Composite Finite‐time Convergent Guidance Law for Maneuvering Targets with Second‐order Autopilot Lag

This paper aims to develop a new finite‐time convergent guidance law for intercepting maneuvering targets accounting for second‐order autopilot lag. The guidance law is applied to guarantee that the line of sight (LOS) angular rate converges to zero in finite time and results in a direct interception. The effect of autopilot dynamics can be compensated based on the finite‐time backstepping control method. The time derivative of the virtual input is avoided, taking advantage of integral‐type Lyapunov functions. A finite‐time disturbance observer (FTDOB) is used to estimate the lumped uncertainties and high‐order derivatives to improve the robustness and accuracy of the guidance system. Finite‐time stability for the closed‐loop guidance system is analyzed using the Lyapunov function. Simulation results and comparisons are presented to illustrate the effectiveness of the guidance strategy.     

Adaptive disturbance observer‐based finite‐time continuous fault‐tolerant control for reentry RLV

The control effectors of reusable launch vehicle (RLV) can produce significant perturbations and faults in reentry phase. Such a challenge imposes tight requirements to enhance the robustness of vehicle autopilot. Focusing on this problem, a novel finite‐time fault‐tolerant control strategy is proposed for reentry RLV in this paper. The key of this strategy is to design an adaptive‐gain multivariable finite‐time disturbance observer (FDO) to estimate the synthetical perturbation with unknown bounds, which is composed of model uncertainty, external disturbance, and actuator fault considered as the partial loss of actuator effectiveness in this work. Then, combined with the finite‐time high‐order observer and differentiator, a continuous homogeneous second‐order sliding mode controller based on the terminal sliding mode and super‐twisting algorithm is designed to achieve a fast and accurate RLV attitude tracking with chattering attenuation. The main features of the integrated control strategy are that the adaptation algorithm of FDO can achieve non‐overestimating values of the observer gains and the second‐order super‐twisting sliding mode approach can obtain a more elegant solution in finite time. Finally, simulation results of classical RLV (X‐33) are provided to verify the effectiveness and robustness of the proposed fault‐tolerant controller in tracking the guidance commands. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed method.     

Composite Nonlinear Bilateral Control for Teleoperation Systems With External Disturbances

This paper presents a new composite nonlinear bilateral control method based on the nonlinear disturbance observer (NDOB) for teleoperation systems with external disturbances. By introducing the estimations of NDOB and systems' nominal nonlinear dynamics into controller design, a NDOB based composite nonlinear bilateral controller is constructed to attenuate the influence of disturbance and uncertain nonlinearities. As compared with the existing bilateral control methods which usually achieve force haptic (i.e., contact force tracking) through a passive way, the newly proposed method has two major merits: 1) asymptotical convergence of both position and force tracking errors is guaranteed; 2) disturbance influence on force tracking error dynamics is rejected through the direct feedforward compensation of disturbance estimation. Simulations on a nonlinear teleoperation system are carried out and the results validate the effectiveness of the proposed controller.      

Distributed finite‐time formation control for multiple quadrotors via local communications

This paper investigates finite‐time formation tracking control problem for multiple quadrotors with external disturbance. The states of the virtual leader are not available to all the followers and the network topology is described by a directed graph. The model of each quadrotor is divided into position subsystem and attitude subsystem. Firstly, novel distributed finite‐time state observers are designed to estimate the relative state errors between followers and the virtual leader. Secondly, the values of these observers are used to design controllers that achieve finite‐time robust coordinated tracking in the position subsystem. Thirdly, the terminal sliding mode disturbance observers and finite‐time attitude tracking controllers are proposed, respectively, in the attitude subsystem to estimate the external disturbance and achieve attitude tracking control. The finite‐time stability analysis of the control algorithms is carried out using the Lyapunov theory and the homogeneous technique. Finally, the efficiency of the proposed algorithm is illustrated by numerical simulations.     

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.     

