Stochastic Actuator Failures Research Articles

Adaptive time-varying state safety constraint control for discrete-time nonlinear systems with random actuator failures

This work investigates the adaptive time-varying state safety constraint control problem for a class of discrete-time nonlinear systems subject to large parameter uncertainties and stochastic actuator failures for the first time. The existence of time-varying full-state constraints, large parameter uncertainties and stochastic actuator failures leads to a series of difficulties for realizing all control objectives. Due to the absence of the linearity property of the derivative in discrete-time log type barrier Lyapunov functions, they are not used to deal with the state constraint problem of nonlinear discrete-time systems. The discrete quadratic-fraction time-varying barrier Lyapunov function is employed to guarantee that all states are constrained in the time-varying predefined regions. By virtue of the constructed multiple-model set, an adaptive identification algorithm is developed to deal with large parameter uncertainties and it has a clear advantage that this method does not requires cn (where n is the dimension of the parameter vector and c is an integer) identification models and only relies on n+1 identification models, thereby heavily reducing the computational burden. By employing the discrete-time filter and backstepping techniques, the adaptive failure compensation controller is designed to ensure the boundedness in probability of the considered systems with respect to stochastic actuator failures. Finally, the effectiveness of the proposed scheme is proved by two simulation examples.

Probabilistic Event-Triggered Policy for Extended Dissipative Finite-Time Control of MJSs under Cyber-Attacks and Actuator Failures

This technical note investigates the problem of extended dissipative finite-time control for Markov jump systems (MJSs) with cyber-attacks and actuator failures. A probabilistic event-triggered mechanism (PETM) is proposed to relieve the communication burden by exploiting both the pattern variation of triggering thresholds and the time-varying characteristic of transmission delays. To characterize the actual control inputs, a stochastic actuator failure model (SAFM) is established using a random variable of any discrete-time distribution over [0,1]. Firstly, based on the PETM and SAFM, static output feedback controllers are devised which may not switch with the system synchronously. Then, novel sufficient conditions with less conservatism are obtained to achieve the extended dissipative finite-time control performance of the closed-loop system under admissible cyber-attacks and actuator failures. Furthermore, controller gains with non-convex constraints are calculated with the aid of a newly proposed lemma. Finally, an application oriented example is provided to verify the effectiveness and superiority of the proposed results.

HMM-based asynchronous synthesis for Interval type-2 fuzzy semi-Markovian jump systems with its applications: A bilateral looped functional methodology

This article mainly addresses the hidden-Markovian model-based asynchronous sampled-data control (SDC) synthesis problem for interval type-2 (IT2) fuzzy semi-Markovian jump systems (S-MJSs) with stochastic actuator failures (SAFs). Herein, the asynchronous factor resulted from twofold: (1) hidden Markovian model (HMM) and (2) imperfectly matched membership functions (IMMFs) between the original plant and the controller. Aiming at approximating the nonlinearity along with randomness with high accuracy and broadening practical application background, the IT2 fuzzy S-MJSs associated with IMMFs is established. At the beginning, a HMM is borrowed to portray the discrepancy between the corresponding plant and the desired controller. Additionally, in comparison with majority of some previous sampled-data control mechanisms, a intrinsic lag signal and gain fluctuations are purposefully introduced in the double asynchronous control strategy, which exploited initially to settle the control synthesis issue. By considering the information of sampling intervals x(tk)→x(t)→x(tk+1) along with x(tk−τ)→x(t−τ)→x(tk+1−τ) adequately, a fresh looped Lyapunov functional called bilateral looped Lyapunov functional is innovatively constructed. Whereafter, by suitably incorporating with the skills of stochastic analysis and relaxed integral inequality (including generalized free matrix-based integral inequality and canonical Bessel–Legendre integral inequality) together with symmetric slack matrices, numerically testable sufficient conditions are established in the form of a group of feasible multi-parameterized linear matrix inequalities (M-PLMIs). The theoretical developments are implies the hierarchy character, and the conservatism decreases with the increase of the degree of hierarchy. Conclusively, the design methodology brought forward herein is demonstrated by two practical examples, which show the potency and practicability.

