Global finite-time attitude consensus tracking control for a group of rigid spacecraft

The problem of finite-time attitude consensus for multiple rigid spacecraft with a leader–follower architecture is investigated in this paper. To achieve the finite-time attitude consensus, at the first step, a distributed finite-time convergent observer is proposed for each follower to estimate the leader's attitude in a finite time. Then based on the terminal sliding mode control method, a new finite-time attitude tracking controller is designed such that the leader's attitude can be tracked in a finite time. Finally, a finite-time observer-based distributed control strategy is proposed. It is shown that the attitude consensus can be achieved in a finite time under the proposed controller. Simulation results are given to show the effectiveness of the proposed method.     

Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data

This paper addresses the distributed observer‐based consensus problem of second‐order multi‐agent systems via sampled data. Firstly, for the case of fixed topology, a velocity‐independent distributed control law is proposed by designing a distributed observer to estimate the unavailable velocity, then a sufficient and necessary condition of consensus on design parameters and sampling period is obtained by using the matrix analysis method. Secondly, for the case of stochastically switching topology, a sufficient and necessary condition of mean square consensus is also proposed and proven, and an algorithm is provided to design the parameters in the consensus protocol. Two simulation examples are given to illustrate the effectiveness of the proposed consensus algorithms. Copyright © 2012 John Wiley & Sons, Ltd.     

Leader‐following attitude consensus of multiple uncertain spacecraft systems subject to external disturbance

The attitude consensus problem of multiple rigid spacecraft systems is one of the key issues in spacecraft formation flying and has been extensively studied. In this paper, we further consider the leader‐following attitude consensus problem of multiple rigid uncertain spacecraft systems subject to a class of multi‐tone sinusoidal disturbances with arbitrarily unknown amplitudes, initial phases, frequencies, and constant biases. In contrast to the existing results, in order to achieve asymptotic reference tracking and disturbance rejection by smooth control, we have integrated the distributed observer approach with internal model and adaptive control techniques. Simulation results are shown to validate the effectiveness of the proposed control law. Copyright © 2016 John Wiley & Sons, Ltd.     

A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach

This paper addresses the specified‐time control problem for control‐affine systems and rigid bodies, wherein the specified‐time duration can be designed in advance according to the task requirements. By using the time‐rescaling approach, a novel framework to solve the specified‐time control problem is proposed, and the original systems are converted to the transformation systems based on which the specified‐time control laws for both control‐affine systems and rigid bodies are studied. Compared with the existing approaches, our proposed specified‐time control laws can be derived from the known stabilization control laws. To our best knowledge, it is the first time that transformation system–based specified‐time control framework for control‐affine system and rigid body dynamics is proposed. To further improve the convergence performance of specified‐time control, a finite‐time attitude synchronization control law for rigid bodies on rotation matrices is proposed, and thereby, the finite‐time–based specified‐time control law is designed eventually. In the end, numerical simulations and SimMechanics experiments are provided to illustrate effectiveness of the theoretical results.     

The leader-following attitude control of multiple rigid spacecraft systems

In this paper, we consider the leader-following consensus problem for a multiple rigid spacecraft system whose attitude is represented by the unit quaternion. Most results on this problem rely on the assumption that every follower can access the state of the leader and are obtained via a decentralized control manner. By developing a nonlinear distributed observer for the leader system, we can solve this problem via a distributed control scheme under the mild assumptions that the state of the leader can reach every follower through a path and that the communication between followers is bidirectional. Moreover, our result can accommodate a class of desired angular velocities generated by a marginally stable linear autonomous system.     

Fault‐tolerant spacecraft attitude control under actuator saturation and without angular velocity

In this paper, a fault‐tolerant control scheme is proposed to control the attitude of a rigid spacecraft subject to external disturbances and multiple system uncertainties, as well as actuator faults and saturation. More challengingly, it is assumed that the angular velocity is unavailable. A super‐twisting observer with time‐varying gain is firstly designed to accurately estimate the angular velocity in finite time. The choice of the time‐varying gain is dependent on a state‐norm estimate. Then, using the information from the observer (estimate of angular velocity), a fault‐tolerant controller is proposed, where an adaptive law is introduced to address the unknown loss of effectiveness and neural networks are used to approximate the unknown nonlinear functions. It is proved that the attitude orientations converge to the desired values at a fixed time. Finally, a simulation example is utilized to verify the effectiveness of the proposed scheme.     

