Adaptive fault‐tolerant control for feedback linearizable systems with an aircraft application

This paper investigates fault‐tolerant control (FTC) for feedback linearizable systems (FLSs) and its applications. The dynamic effects caused by the actuator faults on the feedback linearized model are firstly analyzed, which reveals that under actuator faults, the control input in the linearized model is affected by uncertain terms. In the framework of model reference control, the first FTC strategy is proposed as a robust controller, which achieves asymptotic tracking control of the FLS under actuator faults. A disadvantage of this strategy is that it relies on explicit information about several parameters in the actuator faults. This requirement is later relaxed by combining the robust FTC strategy with an adaptive technique to generate the adaptive FTC law, which is then improved to alleviate possible chattering of the actuator and estimation drifting of the adaptive parameter. Finally, the proposed FTC strategies are evaluated by reference command tracking control of a pendulum and an air‐breathing hypersonic vehicle under actuator faults. Simulation results demonstrate good tracking performance, which confirms effectiveness of the proposed strategies. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive prescribed performance tracking control for strict‐feedback nonlinear systems with zero dynamics

This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously.     

一类非线性系统的输出反馈容错控制

针对一类非线性系统,研究了故障情况下基于输出反馈的容错控制问题．首先基于Zhang的自适应观测器和Lin的输出反馈控制律设计了正常系统的标称控制律,分析了该控制律的性能,并得到了故障发生后仍然采用该控制律时闭环系统状态有界的充分条件．在此基础上,设计了故障系统的容错控制律,证明了若发生的故障满足前述的充分条件,则故障系统在该容错控制律下稳定．数值仿真表明了该方法的有效性．     

Adaptive fault-tolerant control for a class of flexible air-breathing hypersonic vehicles

In this paper, a novel adaptive fault-tolerant control (FTC) scheme is proposed for a class of flexible air-breathing hypersonic vehicles with unknown inertial and aerodynamic parameters and even input constraints. The fault model under consideration covers the case that all actuators suffer from unknown time-varying faults. In the controller design and stability analysis, we introduce new Lyapunov functions, some differentiable auxiliary functions, a bound estimation approach, and a Nussbaum function, which help us successfully circumvent the obstacle caused by the faults, input constraints, and flexible modes. In addition to higher reliability, the proposed scheme is able to ensure that all closed-loop signals are globally uniformly bounded and to steer the tracking errors of altitude and velocity into predefined arbitrarily small residual sets. As a result, the tracking accuracy can be designated in advance. Simulation results illustrate the effectiveness of the proposed scheme.     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

Robust resilient control for parametric strict feedback systems with prescribed output and virtual tracking errors

This paper investigates the robust resilient control problem for a class of parametric strict feedback nonlinear systems with prescribed output and virtual tracking errors performance. The resilience is governed by a continuously nonlinear control gains function, which endows the virtual and actual controllers with self‐adjusting abilities with respect to transformed error surfaces. The proposed control scheme is adaptation, estimation, and approximation‐free in the presence of unknown parameters and nonlinearities, and only a number of control gains, which is equal to the relative degree of the considered plants, need to be selected in applications. It is proved by rigorous analysis that the output tracking errors are confined in predefined prescribed performance functions under some nonrestrictive initial conditions, and the bounds of states are obtained characterized as control gains and systemic function‐associated constants. Finally, comparative illustrative examples are given to demonstrate the effectiveness of the proposed control scheme.     

Adaptive robust fault-tolerant control for linear MIMO systems with unmatched uncertainties

In this paper, two novel fault-tolerant control design approaches are proposed for linear MIMO systems with actuator additive faults, multiplicative faults and unmatched uncertainties. For time-varying multiplicative and additive faults, new adaptive laws and additive compensation functions are proposed. A set of conditions is developed such that the unmatched uncertainties are compensated by actuators in control. On the other hand, for unmatched uncertainties with their projection in unmatched space being not zero, based on a (vector) relative degree condition, additive functions are designed to compensate for the uncertainties from output channels in the presence of actuator faults. The developed fault-tolerant control schemes are applied to two aircraft systems to demonstrate the efficiency of the proposed approaches.     