Trajectory tracking control for manned submersible system with disturbances via disturbance characterization index approach

This paper investigates a novel disturbance estimation and characterization‐based robust control scheme of the manned submersible in the presence of external disturbances and model uncertainties. First of all, a finite‐time disturbance observer is designed to estimate the lumped disturbances of the manned submersible system. Then, a novel disturbance characterization index is defined via Lyapunov theory to indicate whether the lumped disturbances harm or benefit the manned submersible system. The control law is developed via the disturbance characterization–based backstepping control (DCB‐BC) method to remove the detrimental disturbances and to keep the beneficial disturbances of the manned submersible. Additionally, the rigorous stability analysis is given based on Lyapunov theory. Furthermore, some simulation results verify the effectiveness of the proposed DCB‐BC method. The key novelty of this paper is that the disturbances are explicitly used in the controller design to achieve better control performance and disturbance rejection capability.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling of Maglev Yaw System of Wind Turbines and its Robust Trajectory Tracking Control in the Levitating and Landing Process Based on Ndob

The yaw system is one of the important parts of the horizontal axis wind turbines. In this paper, a novel maglev yaw system (MYS) is introduced, a novel robust controller based on nonlinear disturbance observer (NDOB) is proposed to improve the dynamic suspension stability of the MYS in its levitating and landing process. First, the dynamic model of the MYS is built and analyzed as well as the model of the force caused by crosswind exerting on the MYS, and then the mathematical model of the MYS is derived from its dynamic model. Second, since the uncertain internal disturbance originated from the MYS itself exists, in order to realize the finite time convergence and improve the robustness of the MYS, a NDOB‐based robust controller is designed via like nonsingular terminal sliding mode (LNTSM) method with the aid of backstepping design idea (BDI) to guarantee that the system output asymptotically tracks the reference trajectory, and the levitating and landing velocities of the MYS converge to their expectations globally and asymptotically in finite time. Finally, compared the conventional backstepping control (BC), the extensive simulation results show that the proposed robust controller has a better robustness and the MYS can realize smooth and reliable operations in its levitating and landing process in finite time, therefore the novel robust controller is substantiated to be effective and feasible.     

Robust output feedback tracking control for a class of perturbed systems using NDOB and nonlinear continuous predictive control

This paper presents a new robust output feedback tracking control scheme for a class of higher-order uncertain systems. Since traditional nonlinear continuous predictive control requires accurate system model as well as full system states to synthesize a controller, a composite control methodology is adopted in the proposed scheme. Specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty and the unmeasured system states in an integrated manner while the nonlinear continuous predictive control regulates the system states to track the desired reference signal asymptotically. Detailed stability analysis is also presented for the closed-loop nonlinear observer-controller structure through two steps. Then, the obtained results are applied to missile autopilot design to track the desired angle-of-attack signal. Finally, numerical simulations with some comparisons are provided to demonstrate the effectiveness of the proposed formulation.     

Three‐dimensional impact angle‐constrained adaptive guidance law considering autopilot lag and input saturation

This work investigates three‐dimensional accurate guidance problem in the presence of impact angle constraint, input saturation, autopilot lag, and external disturbance, and presents a robust adaptive guidance method for maneuvering targets. More specifically, based on integral Lyapunov control algorithm, a robust guidance law, which can drive both terminal line‐of‐sight angle error and its rate to a small region around zero, while resisting the terrible influence caused by external disturbance, is proposed in this work. To deal with input saturation, guidance command is separated into two parts: real input and saturation error, and an adaptive control technique is employed to compensate the influence resulting from external disturbance and saturation error. Moreover, regarding autopilot lag as a first‐order dynamics, a backstepping designed controller with an adaptive term is proposed. Numerical simulations are carried out and their results demonstrate the proposed properties.     

Event‐Triggered Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance

This paper addresses the consensus problem of nonlinear multi‐agent systems with unknown external disturbance. First, a distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously. Then, a novel event‐triggered control scheme based on the agent state estimation and disturbance estimation is proposed. Unlike the existing strategies, our event‐triggered conditions depend on agent state estimation and disturbance estimation, which are more effective and practical. Under this observer and control strategy, some sufficient conditions are derived to ensure the consensus of the multi‐agent system with unknown external disturbance. Moreover, the Zeno‐behavior of triggering time sequences is also excluded. Finally, a simulation example is given to verify the theoretical analysis.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

