Adaptive fault diagnosis and fault-tolerant control of MIMO nonlinear uncertain systems

This article presents an integrated fault diagnosis and fault-tolerant control (FTC) methodology for a class of nonlinear multi-input–multi-output systems. Based on the fault information obtained during the diagnostic procedure, an FTC component is designed to compensate for the effect of faults. In the presence of a fault, a baseline controller guarantees the boundedness of all the system signals until the fault is detected. After fault detection and then again after isolation, the controller is reconfigured to improve the tracking performance using online fault diagnostic information. Under certain assumptions, the stability and tracking performances of the closed-loop system are rigorously investigated. It is shown that the system signals always remain bounded and the output tracking error converges to a neighbourhood of the origin of the state space.     

H2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty

This paper presents a design method of H₂ guaranteed cost (GC) fuzzy controllers for discrete-time nonlinear systems with parameter uncertainties. The Takagi and Sugeno (T-S) fuzzy model with parameter uncertainties is employed to represent an uncertain discrete-time nonlinear system. A sufficient condition for the existence of H₂ GC fuzzy controllers is presented in terms of linear matrix inequalities (LMIs). The resulting fuzzy controllers not only guarantee that the closed-loop fuzzy system is quadratically stable, but also provide a guaranteed cost on the H₂ performance index. Furthermore, an optimal H₂ GC fuzzy controller in the sense of minimizing a bound on the guaranteed cost is provided by means of an LMI optimization procedure. Finally, it is also demonstrated, through numerical simulations on the backing up control of a truck-trailer, that the proposed design method is effective.     

Robust stabilisation control for discrete-time networked control systems

We consider the analysis and synthesis of discrete-time networked control systems (NCSs), where the plant has additive uncertainty and the controller is updated with the sensor information at stochastic time intervals. It is shown that the problem is linked to H_∞-control of linear discrete-time stochastic systems and a new small gain theorem is established. Based on this result, sufficient conditions are given for ensuring mean square stability of the NCS, and the genetic algorithm is utilised to design the controller of the NCS based on a linear matrix inequality technique. An illustrative example is given to demonstrate the effectiveness of our proposed method.     

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT

This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

Fault-tolerant optimised tracking control for unknown discrete-time linear systems using a combined reinforcement learning and residual compensation methodology

This paper considers the fault-tolerant optimised tracking control (FTOTC) problem for unknown discrete-time linear system. A research scheme is proposed on the basis of data-based parity space identification, reinforcement learning and residual compensation techniques. The main characteristic of this research scheme lies in the parity-space-identification-based simultaneous tracking control and residual compensation. The specific technical line consists of four main contents: apply subspace aided method to design observer-based residual generator; use reinforcement Q-learning approach to solve optimised tracking control policy; rely on robust H_∞ theory to achieve noise attenuation; adopt fault estimation triggered by residual generator to perform fault compensation. To clarify the design and implementation procedures, an integrated algorithm is further constructed to link up these four functional units. The detailed analysis and proof are subsequently given to explain the guaranteed FTOTC performance of the proposed conclusions. Finally, a case simulation is provided to verify its effectiveness.     

Sensor fault estimation for Lipschitz nonlinear systems in finite-frequency domain

In this study, the problem of sensor fault estimation observer design for Lipschitz nonlinear systems with finite-frequency specifications is investigated. First, the sensor fault is considered as an auxiliary state vector and an augmented system is established. Then, by transforming the nonlinear error dynamics into a linear parameter varying system, a sufficient condition for the observer-error system with a finite-frequency H_∞ performance is derived in terms of linear matrix inequalities (LMIs). Based on the obtained condition, novel nonlinear observers are designed to simultaneously estimate the system states and the fault signals and attenuate the disturbances in the finite-frequency domain. The proposed design method can provide less restrictive LMI conditions and get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. A numerical example is given to show the effectiveness and superiority of the new results.     

Finite-time mixed H∞ and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems

This paper is concerned with the finite-time mixed H_∞ and passivity performance analysis and filter design for a class of uncertain nonlinear discrete-time Markovian jump systems (MJSs) described by Takagi–Sugeno fuzzy model with nonhomogeneous jump processes. In this paper, the proposed MJSs fuzzy model is formulated with norm-bounded parameter uncertainties and time-varying jump transition probability matrices. In particular, the time-varying transition probability matrices are expressed in respect of a polytope. By constructing a suitable Lyapunov functional, a new set of sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to ensure that the filtering error system is robustly stochastically finite-time bounded and a prescribed mixed H_∞ and passive performance index is achieved. Moreover, the robust mixed H_∞ and passivity filter design gain matrices can be computed from the obtained LMIs. Furthermore, the developed results unify H_∞ and passive filtering problems in a single framework. Finally, two numerical examples including an application-oriented example are provided to demonstrate the effectiveness of the proposed filter design technique.     

Robust analysis and control for a class of uncertain nonlinear discrete-time systems

This paper deals with the problem of robust analysis and control of a class of nonlinear discrete-time systems with (constant) uncertain parameters. For the analysis problem we use a polynomial Lyapunov function and we generalize, for nonlinear systems, the “extended stability” notion proposed by Oliveira et al. (1999) in the context of linear discrete-time uncertain systems. As a result, we propose an LMI optimization problem to maximize an estimate of the domain of attraction, and also extend this approach to the synthesis problem by considering parameter-dependent Lyapunov functions and nonlinear multipliers. Numerical examples illustrate the approach and show its potential for solving analysis and control problems of nonlinear discrete-time systems.     