Observer-based feedback control of interval-valued fuzzy singular system with time-varying delay and stochastic faults

There are countless applications of non-linear systems that incorporate delay and algebraic equations. Despite current improvements in control theory, stochastic actuator defects still pose challenges when it comes to these systems. Furthermore, when it is not possible to measure the states of the system, and when uncertainties affect the system under investigation, the problem becomes even more complex. This paper is concerned with fault-tolerant observer-based controller synthesis for non-linear delayed singular systems with uncertainties and stochastic actuator failures. On the basis of interval valued models, a new Lyapunov-Krasovskii functional is built to develop a less conservative criterion to ensure that the closed-loop system is admissible in the mean-square sense. In addition, as these matrices are coupled with multiple variables, finding the parametric matrices of the observer and controller in terms of the obtained condition is more complex and challenging. The proposed method employs the matrix inequality decoupling technique to resolve this issue. Eventually, simulations are carried out to demonstrate the applicability of the proposed method.

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.

Resilient Reliable Hθ Load Frequency Control of Power System With Random Gain Fluctuations

This article proposes a resilient reliable H∞ load frequency control (LFC) design for power system involving the external load disturbances, stochastic actuator failures, and randomly occurring gain fluctuations. In this regard, the separate random variables are introduced which characterize the actuator failures and gain fluctuations in an individual manner that satisfies the Bernoulli distribution. The resilient reliable proportional-integral (PI)-type LFC is proposed by utilizing the resilient control scheme and the reciprocal convex technique along with the Lyapunov-Krasovskii functional (LKF), which guarantees the mean-square asymptotic stability of power system via H∞ performance index. Finally, the simulations are given to ensure the less conservative results of the proposed method when compared to the existing results.

Reliable Control for Flexible Spacecraft Systems With Aperiodic Sampling and Stochastic Actuator Failures.

This article addresses the aperiodic sampled-data control problem for flexible spacecraft with stochastic actuator failures. Flexible spacecraft dynamics are approximated by a group of T-S fuzzy models due to strong nonlinearity, and the multi-stochastic failures of spacecraft are depicted by a time-continuous and state-discrete Markov chain. To reduce the design conservativeness, a membership-sampling-dependent Lyapunov-Krasovskii functional (MSDLKF) is introduced to utilize the information of fuzzy membership functions and aperiodic sampling modes. Furthermore, a number of reliable fuzzy controllers are designed to obtain the exponential attitude stabilization under the circumstances of stochastic failures. At the same time, disturbance attenuation is ensured. The solution of the fuzzy controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). In the end, an example of the practical flexible spacecraft system is given to illustrate the feasibility and validity of the proposed fuzzy control methods.

Extended Dissipative Control for Markovian Jump Time-Delayed Systems with Bounded Disturbances

In this work, the result of reachable set bounding and extended dissipative control synthesis of the Markovian jump time-delayed system is studied subject to stochastic actuator failures and partially known transition probabilities. Specifically, a novel actuator fault model is designed, in which the actuator fault matrix satisfies a certain probabilistic condition. Under the construction of an appropriate Lyapunov–Krasovskii functional (LKF), as well as reciprocal convex approach, Jensen’s integral inequality, and reachable set lemma, delay-dependent sufficient criteria are obtained in terms of linear matrix inequalities (LMIs) for finding an ellipsoid to bound the reachable sets of the Markovian jump time-delayed system with bounded disturbances. Finally, two numerical examples are provided to validate the effectiveness of the proposed strategy.

Reliable Fuzzy Tracking Control of Near-Space Hypersonic Vehicle Using Aperiodic Measurement Information

This paper is concerned with reliable fuzzy tracking control for a near-space hypersonic vehicle (NSHV) subject to aperiodic measurement information and stochastic actuator failures. The NSHV dynamics is approximated by the Takagi–Sugeno fuzzy models and the stochastic failures are characterized by a Markov chain. Different with the existing tracking results on NSHV, only the aperiodic sampling measurements are available during system operation. To realize the tracking objective, a reliable fuzzy sampled-data tracking control strategy is presented. An appropriate time-dependent Lyapunov function is constructed to fully capture the real sampling pattern. The sampling-interval-dependent mean square exponential stability criterion with disturbance attenuation is then established. The solution of the tracking controller gains can be obtained by solving an optimization problem. Finally, the simulation studies on NSHV dynamics in the entry phase are performed to verify the validity of the developed fuzzy tracking control strategy.