无人驾驶飞行器姿态的非线性扰动抑制控制

本文研究了无人驾驶飞行器(unmanned aerial vehicle,UAV)的姿态跟踪控制问题.针对在飞行器姿态跟踪时存在的系统模型不确定性和外界扰动,提出了一种基于四元数的姿态跟踪控制方法,基于UAV的姿态误差模型分别设计系统的观测器和控制器.首先,以四元数为姿态参数建立系统的非线性误差模型;在此基础之上,设计一种非线性干扰观测器(nonlinear disturbance observer,NDOB)用以在线估计误差模型中的复合扰动,并在控制输入端进行相应的补偿.然后通过设计非线性广义预测控制律设镇定误差系统,实现姿态跟踪.最后基于频域理论分析了非线性干扰观测器的扰动抑制性能.仿真与实验结果表明本文提出的方法在系统存在复合扰动的情况下能使系统姿态有效的跟踪期望值.     

Adaptive‐gain multivariable super‐twisting sliding mode control for reentry RLV with torque perturbation

Reusable launch vehicle (RLV) should be under control in the presence of model uncertainty and external disturbance, which is considered as torque perturbation in this paper during the reentry phase. Such a challenge imposes tight requirements to the enhanced robustness and accuracy of the vehicle autopilot. The key of this paper is to propose an adaptive‐gain multivariable super‐twisting sliding mode controller when considering that the bounds of uncertainty and perturbation are not known. The important features of the controller are that the adaptation algorithm can achieve non‐overestimating values of the control gains and the multivariable super‐twisting sliding mode approach can obtain a more elegant solution in finite time. According to the multiple‐time scale features, the dynamics of RLV attitude motion are divided into outer‐loop subsystem and inner‐loop subsystem. On this basis, the controllers are designed respectively to ensure the finite‐time reentry attitude tracking. In addition, a proof of the finite‐time convergence for the overall system is derived using the Lyapunov function technique and multiple‐time scale characteristic. Finally, simulation results of six degree‐of‐freedom RLV are provided to verify the effectiveness and robustness of the proposed controller in tracking the guidance commands as well as achieving a safe and stable reentry flight. Copyright © 2016 John Wiley & Sons, Ltd.     

Boundary control of an axially moving accelerated/decelerated belt system

In this paper, a boundary controller with disturbance observer is proposed for the vibration suppression of an axially moving belt system. The model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations with consideration of the high‐acceleration/deceleration and unknown spatiotemporally varying distributed disturbance. Applying the finite‐dimensional backstepping control and Lyapunov's direct method, a boundary controller is developed to stabilize the belt system at the small neighborhood of its equilibrium position and a disturbance observer is introduced to attenuate the effect of unknown external disturbance. The S‐curve acceleration/deceleration method is adopted to plan the speed of the belt. With the proposed control scheme, the spillover instability problems are avoided, the uniform boundedness and the stability of the closed‐loop belt system can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Active Disturbance Rejection Control of a Magnetic Suspension System

This paper proposes a novel output feedback control scheme for robust stabilization and tracking tasks in a magnetic suspension system. Active disturbance rejection control, differential flatness and on‐line asymptotic disturbance estimation are properly used for the proposed control synthesis. The controlled system is subjected to a wide spectrum of unknown significant matched and unmatched disturbances due to external forces and voltages, parametric uncertainties, control and state‐dependent perturbations and possibly input unmodeled dynamics. The effectiveness and robustness of the proposed active disturbance control scheme is verified by computer simulations for the robust tracking of a rest‐to‐rest reference position trajectory specified to firstly stabilize the suspended mass at a desired vertical position and next transfer it to another equilibrium position for both continuous and switched control voltage signals.     

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

In this paper, an efficient finite difference method is presented for the solution of time‐delay optimal control problems with time‐varying delay in the state. By using the Pontryagin's maximum principle, the original time‐delay optimal control problem is first transformed into a system of coupled two‐point boundary value problems involving both delay and advance terms. Then the derived system is converted into a system of linear algebraic equations by using a second‐order finite difference formula and a Hermite interpolation polynomial for the first‐order derivatives and delay terms, respectively. The convergence analysis of the proposed approach is provided. The new scheme is also successful for the optimal control of time‐delay systems affected by external persistent disturbances. Numerical examples are included to demonstrate the validity and applicability of the new technique. Some comparative results are included to illustrate the effectiveness of the proposed method.