Adaptive finite‐time fault‐tolerant tracking control for a class of MIMO nonlinear systems with output constraints

In this work, we present a novel adaptive finite‐time fault‐tolerant control algorithm for a class of multi‐input multi‐output nonlinear systems with constraint requirement on the system output tracking error. Both parametric and nonparametric system uncertainties can be effectively dealt with by the proposed control scheme. The gain functions of the nonlinear systems under discussion, especially the control input gain function, can be not fully known and state‐dependent. Backstepping design with a tan‐type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, finite‐time convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output tracking error will not be violated during operation. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive decentralized fault‐tolerant tracking control for large‐scale nonlinear systems with input quantization

In this paper, an adaptive decentralized tracking control scheme is designed for large‐scale nonlinear systems with input quantization, actuator faults, and external disturbance. The nonlinearities, time‐varying actuator faults, and disturbance are assumed to exist unknown upper and lower bounds. Then, an adaptive decentralized fault‐tolerant tracking control method is designed without using backstepping technique and neural networks. In the proposed control scheme, adaptive mechanisms are used to compensate the effects of unknown nonlinearities, input quantization, actuator faults, and disturbance. The designed adaptive control strategy can guarantee that all the signals of each subsystem are bounded and the tracking errors of all subsystems converge asymptotically to zero. Finally, simulation results are provided to illustrate the effectiveness of the designed approach.     

Adaptive finite‐time attitude stabilization for rigid spacecraft with actuator faults and saturation constraints

The attitude stabilization problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator saturations, and actuator faults is addressed in this paper. First, a novel fast terminal sliding mode manifold is designed to avoid the singularity problem while providing high control ability. In addition, fast terminal sliding mode control laws are proposed to make the spacecraft system trajectory fast converge onto the fast terminal sliding mode surface and finally evolve into small region in finite time, which cannot be achieved by the previous literatures. Based on the real sliding mode context, a practical adaptive fast terminal sliding mode control law is presented to guarantee attitude stabilization in finite time. Also, simulation results are presented to illustrate the effectiveness of the control strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive event‐triggered global fast finite‐time control for a class of uncertain nonlinear systems

This article designs an adaptive event‐triggered controller to solve the problem of global finite‐time stabilization for a class of uncertain nonlinear systems. By using the symbol function technique, the event‐triggered error is completely compensated, the adaptive technique and the back‐stepping method are simultaneously applied to the controller design, and the new way of designing controller is completed on the basis of fast finite‐time stability theory. Subsequently, taking Lyapunov stability theorem into account, the system stability is proved, and the system is demonstrated by contradiction to be non‐zeno. Finally, giving a simulation example to display the feasibility of this method.     

Finite‐time output tracking for a class of switched nonlinear systems

This paper investigates the finite‐time output tracking for a class of switched nonlinear systems in p‐normal form. Compared with the existing results, the restrictions on power orders of the system are relaxed. Using the convex combination method and the adding a power integrator technique, a state‐dependent switching and law, and state feedback controllers of individual subsystems are constructed. It is shown that all states of the closed‐loop system are bounded, and the tracking error can converge to a small neighborhood of zero in finite time. An example is provided to show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive finite‐time neural backstepping control for multi‐input and multi‐output state‐constrained nonlinear systems using tangent‐type nonlinear mapping

This article focuses on the problem of adaptive finite‐time neural backstepping control for multi‐input and multi‐output nonlinear systems with time‐varying full‐state constraints and uncertainties. A tan‐type nonlinear mapping function is first proposed to convert the strict‐feedback system into a new pure‐feedback one without constraints. Neural networks are utilized to cope with unknown functions. To improve learning performance, a composite adaptive law is designed using tracking error and approximate error. A finite‐time convergent differentiator is adopted to avoid the problem of “explosion of complexity.” By theoretical analysis, all the signals of system are proved to be bounded, the outputs can track the desired signals in a finite time, and full‐state constraints are not transgressed. Finally, comparative simulations are offered to confirm the validity of the proposed control scheme.     

Event‐triggered practical finite‐time output feedback stabilization of a class of uncertain nonlinear systems

This paper studies the event‐triggered practical finite‐time output feedback stabilization problem for a class of uncertain nonlinear systems with unknown control gains. First, a reduced‐dimensional observer is employed to implement the reconstruction of the unavailable states. Furthermore, a novel event‐triggered output feedback control strategy is proposed based on the idea of backstepping design and sign function techniques. It is shown that the practical finite‐time stability of the closed‐loop systems is ensured by Lyapunov analysis and related stability criterion. Compared with the existing methods, the main advantage of this strategy is that the observer errors and event‐trigger errors can be processed simultaneously to achieve the practical finite‐time stability. Finally, an example is adopted to demonstrate the validity of the proposed scheme.     

Finite‐time optimal control for interconnected nonlinear systems

This work addresses the finite‐time optimal control problem for a class of interconnected nonlinear systems with powers of positive odd rational numbers. A series of homogeneous controllers, which are capable of guaranteeing the local finite‐time stability of the closed‐loop systems, are first developed using the adding one power integrator method and backstepping technique. Then, the nested saturation controllers are further proposed to achieve global finite‐time stability. Furthermore, the corresponding design parameters are optimized, and thus, an optimal controller is obtained. A numerical simulation example is finally given to illustrate the effectiveness of the proposed control strategy.     

A unified approach to finite‐time stabilization of high‐order nonlinear systems with and without an output constraint

This paper considers the problem of state feedback finite‐time stabilization for a class of high‐order nonlinear systems with an output constraint. By proposing a novel tan‐type barrier Lyapunov function combined with manipulating sign functions, the technique of adding a power integrator is skillfully revamped to develop a systematic approach that guides us to construct a state feedback finite‐time stabilizer for high‐order nonlinear systems while preventing the violation of a prespecified output constraint during operation. The proposed approach is a unified tool in the sense that it can provide a finite‐time stabilizer design even when the constraint is infinite, or equivalently, there is no need for a constraint. A simple example is presented to demonstrate the effectiveness of the proposed strategy.     

Adaptive finite‐time control for nonlinear teleoperation systems with asymmetric time‐varying delays

This paper addresses the adaptive finite‐time control problem of nonlinear teleoperation system in the presence of asymmetric time‐varying delays. To achieve the finite‐time position tracking, a novel adaptive finite‐time coordination algorithm based on subsystem decomposition is developed. By introducing a switching‐technique‐based error filtering into our design framework, the complete closed‐loop master (slave) teleoperation system is modeled as a special class of switched system, which is composed of two subsystems. To analyze such system, a finite‐time state‐independent input‐to‐output stability criterion is first developed for some normal switched nonlinear delayed systems. Then based on the classical Lyapunov–Krasovskii method, the stability of complete closed‐loop systems is obtained. It is shown that the proposed scheme can make the position errors converge into a deterministic domain in finite time when the robots continuously contact with human operator and/or the environment in the presence of asymmetric time‐varying delays. Finally, the simulation results are given to demonstrate the effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Semi‐global finite‐time observers for multi‐output nonlinear systems

Finite‐time stability is investigated for nonlinear systems, which satisfy uniqueness of solution. First, a new sufficient condition for local finite‐time stability is presented. Next, by using the high‐gain observers and carefully selecting the homogeneity powers and weights, the problem of semi‐global and finite‐time stable observers is studied for multi‐output nonlinear systems with uniform observability and a triangular structure. Then, a design procedure is worked out for such observers. Finally, two numerical examples further verify the validity of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive neural network dynamic event-triggered control for strong interconnected stochastic nonlinear systems with output constraint

This paper proposes a dynamic event-triggered mechanism based command filtered adaptive neural network (NN) tracking control scheme for strong interconnected stochastic nonlinear systems with time-varying output constraints. By designing a state observer, the unmeasured states of the systems can be estimated. The NNs are utilized to handle the unknown intermediate functions. In the controller design process, the asymmetric time-varying barrier Lyapunov functions are used to guarantee that the systems outputs do not violate the constraint regions. By integrating the command filter with variable separation technique, the controller design process is more simple, and the problem of algebraic-loop can be solved which caused by interconnected functions. According to the Lyapunov stability theory, it can be ensured that all signals of the systems are bounded in probability. Finally, the availability of the developed control scheme can be showed by the simulation example.     

Robust decentralized adaptive fuzzy control for a class of large‐scale MIMO nonlinear systems

In this paper, a novel decentralized robust adaptive fuzzy control scheme is proposed for a class of large‐scale multiple‐input multiple‐output uncertain nonlinear systems. By virtue of fuzzy logic systems and the regularized inverse matrix, the decentralized robust indirect adaptive fuzzy controller is developed such that the controller singularity problem is addressed under a united design framework; no a priori knowledge of the bounds on lumped uncertainties are being required. The closed‐loop large‐scale system is proved to be asymptotically stable. Simulation results confirmed the validity of the approach presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive finite‐time control for bilateral teleoperation systems with jittering time delays

In this paper, we present a robust adaptive control algorithm for a class of bilateral teleoperation systems with system uncertainties and jittering time delays. The remarkable feature of jittering delays is that time delays change sharply and randomly. Conventional controllers would fail because jittering time delays introduce serious chattering. To address the jittering issue, a novel jittering‐free scheme is developed by relaxing and extending the frequently used constant upper bound. Moreover, an adaptive law was incorporated with the Chebyshev neural network to deal with the system uncertainties. To obtain finite‐time synchronization performance, a fast terminal sliding mode controller is proposed through the technique of “adding a power integrator.” With the proposed control scheme, the robust finite‐time convergence performance is guaranteed. The settling time can be further calculated with the controller parameters. The simulation and experiment results have demonstrated the effectiveness of the proposed method.     

Adaptive fuzzy output feedback decentralized control of pure‐feedback nonlinear large‐scale systems

In this paper, an adaptive fuzzy decentralized output feedback control approach is presented for a class of uncertain nonlinear pure‐feedback large‐scale systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the immeasurable states. On the basis of the adaptive backstepping recursive design technique, an adaptive fuzzy decentralized output feedback is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

时变关联系统的分散自适应输出反馈控制

针对一类具有动静态关联项和未建模动态的时变关联系统,通过引入输入滤波器及一系列坐标变换,给出了一种分散自适应输出反馈控制器的设计方案.当时变参数的变化率属于L1∩L∞,外界干扰属于L2∩L∞,未建模动态的幅值在某砦范围内变化时,证明了闭环系统的稳定性,且每一个子系统的输出收敛于零.仿真例子验证了这一控制方案的有效性.     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

In this work, we propose a novel iterative learning control algorithm to deal with a class of nonlinear systems with system output constraint requirements and quantization effects on the system control input. Actuator faults have also been considered, which include multiplicative, additive, and stuck actuator faults. To the best of our knowledge, this is the first reported work in the iterative learning control literature to deal with quantization effects for the control input of nonlinear systems under the effects of actuator faults and system output constraints. Under the proposed scheme, using backstepping design and composite energy function approaches in the analysis, we show that uniform convergence of the state tracking errors can be guaranteed over the iteration domain, and the constraint requirement on the system output will not be violated at all time. In the end, a simulation study on a single‐link robot model is presented to demonstrate the effectiveness of the proposed scheme.     

Adaptive tracking for MIMO nonlinear systems with Unknown fast time‐varying parameters

In this paper, we consider a class of MIMO nonlinear systems with fast time‐varying parametric uncertainties. First, the tracking problem of general nonlinearly time‐varyingly parameterized systems is solved. Then, a Lyapunov‐based singularity free adaptive controller is proposed for the considered system. Specifically, an estimation approach with a proportional plus integral adaptation scheme is utilized to update the estimations of the unknown parameters under a mild assumption that the signs of the leading minors of the input gain matrix are known. The asymptotic stability is achieved with full state feedback. Furthermore, we design an output feedback controller by utilizing a standard high‐gain observer and achieve uniformly ultimately bounded convergence. Simulation examples illustrate the effectiveness of the proposed methods.     

带有界扰动的一类大型互联非线性系统的鲁棒分散控制

研究带有界扰动的一类大型互联非线性系统的鲁棒分散控制问题, 该系统的第i个子系统的标称模型具有相对阶r_i及指数稳定的零动态, 且每个子系统的互联项满足匹配条件. 通过子系统状态的线性变换得到鲁棒分散状态反馈控制器, 当该控制律作用于系统时, 系统的状态能够收敛到原点的一个小邻域内, 并给出仿真算例说明该结论的可行性和有效性.