Distributed fixed‐time attitude coordination control for multiple rigid spacecraft

In this paper, the fixed‐time attitude coordination control for multiple rigid spacecraft under an undirected communication graph is investigated. By using the backstepping technique, the distributed fixed‐time observer, and the method of “adding a power integrator,” a distributed fixed‐time attitude coordination control law is designed for a group of spacecraft. The proposed control scheme is nonsingular and can guarantee a group of rigid spacecraft simultaneously tracking a common desired attitude within fixed time even when the time‐varying reference attitude is available only to a subset of the group members. Rigorous analysis is provided to show that the attitude consensus tracking errors can converge to 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.     

Optimal Output Feedback Controllers for Spacecraft Attitude Tracking

This paper investigates the problem of output feedback attitude tracking control of a rigid spacecraft in the presence of external disturbances. Two optimal control laws with a disturbance estimator are developed to deal with this problem. An adapted extended state observer is used to estimate the angular velocity tracking errors and to allow for compensation for the total disturbances. The proposed control can be expressed as the sum of a nonlinear optimal controller and an estimated disturbance. For the optimal controller, the state‐dependent Riccati equation and optimal Lyapunov techniques are employed to solve the infinite‐time nonlinear optimal control problem. The developed controllers can minimize a performance index and ensure the stability of the closed‐loop system and external disturbance attenuation. On the other hand, using the adapted extended state observer, the asymptotic convergence of estimation error dynamics is proven. An example of multiaxial attitude manoeuvres is given and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.     

Velocity‐free attitude stabilization with inertial vector measurements

This paper deals with the attitude stabilization problem of a rigid body, where neither the angular velocity nor the attitude is used in the feedback; only body‐referenced vector measurements are needed. The proposed control scheme is based on an angular velocity observer‐like system relying solely on vector measurements. The proposed controller ensures almost global asymptotic stability and provides some interesting performance properties through an appropriate tuning of the control gains. The performance and effectiveness of the proposed control scheme are illustrated via simulation results where the control gains are adjusted using a nonlinear optimization. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust State‐and‐Disturbance Observer Design for Linear Non‐minimum‐phase Systems

When there are external disturbances acting on the system, the conventional Luenberger observer design for state estimation usually results in a biased state estimate. This paper presents a robust state and disturbance observer design that gives both accurate state and disturbance estimates in the face of large disturbances. The proposed robust observer is structurally different from the conventional one in the sense that a disturbance estimation term is included in the observer equation. With this disturbance estimation term, the robust observer design problem is skillfully transformed into a disturbance rejection control problem. We then can utilize the standard H_∞ control design tools to optimize the robust observer between the disturbance rejection ability and noise immune ability. An important advantage of the proposed robust observer is that it applies to both minimum‐phase systems and non‐minimum phase systems.     

Distributed attitude and translation consensus for networked rigid bodies based on unit dual quaternion

This paper provides unified solutions for distributed attitude and translation consensus problems for networked fully actuated rigid bodies under the fixed and undirected communication topology with the tool of unit dual quaternion. We investigate two kinds of consensus, that is, leaderless consensus and leader‐following consensus with a static leader. Firstly, the dynamics of rigid bodies are presented by unit dual quaternion. The control inputs of rigid bodies are also obtained from unit dual quaternion. Secondly, we propose a distributed consensus law in the form of dual quaternion to guarantee that the attitudes and translations of all rigid bodies reach consensus, respectively, without a leader. Thirdly, the leader‐following consensus problem with a static leader is studied. With the proposed leader‐following consensus law, the states of all rigid bodies converge to the corresponding states of the static leader, including the attitude and the translation. Finally, numerical examples are provided to validate the effectiveness of the theoretical results. Copyright © 2017 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.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.     

Heterogeneous consensus of higher‐order multi‐agent systems with mismatched uncertainties using sliding mode control

A robust consensus controller is proposed for heterogeneous higher‐order nonlinear multi‐agent systems, when the agent dynamics are involved with mismatched uncertainties. A distributed consensus protocol based on a time‐varying nonhomogeneous finite‐time disturbance observer and sliding mode control is designed to realize the network consensus of higher‐order multi‐agent systems. The time‐varying finite‐time disturbance observer overcomes the problem of peaking value near the initial time caused by the constant gain one and is designed to estimate the uncertainties and to mitigate the effect of mismatched uncertainties during the sliding mode. To eliminate the chattering phenomenon and ensure finite‐time convergence to the sliding surface, the control law is designed by using the super twisting algorithm. Finally numerical simulations are given to illustrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking

This paper studies finite-time attitude tracking control problem of a rigid spacecraft system with external disturbances and inertia uncertainties. Firstly, a new finite-time attitude tracking control law is designed using nonsingular terminal sliding mode concepts. In the absence and presence of external disturbances and inertia uncertainties, this controller can drive the attitude and angular velocity tracking errors to reach zero in finite time. Secondly, a finite-time disturbance observer is introduced to estimate the disturbance, and a composite controller is developed which consists of a feedback control based on nonsingular terminal sliding mode method and compensation term based on finite-time disturbance observer. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system is ensured by the Lyapunov approach. Numerical simulations on attitude control of spacecraft are also given to demonstrate the performance of the proposed controllers.     

