩阵不等式(LMIs)方法,得到了系统均方渐近同步的充分条件.最后,数值例子说明了所给结果的有效性.     

Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities

In this paper, dissipative synchronization problem for the Markovian jump neural networks with time‐varying delay and general transition probabilities is investigated. An event‐triggered communication scheme is introduced to trigger the transmission only when the variation of the sampled vector exceeds a prescribed threshold condition. The transition probabilities of the Markovian jump delayed neural networks are allowed to be known, or uncertain, or unknown. By employing delay system approach, a new model of synchronization error system is proposed. Applying the Lyapunov‐Krasovskii functional and integral inequality combining with reciprocal convex technique, a delay‐dependent criterion is developed to guarantee the stochastic stability of the errors system and achieve strict (Q,S,R)?α dissipativity. The event‐triggered parameters can be derived by solving a set of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed design method.     

Finite‐time guaranteed cost control for Itô Stochastic Markovian jump systems with incomplete transition rates

This paper is concerned with the finite‐time guaranteed cost control problem for stochastic Markovian jump systems with incomplete transition rates. By a mode‐dependent approach (MDA), several new sufficient conditions for the existence of state and output feedback finite‐time guaranteed cost controllers are provided, and the upper bound of cost function is more accurately expressed. Moreover, these results' superiorities are analyzed and shown. A new N‐mode optimization algorithm is given to minimize the upper bound of cost function. Finally, a detailed example is utilized to demonstrate the merit of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.     

Sliding mode observer–controller design for uncertain Markovian jump systems with time delays

This paper proposes a sliding mode observer–controller design method for uncertain Markovian jump systems with time delays and uncertain switching probabilities. Both the structures of a sliding mode observer and a sliding mode controller are given. By the mode‐dependent Lyapunov functional approach, a sufficient condition for the stochastic stability of the closed‐loop system is given, which can be converted into a convex optimization problem. The reachability of the sliding surfaces in both the estimation error space and the state estimate space can be ensured by the presented control scheme. Finally, the effectiveness of the proposed design method is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd.