Acceleration of finite‐time stable homogeneous systems

Stabilization rates of power‐integrator chains are easily regulated. It provides a framework for acceleration of uncertain multiple‐input–multiple‐output dynamic systems of known relative degrees (RDs). The desired rate of the output stabilization (sliding‐mode control) is ensured for an uncertain system if its RD is known, and a rough approximation of the high‐frequency gain matrix is available. The uniformly bounded convergence time (fixed‐time stability) is obtained as a particular case. The control can be kept continuous everywhere except the sliding‐mode set if the partial RDs are equal. Similarly, uncertain smooth systems of complete multiple‐input–multiple‐output RDs (ie, lacking zero dynamics) are stabilized by continuous control at their equilibria in finite time and are accelerated. Output‐feedback controllers are constructed. Computer simulation demonstrates the efficiency of the proposed approach.     

Multi‐surface sliding control for fast finite‐time leader–follower consensus with high order SISO uncertain nonlinear agents

In this paper, multi surface sliding cooperative control scheme is presented and new multiple sliding surfaces are proposed. It is proven that, for the setup that each agent is described by a chain of integrators, where the last integrator is perturbed by a bounded disturbance, leader–follower consensus can be achieved on these sliding surfaces if the communication graph has a directed spanning tree. Also, sliding variables can be driven to the sliding surfaces in fast finite time by the nonsmooth control law. The fast finite‐time Lyapunov stability theorem, the terminal sliding control technique, and the adding a power integrator design approach are used in our proposed control. Simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

基于终端滑模的机械手鲁棒自适应控制

对于不确定的机械手系统,提出一种鲁棒自适应控制方法,用自适应控制来估计系统的未知参数,用终端滑模控制来减少不确定因素的影响,为了避免因干扰的存在使自适应的估计参数发生漂移,引入死区自适应控制．仿真表明,滑模控制不仅抑制了误差,而且消除了死区自适应算法的局限性,该算法在取得较好控制效果的同时,具有很强的鲁棒性．     

Robust finite‐time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback

The finite‐time formation control for multiple nonholonomic wheeled mobile robots with a leader‐following structure is studied. Different from the existing results, the considered mobile robot has the following features: (i) a higher‐order dynamic model, (ii) the robot's velocities cannot be measured, and (iii) there are external disturbances. To solve the problem, a finite‐time consensus formation control algorithm via output feedback is explicitly given. At the first step, some finite‐time convergent observers are skillfully constructed to estimate both the unknown velocity information and the disturbance in finite time by imposing certain assumptions on the disturbances. Then, on the basis of the integral sliding‐mode control method, a disturbance observer‐based finite‐time output feedback controller is developed. Rigorous proof shows that the finite‐time formation can be achieved in finite time. An example is finally given to verify the efficiency of the proposed method.     

Adaptive sliding‐mode control for Mars entry trajectory tracking with finite‐time convergence

This paper presents a novel adaptive sliding‐mode control (ASMC) method for Mars entry guidance and the finite‐time convergence in the presence of large uncertainties can be guaranteed. With the help of gain adaptive law, the nonoverestimating value of control gains can be achieved, and then, the chattering can be attenuated by the proposed ASMC method. Meanwhile, the extended state observer is introduced to estimate and compensate for uncertainties and the nonoverestimating problem is resolved further. In addition, the proposed method does not require any knowledge on the upper bound of uncertainty, which yields to be used in practical systems. Finally, the numerical simulation results are given to demonstrate the effectiveness of the proposed guidance law.     

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.     

Reaction wheel fault‐tolerant finite‐time control for spacecraft attitude tracking without unwinding

This article proposes fault‐tolerant finite‐time attitude tracking control of a rigid spacecraft actuated by four reaction wheels without unwinding problem in the presence of external disturbances, uncertain inertia parameter, and actuator faults. First, a novel antiunwinding finite‐time attitude tracking control law is derived with a designed control signal which works within a known actuator‐magnitude constraint using a continuous nonsingular fast terminal sliding mode (NFTSM) concept. Second, a finite‐time disturbance observer (FTDO) is introduced to estimate a lumped disturbance due to external disturbances, uncertain inertia parameter, actuator faults, and input saturation. Third, a composite controller is developed which consists of a feedback control based on the continuous NFTSM method and compensation term based on the FTDO. The global finite‐time stability is proved using Lyapunov stability theory. Moreover, the singularity and unwinding phenomenon are avoided. Simulation results are conducted under actuator constraints in the presence of external disturbances, inertia uncertainty, and actuator faults and results are illustrated to show the effectiveness of the proposed method. In addition, to show the superiority of the proposed control method over the recently reported control methods, comparative analysis is also presented.     

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.     