Robust H ∞ reliable control of time delay nonlinear systems via Takagi–Sugeno fuzzy models

This article is focused on reliable fuzzy H _∞ controller design for a class of Takagi–Sugeno (T–S) fuzzy systems with state delay, actuator failures, disturbance input and norm bounded uncertainties. In the design, the H _∞ performance of the closed-loop system is optimised during normal operation (without failures) while the system satisfies a prescribed H _∞ performance level in the case of actuator failures. Two methods are presented in this study. In the first method, delay-dependent conditions are derived based on a single Lyapunov–Krasovskii function. This method improves delay-independent results existing in the literature. Next, to further reduce the conservatism, we use a parameter-dependent Lyapunov–Krasovskii function. The new sufficient conditions for the existence of the suboptimal robust reliable controller are shown in terms of linear matrix inequalities (LMIs), which can be solved by using LMI optimisation techniques. A simulation example shows the effectiveness of the proposed methods.     

Robust fault-tolerant prescribed performance tracking for uncertain switched pure-feedback nonlinear systems under arbitrary switching

This paper presents a model-free prescribed performance design methodology for the robust fault-tolerant tracking (RFTT) of uncertain switched pure-feedback nonlinear systems under arbitrary switching. Unexpected faults in switched non-affine nonlinearities and in an actuator are considered. Using the prescribed performance design and the common Lyapunov function method, a common RFTT scheme is proposed to ensure that the tracking error remains within preassigned performance bounds and finally converges to a preselected neighbourhood of the origin, regardless of arbitrary switching and unexpected faults. Contrary to existing results in the literature, the proposed methodology does not require fault compensation mechanisms such as adaptive techniques and function approximators using neural networks or fuzzy systems. Thus, the structure of the proposed RFTT scheme is simpler than that of the existing control schemes. Moreover, the proposed approach can predesign the transient performance bounds at the instants when switching and faults occur. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed theoretical approach.     

A nonlinear trajectory tracking controller for mobile robots with velocity limitation via fuzzy gains

This paper proposes a fuzzy controller for trajectory tracking with unicycle-like mobile robots. Such controller uses two Takagi–Sugeno (TS) fuzzy blocks to generate its gains. The controller is able to limit the velocity and control signals of the robot, and to reduce the errors arising from its dynamics as well. The stability of the developed controller is proven, using the theory of Lyapunov. Experimental results show that the use of the proposed controller is attractive in comparison with the use of a controller with fixed saturation function.     

Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations

This paper studies the robust fuzzy control problem of uncertain discrete-time nonlinear Markovian jump systems without mode observations. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. As a result, an uncertain Markovian jump fuzzy system (MJFS) is obtained. A stochastic fuzzy Lyapunov function (FLF) is employed to analyze the robust stability of the uncertain MJFS, which not only is dependent on the operation modes of the system, but also directly includes the membership functions. Then, based on this stochastic FLF and a non-parallel distributed compensation (non-PDC) scheme, a mode-independent state-feedback control design is developed to guarantee that the closed-loop MJFS is stochastically stable for all admissible parameter uncertainties. The proposed sufficient conditions for the robust stability and mode-independent robust stabilization are formulated as a set of coupled linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, it is also demonstrated, via a simulation example, that the proposed design method is effective.     

Event-triggered simultaneous fault detection and tracking control for multi-agent systems

The main aim of this study is to design distributed simultaneous fault detection and control units for multi-agent systems subject to limited communication and energy resources. For this purpose, each agent is equipped with a single module that generates both the residual signal for the fault detection task, as well as the control input of each agent for the tracking objective. To reduce the communication among the agents, an event-triggered data transmission paradigm is considered by using a dynamic triggering rule which results in higher data transmission reduction in comparison with the static triggering condition. Moreover, the proposed dynamic observer-based structure for the detector-controller module provides more degrees of freedom compared to the static Luenberger observer. The design parameters are obtained by solving a multi-objective optimisation problem considering the fault detection, tracking, and communication objectives. Simulation results illustrate the effectiveness and capabilities of the proposed method.     

Robust stability and control of uncertain linear discrete-time periodic systems with time-delay

This paper deals with the problems of robust stability analysis and robust control of linear discrete-time periodic systems with a delayed state and subject to polytopic-type parameter uncertainty in the state-space matrices. A robust stability criterion independent of the time-delay length as well as a delay-dependent criterion is proposed, where the former applies to the case of a constant time-delay and the latter allows for a time-varying delay lying in a given interval. The developed robust stability criteria are based on affinely uncertainty-dependent Lyapunov–Krasovskii functionals and are given in terms of linear matrix inequalities. These stability conditions are then applied to solve the problems of robust stabilization and robust _H∞$H_{\infty }$  control via static periodic state feedback. Numerical examples illustrate the potentials of the proposed robust stability and control methods.     

Robust adaptive control of a class of nonlinear uncertain systems

A smooth robust dynamic feedback controller is constructed, and the problem of robust H∞ almost disturbance attenuation with internal stability is solved for high-order nonlinear systems with parameter uncertainties. Finally, illustrative example and simulation results demonstrate the effectiveness of the proposed method.