Finite-Time Extended Dissipative Based Optimal Guaranteed Cost Resilient Control for Switched Neutral Systems With Stochastic Actuator Failures

This work is devoted to the results of extended dissipative based on finite-time resilient guaranteed cost control of switched neutral time-delayed system subject to mismatched uncertainties and stochastic actuator failures. Particularly, a new novel actuator fault is implemented by considering that the actuator fault follows a certain probabilistic distribution. The proper guaranteed cost function is chosen to achieve an adequate level of performance. Moreover, the extended dissipative inequality includes some well-known weighting matrices such as H ∞ performance, L 2 - L ∞ performance, passivity case, mixed H ∞ and passivity case, and dissipativity performance, respectively. The main aim of this work is to model a resilient guaranteed cost sampled-data controller such that the proposed system is finite-time stable and satisfies the finite-time extended dissipative performance index. Under the Lyapunov stability theory and proper Lyapunov-Krasovskii functional (LKF) together with Writinger-based integral inequality, a new set of delay-dependent sufficient conditions is obtained to ensure the finite-time stability of the switched neutral system. Moreover, the obtained finite-time sufficient conditions are derived in the form of linear matrix inequalities (LMIs), which can be determined via Matlab LMI software. At last, the examples are exploited to show the effectiveness of the considered design procedures.

Reliable Finite-Time Robust Control for Sampled-Data Mechanical Systems Under Stochastic Actuator Failures

This paper considers the problem of reliable finite-time robust control for uncertain mechanical systems with stochastic actuator failures and aperiodic sampling. A novel model of actuator failure capable of depicting various faulty modes is developed on the basis of homogenous Markov variable. To guarantee the finite-time stability (FTS) and boundedness, a novel fault-tolerant switching controller is developed by virtue of Lyapunov–Krasovskii functional and stochastic analysis technique, simultaneously, the finite-time H∞ performance is also ensured to attenuate the mechanical vibration caused by external disturbances. With convex optimization algorithm, the anticipated controller can be procured by solving a set of linear matrix inequalities (LMIs). Finally, two practical examples of mechanical systems, one of which is governed by lumped parameters and the other is described by distributed parameters, are proposed to prove the effectiveness of the theoretical developments of this study.

Finite-Time Fuzzy Sampled-Data Control for Nonlinear Flexible Spacecraft With Stochastic Actuator Failures

This paper deals with the problem of finite-time sampled-data control for nonlinear flexible spacecraft described by Takagi–Sugeno (T–S) fuzzy model with stochastic actuator failures. Different from the existing literatures, T–S fuzzy approach is used to model the nonlinear behaviors of flexible spacecraft for its good approximation performance. A novel and general input model related to Markovian variables is developed to depict the stochastic actuator failures, which is capable of covering various faulty modes. With the aid of stochastic analysis and convex optimization techniques, a novel fault-tolerant fuzzy switching controller is designed to carry out the finite-time attitude stabilization for flexible spacecraft with the existence of stochastic failures and sampled-data inputs, and an optimal $H_\infty$ performance level is ensured simultaneously. Finally, a practical example with simulation results are provided to validate the effectiveness of the developed control strategy.

Adaptive Reliable $H_\infty $ Control for a Class of T-S Fuzzy Systems With Stochastic Actuator Failures

This paper studies the problem of adaptive reliable $H_\infty $ control for a class of T-S fuzzy systems with actuator failures. In contrast to work found in the literature, stochastic actuator failures are considered, and stochastic functions are used to denote failure scaling factors. By combining an adaptive method with a switching-type control mechanism, a novel and reliable static output feedback control scheme is developed, where adaptive parameters are updated such that failure effects are compensated effectively. Furthermore, an $H_{\infty }$ performance index is proposed to attenuate the effects of sensor noises. Finally, a nonlinear mass-spring-damper example is presented to verify the effectiveness of the method proposed in this paper.

Adaptive Fault Tolerant Control of a Half-Car Active Suspension Systems Subject to Random Actuator Failures

Adaptive fault tolerant control problem for half-car active suspension systems subject to stochastic actuator failures is considered in this paper. Two stochastic functions related to Markovian variables have been introduced to denote the failure for the front and the rear actuators embedded between the car body and the wheel–axle. This makes the problem practical, yet it makes the stability analysis of zero dynamics involving Markovian variables very challenging. By employing adaptive backstepping technique, a new adaptive fault tolerant control scheme is proposed, which ensures the boundedness in probability of the considered systems. Comparative simulation results for a half-car active suspension system are presented to show the effectiveness of the proposed control scheme.