Adaptive hierarchical control for output feedback systems

In this paper, we address the problem of adaptive hierarchical control for a class of so-called uncertain output feedback systems. The proposed approach is to design an adaptive output interface dynamic by estimating the uncertainties. With the interface connected to the uncertain nonlinear system and a linear abstract system, the system could track approximately the abstraction. Finally, two examples are presented to illustrate our approach.     

一类时变时延网络控制系统的鲁棒容错控制

针对一类具有时变时延的不确定网络控制系统,研究存在执行器失效情况的系统鲁棒容错控制问题.基于完整性容错控制思想和李亚普诺夫时延依赖稳定理论,给出了系统对执行器失效具有完整性的充分条件,设计了鲁棒容错控制器.仿真结果表明,该控制器不仅能保证系统鲁棒渐近稳定,而且使系统具有良好的动态性能.     

具有传感器故障的网络控制系统保性能可靠控制

基于存在时延和丢包的网络传输环境.针对具有参数不确定性的网络化控制系统,研究了其在传感器故障条件下的保性能可靠控制问题.根据Lyapunov稳定性理论和线性矩阵不等式(LMIs)方法,推导出使闭环网络控制系统在传感器故障条件下渐近稳定且保证综合性能指标满足要求的充分条件,并利用LMIs提出了保性能可靠控制率的设计方法.该控制算法在提高网络化控制系统可靠性的同时有利于系统综合体性能的优化.数值仿真验证了该方法的可行性和有效性.     

Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers

The distributed consensus output tracking problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances and uncertain nonlinear virtual control coefficients of the subsystems. The systems are under a directed communication graph, where the leader node is the root. The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid direct differentiation. At each step of virtual controller design, a prescribed performance controller is constructed to achieve prescribed transient performance so that the system states remain in the feasible domain. Then each virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the control system are analysed theoretically. It is clarified that the prescribed performance control technique ensures that the system signals stay in the feasible domain, whereas sufficiently small ultimate control errors can be achieved by the finite-time disturbance observers. Finally, the performance of the proposed methods is confirmed by numerical studies.     

Non-smooth state feedback prescribed performance control for interconnected nonlinear systems with unmodelled dynamics

This paper investigates the problem of non-smooth state feedback control for a group of high-order p-normal form interconnected nonlinear systems with prescribed performance. Each subsystem is in the form of triangular structure with the unmodelled dynamics. With the help of appropriate Lyapunov function, a state feedback controller is constructed via backstepping method. It is strictly proved that the closed-loop system is asymptotically stable and both transient and steady-state performances of the outputs are preserved. Finally, simulation results are presented to illustrate the effectiveness of proposed method.     

Adaptive quantised fault-tolerant tracking control of uncertain nonlinear systems with unknown control direction and the prescribed accuracy

In this paper, the problem of adaptive fault-tolerant tracking control for a class of uncertain nonlinear systems in the presence of input quantisation and unknown control direction is considered. By choosing a class of particular Nussbaum functions, an adaptive fault-tolerant control scheme is designed to compensate actuator faults and input quantisation while the control direction is unknown. Compared with the existing results, the proposed controller can directly compensate for the nonlinear term caused by actuator faults and the nonlinear decomposition on the quantiser without estimating its bound. Furthermore, via Barhalant's Lemma, it is proven that all the signals of the closed-loop system are globally uniformly bounded and the tracking error converges into a prescribed accuracy in prior. Finally, an illustrative example is used for verifying effectiveness of the proposed approach.     

Distributed low-complexity output feedback tracking control for nonlinear multi-agent systems with unmodeled dynamics and prescribed performance

This paper investigates the prescribed performance distributed output consensus problem under directed graphs. With the utilisation of a filter, the original system of each follower can be converted into a strict-feedback system. Then, we design a prescribed performance output feedback distributed control protocol by applying the backstepping approach in the converted system. The proposed protocol can guarantee that the consensus tracking error of each agent evolves in predefined decaying bounds to achieve the prescribed performance, that is, the consensus tracking error of each agent converges to a predetermined residual set at a convergence rate no less than a prespecified value and exhibiting a maximum overshoot less than a preassigned constant. Moreover, during the process of consensus, all the signals in the closed-loop system are globally uniformly bounded. A simulation example is given to verify the effectiveness of the proposed control protocol.     