Practical time‐varying formation tracking for high‐order nonlinear multiagent systems with multiple leaders based on the distributed disturbance observer

Practical time‐varying formation tracking analysis and design problems for high‐order nonlinear multiagent systems with directed interaction topologies are investigated by using the distributed disturbance observer, where the time‐varying formation tracking error can be controlled within an arbitrarily small bound. Different from the previous work, there exists a predefined time‐varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the leaders can be multiple, and the dynamics of each follower has heterogeneous nonlinearity and disturbance. First, a distributed disturbance observer‐based practical time‐varying formation tracking protocol is constructed using neighboring relative information, where only a part of the followers, which are named as well‐informed ones, are required to obtain the information of the multiple leaders. The proposed protocol can process the heterogeneous nonlinearity, the disturbance of each follower, and the unknown control inputs of the leaders simultaneously. Then, an algorithm with 2 steps is presented to design the practical time‐varying formation tracking protocol by solving an algebraic Riccati equation and an algebraic equation, where the time‐varying formation tracking feasibility condition is introduced. Moreover, the stability of the closed‐loop multiagent system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, a numerical simulation example is provided to illustrate the effectiveness of the obtained theoretical results.     

采用滑模观测器的六旋翼指令滤波鲁棒控制

针对包含复合干扰的六旋翼无人机鲁棒控制问题,提出了一种基于滑模观测器的指令滤波鲁棒控制方法。建立了包含复合干扰的六旋翼无人机位置和姿态的数学模型,并对位置回路设计了滑模控制律,从而解算出姿态指令;根据姿态角回路输出的虚拟控制律,设计了指令滤波器来抑制微分爆炸现象,并利用辅助滤波器补偿指令滤波的误差;在角速度回路鲁棒控制律中引入滑模观测器,对包括模型误差和外界扰动的复合干扰进行补偿,实现了六旋翼UAV的指令滤波鲁棒控制。仿真结果表明：提出的指令滤波鲁棒控制律与指令滤波自适应控制方法相比,在复合干扰下具有更优的稳定性、准确性和快速性,位置和姿态的最大误差分别仅为0.05?m和0.5°,滑模观测器的估计误差也仅为0.2 （°）/s,能够在更短的时间内实现对六旋翼UAV位移和姿态的鲁棒控制。     

Distributed adaptive formation tracking for heterogeneous multiagent systems with multiple nonidentical leaders and without well‐informed follower

This paper studies the time‐varying output formation tracking (OFT) problems for linear heterogeneous multiagent systems with multiple leaders, where both the followers and the leaders can have nonidentical dynamics and dimensions. The existing results on formation tracking with multiple leaders depend on the assumption that each follower is well‐informed or uninformed, where the well‐informed follower has all the leaders as its neighbor. To remove this assumption, a novel OFT approach is presented using a distributed observer scheme. Firstly, based on the local estimation and the interaction with neighboring followers, a fully distributed observer is designed for each follower to estimate the dynamical matrices and the states of multiple leaders without requiring the well‐informed follower assumption. The convergence of the distributed observer is proved by using Lyapunov theory. Then, an adaptive algorithm is proposed to solve the regulator equations in finite time based on the estimation of the leaders' dynamical matrices. Furthermore, the desired time‐varying output formation of each follower is generated by a local active exosystem. A time‐varying OFT protocol is presented using the estimated states of multiple leaders, the online solutions of the regulator equations, and the desired formation vector generated by the local exosystem. It is proved that the outputs of the followers can not only realize the expected formation shape but also track the predefined convex combination of multiple leaders. Finally, a simulation example is given to verify the theoretical results.     

Leader–follower consensus of linear multi-agent systems with unknown external disturbances

This paper addresses the leader–follower consensus tracking problem for multi-agent systems with identical general linear dynamics and unknown external disturbances. First, a distributed extended state observer is proposed, where both the local states and disturbance of each agent are estimated simultaneously by using the relative output information between neighbors. Then a consensus algorithm is proposed for each agent based on the relative estimated states between neighbors and its own disturbance estimate. It is shown that, with the proposed observer-based consensus algorithm, the leader–follower consensus problem can be solved. Finally, we present a simulation example to demonstrate the effectiveness of the proposed algorithm.