Stabilization of nonlinear uncertain systems with stochastic actuator failures and time-varying delay

Summary In this paper, we investigate the adaptive state-feedback stabilization problem for a class of nonlinear systems subject to parametric uncertainties, time-varying delay, and Markovian jumping actuator failures. First, some fundamental results, including the infinitesimal generator and conditions for the existence and uniqueness of the solution, are established for nonlinear systems w.r.t. Markovian vector and time-varying delay. Subsequently, corresponding stability criterion is generalized to the considered systems. By employing the backstepping method and the tuning function technique, a systematic adaptive fault-tolerant control scheme is proposed, which guarantees the boundedness in probability of all the closed-loop signals. It is noted that no fault detection and diagnostic block are needed, and the control law can be adapted automatically by taking account of the innovative state information. The efficiency of the designed controller is demonstrated by an illustrative example. Copyright © 2015 John Wiley & Sons, Ltd.

Adaptive Failure Compensation Control for Uncertain Systems With Stochastic Actuator Failures

In this technical note, an adaptive failure compensation problem has been studied for a class of nonlinear uncertain systems subject to stochastic actuator failures and unknown parameters. The stochastic functions related to Markovian variables have been introduced to denote the failure scaling factors for each actuators which is much more practical and challenging. Firstly, by taking into account of the Markovian variables existing in the system, some preliminary knowledges have been established. Then, by employing backstepping strategy, an adaptive failure compensation control scheme has been proposed, which ensures the boundedness in probability of all the closed-loop signals in the presence of stochastic actuator failures. A simulation example is presented to show the effectiveness of the proposed scheme.

Adaptive Fault-Tolerant Control for Time-Delay Nonlinear Systems with Stochastic Actuator Failures

In [18], a class of nonlinear systems with stochastic actuator failures have been studied. Stochastic functions related to Markovian variables have been introduced to describe the failure scaling factors for each actuators. In this paper we consider the kind of systems involving state-delay, which is much more practical, and adaptive fault-tolerant control problem has been studied. Two main challenges arise: how to establish the infinitesimal generator for systems involving multi-Markovian variables and state-delay simultaneously; then how to handle the delayed terms and the extra transition rate related ones appearing in the wisely designed Lyapunov-Krasovskii functional. By proposing an adaptive fault-tolerant control scheme, the existence and uniqueness of the solution process to the closed-loop system is guaranteed and the boundedness in probability of all the closed-loop signals can be ensured. An example is worked out to illustrate the effectiveness of the proposed scheme.

Fault Detection for a Class of Uncertain Linear Discrete-time Systems with Intermittent Measurements and Probabilistic Actuator Failures

This paper deals with fault detection (FD) problem for linear discrete-time systems subject to random intermittent measurements, probabilistic actuator failures, norm-bounded model uncertainty, and stochastic model uncertainty. By taking into account the probabilistic actuator failures, a new reference residual model is proposed to formulate the FD issue as an H∞, model-matching problem. The corresponding reference residual is generated through maximizing a stochastic H–/H∞ or H∞/H∞ performance index via solving an algebraic Riccati equation (ARE). By the aid of the linear matrix inequality (LMI) techniques, a fault detection filter (FDF) is constructed such that the residual is sensitive to fault but insensitive to unknown inputs, mixed model uncertainties, random intermittent measurements and stochastic actuator failures. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Network‐based precise tracking control of systems subject to stochastic failure and non‐zero input

This study deals with the problem of reliable precise tracking control for the networked control system with non-zero external inputs (NEIs). A new control scheme is developed by introducing an integral item in the control law and taking stochastic actuator failure (SAF) into account, by which a better steady tracking performances can be achieved. Based on Lyapunov theory, a reliable control design method that guarantees the network-based tracking control systems with zero steady-state error in the conditions of both NEIs and SAFs is designed. Simulation results demonstrate the effectiveness of the developed controller design scheme.

Reliable dissipative control of discrete‐time switched singular systems with mixed time delays and stochastic actuator failures

This study is concerned with the problem of reliable dissipative control for a class of discrete-time switched singular systems with mixed time delays and multiple actuator failures. The failure probability of each actuator is individually quantified and is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0, 1]. Attention is focused on identifying a class of slow switching signals and designing a set of reliable mode-dependent state-feedback controllers such that, for all admissible mixed time delays and multiple probabilistic actuators faults, the closed-loop system is stochastically exponentially admissible and strictly (Q, Q, ℛ)-dissipative. By using the Lyapunov function approach and the average dwell-time scheme, sufficient conditions for the existence of such class of stabilising switching signals and the reliable mode-dependent controllers are derived in terms of linear matrix inequalities, and the explicit expression for the desired controller gains is also given. A numerical example is given to demonstrate the effectiveness of the theoretical results.