An adaptive fuzzy design for fault-tolerant control of MIMO nonlinear uncertain systems

This paper presents a novel control method for accommodating actuator faults in a class of multiple-input multiple-output (MIMO) nonlinear uncertain systems.The designed control scheme can tolerate both the time-varying lock-in-place and loss of effectiveness actuator faults.In each subsystem of the considered MIMO system,the controller is obtained from a backstepping procedure;an adaptive fuzzy approximator with minimal learning parameterization is employed to approximate the package of unknown nonlinear functions in each design step.Additional control effort is taken to deal with the approximation error and external disturbance together.It is proven that the closed-loop stability and desired tracking performance can be guaranteed by the proposed control scheme.An example is used to show the effectiveness of the designed controller.     

Robust tracking control for an air-breathing hypersonic vehicle with input constraints

The focus of this paper is on the design and simulation of robust tracking control for an air-breathing hypersonic vehicle (AHV), which is affected by high nonlinearity, uncertain parameters and input constraints. The linearisation method is employed for the longitudinal AHV model about a specific trim condition, and then considering the additive uncertainties of three parameters, the linearised model is just in the form of affine parameter dependence. From this point, the linear parameter-varying method is applied to design the desired controller. The poles for the closed-loop system of the linearised model are placed into a desired vertical strip, and the quadratic stability of the closed-loop system is guaranteed. Input constraints of the AHV are addressed by additional linear matrix inequalities. Finally, the designed controller is evaluated on the nonlinear AHV model and simulation results demonstrate excellent tracking performance with good robustness.     

Fault-tolerant control of flexible air-breathing hypersonic vehicles in linear ODE-beam systems

ABSTRACT

This paper addresses the fault-tolerant control issue for a class of flexible air-breathing hypersonic vehicles. Firstly, a longitudinal dynamic model with process faults is established, which contains an ordinary differential equation (ODE) for rigid body, an Euler–Bernoulli beam equation for flexible modes, and a new boundary connection between them; Secondly, a novel fault-tolerant control scheme is proposed to accommodate process faults and suppress vibrations, which relies on the direct Lyapunov method and the bilinear matrix inequalities (BMIs) technique; Thirdly, in order to compute the gain matrices of the fault-tolerant control law, a two-step algorithm is provided to solve the BMI feasibility problem in terms of linear matrix inequality optimisation technique. Finally, the simulation results are provided to illustrate the effectiveness of the theoretical results.     

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

This work considers an input and output constraint control problem for pure‐feedback systems with nonaffine functions possibly being in‐differentiable. A locally semibounded and continuous condition for nonaffine functions is presented to guarantee the controllability, and the nonaffine system is transformed to an equivalent pseudoaffine one based on the mild condition. Combined with backstepping technique, a novel prescribed performance controller with new performance functions is constructed to circumvent high frequency chattering in control input. An auxiliary system with bounded compensation term is utilized in this paper, successfully avoiding the overrun of control input. The methodology achieves the desired transient and steady‐state performance and presents excellent robustness against the system uncertainty. Finally, two numerical simulations are performed to demonstrate the effectiveness of the proposed approach.     

Robust fault-tolerant self-recovering control of nonlinear uncertain systems

In this paper, the problem of devising a fault-tolerant robust control for a class of nonlinear uncertain systems is investigated. Possible failures of the sensor measuring the state variables are considered, and a robust measure is developed to identify the stability- and performance-vulnerable failures. Based on evaluation of the robust measure, a fault-tolerant robust control will switch itself between one robust control strategy designed under normal operation and another under the faulty condition. It is shown that, under two input-to-state stability conditions, the proposed scheme guarantees not only the desired performance under normal operations but also robust stability and best achievable performance when there is a sensor failure of any kind.