Attitude stabilization of rigid spacecraft with finite‐time convergence

The problem of attitude control for a spacecraft model which is nonlinear in dynamics with inertia uncertainty and external disturbance is investigated in this paper. Two sliding mode controllers are proposed to force the state variables of the closed‐loop system to converge to the origin in finite time. Specially, the second control design consists of the estimation of the uncertainty and disturbance by adaptive method and thus it achieves the decrease of undesired chattering effectively. Also, simulation results are presented to illustrate the effectiveness of the control strategies. Copyright © 2010 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.     

Fault estimation observer design for discrete‐time systems in finite‐frequency domain

This paper proposes a framework of fault estimation observer design in finite‐frequency domain for discrete‐time systems. First, under the multiconstrained idea, a full‐order fault estimation observer in finite‐frequency domain is designed to achieve fault estimation by using the generalized Kalman–Yakubovich–Popov lemma to reduce conservatism generated by the entire frequency domain. Then, a reduced‐order fault estimation observer is constructed, which results in a new fault estimator to realize fault estimation using current output information. Furthermore, by introducing slack variables, improved results on full‐order fault estimation observer and reduced‐order fault estimation observer design with finite‐frequency specifications are obtained such that different Lyapunov matrices can be separately designed for each constraint. Simulation results are presented to illustrate the advantages of the theoretic results obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust adaptive fixed‐time tracking control of 6‐DOF spacecraft fly‐around mission for noncooperative target

The fixed‐time relative position tracking and attitude synchronization control problem of a spacecraft fly‐around mission for a noncooperative target in the presence of parameter uncertainties and external disturbances is investigated. Firstly, a novel and coupled relative position and attitude motion model for a noncooperative fly‐around mission is established. Subsequently, a novel nonsingular fast terminal sliding mode (NFTSM) surface is developed, and the explicit estimation of the convergence time independent of initial states is provided. Fair and systematic comparisons among several typical terminal sliding modes show that the designed NFTSM has faster convergence performance than the fast terminal sliding mode. Then, a robust integrated adaptive fixed‐time NFTSM control law with no precise knowledge of the mass and inertia matrix and disturbances by combining the nonsingular terminal sliding mode technique with an adaptive methodology is proposed, which can eliminate the chattering phenomenon and guarantee that the relative position and attitude tracking errors can converge into the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.     

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

This article addresses the problem of global adaptive finite‐time control for a class of p‐normal nonlinear systems via an event‐triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event‐triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite‐time stabilization of p‐normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme.     

Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.     

Robust finite‐time H∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

In this article, the problem of robust finite‐time H_∞ synchronization control is investigated for a class of uncertain discrete‐time master‐slave systems with Markovian switching parameters in the observer‐based case. Parameter uncertainties are assumed to be norm‐bounded, and the polyhedral character is utilized to describe the transition probabilities of nonhomogeneous Markov chain. By using stochastic Lyapunov function method and finite‐time analysis techniques, novel sufficient conditions that include the master‐slave parameters are obtained for designing an observer‐based finite‐time H_∞ synchronization control law in terms of linear matrix inequalities. The effectiveness of the proposed theoretical scheme is finally demonstrated by some simulations.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

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.     

Comments on ‘attitude stabilization of rigid spacecraft with finite‐time convergence’

This note points out that Theorems 1 and 2 in Zhu, Xia, Fu (Int. J. Robust Nonlinear Control 2011 21 (6):686–702) are incorrect. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time attitude stabilization for rigid spacecraft

This paper investigates the finite‐time attitude stabilization problem for rigid spacecraft in the presence of inertia uncertainties and external disturbances. Three nonsingular terminal sliding mode (NTSM) controllers are designed to make the spacecraft system converge to its equilibrium point or a region around its equilibrium point in finite time. In addition, these novel controllers are singularity‐free, and the presented adaptive NTSM control (ANTSMC) laws are chattering‐free. A rigorous proof of finite‐time convergence is developed. The proposed ANTSMC algorithms combine NTSM, adaptation and a constant plus power rate reaching law. Because the algorithms require no information about inertia uncertainties and external disturbances, they can be used in practical systems, where such knowledge is typically unavailable. Simulation results support the theoretical analysis.Copyright © 2013 John Wiley & Sons, Ltd.     

Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems

In this paper, we propose a discrete‐time nonlinear sliding mode observer for state and unknown input estimations of a class of single‐input/single‐output nonlinear uncertain systems. The uncertainties are characterized by a state‐dependent vector and a scalar disturbance/unknown input. The discrete‐time model is derived through Taylor series expansion together with nonlinear state transformation. A design methodology that combines the discrete‐time sliding mode (DSM) and a nonlinear observer design is adopted, and a strategy is developed to guarantee the convergence of the estimation error to a bound within the specified boundary layer. A relation between sliding mode gain and boundary layer is established for the existence of DSM, and the estimation is made robust to external disturbances and uncertainties. The unknown input or disturbance can also be estimated through the sliding mode. The conditions for the asymptotical stability of the estimation error are analysed. Application to a bioreactor is given and the simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2006 John Wiley & Sons, Ltd.