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.     

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.     

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.     

Distance‐based undirected formations of single‐integrator and double‐integrator modeled agents in n‐dimensional space

We study the local asymptotic stability of undirected formations of single‐integrator and double‐integrator modeled agents based on interagent distance control. First, we show that n‐dimensional undirected formations of single‐integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double‐integrator modeled agents in n‐dimensional space is achieved under a gradient‐like control law. Simulation results support the validity of the stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Finite‐time distributed control with time transformation

In this article, we propose distributed control algorithms for first‐ and second‐order multiagent systems for addressing finite‐time control problem with a priori given, user‐defined finite‐time convergence guarantees. The proposed control frameworks are predicated on a recently developed time transformation approach. Specifically, our contribution is twofold: First, a generalized time transformation function is proposed that converts the user‐defined finite‐time interval to a stretched infinite‐time interval, where one can design a distributed control algorithm on this stretched interval and then transform it back to the original finite‐time interval for achieving a given multiagent system objective. Second, for a specific time transformation function, we analytically establish the robustness properties of the resulting finite‐time distributed control algorithms against vanishing and nonvanishing system uncertainties. By contrast to existing finite‐time approaches, it is shown that the proposed algorithms can preserve a priori given, user‐defined finite‐time convergence regardless of the initial conditions of the multiagent system, the graph topology, and without requiring a knowledge of the upper bounds of the considered class of system uncertainties. Illustrative numerical examples are included to further demonstrate the efficacy of the presented results.     

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.     

Leader–follower flocking based on distributed event‐triggered hybrid control

In this paper, we proposed a new hybrid control algorithm to achieve leader–follower flocking in multi‐agent systems. In the algorithm, the position is transmitted continuously, whereas the velocity is utilized discretely, which is governed by a distributed event‐triggered mechanism, and the neighbors' velocity is not required to detect the event‐triggered condition for each agent. It is shown that stable flocking is achieved asymptotically while the connectivity of networks is preserved. A numerical example is provided to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

Distributed robust finite‐time attitude containment control for multiple rigid bodies with uncertainties

This paper investigates the distributed robust finite‐time attitude containment control for multiple rigid bodies with uncertainties including parametric uncertainties, external disturbances, and actuator failures. Two novel types of distributed control laws are designed corresponding to two different cases, respectively, and both of them can drive the orientations of the followers into the convex hull formed by the orientations of leaders in a finite time. Simulation results show the effectiveness of the proposed design. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

This paper investigates the finite‐time robust simultaneous stabilization problem of a set of nonlinear time‐delay systems with general forms and proposes some new simultaneous stabilization results. First, by developing an equivalent form and applying augmented technique, this paper obtains an augmented equivalent form of the original systems. Secondly, based on the equivalent form, we study finite‐time simultaneous stabilization problem and present some new stabilization results by constructing some suitable Lyapunov functionals. Thirdly, using the simultaneous stabilization results obtained, this paper investigates the finite‐time robust simultaneous stabilization problem for the set systems and proposes a delay‐dependent robust simultaneous stabilization result. Finally, the study of an illustrative example shows that the results obtained by this paper work well in the finite‐time robust simultaneous stabilization the set systems. It is shown that, by using the method in this paper, the developed conditions do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden in studying nonlinear time‐delay systems.     

Finite‐time sliding mode stabilization using dirty differentiation and disturbance compensation

Novel robust finite‐time stabilizing algorithms are developed side by side for the state and output feedback designs. Being initially developed for a nonlinear cascade second‐order system, these algorithms are straightforwardly extendible to electromechanical systems of relative degree two. The proposed synthesis is based on the disturbance compensation, relying on the dirty differentiation and sliding mode approach, and it is applicable to a wider class of disturbances than that addressed in the literature. Simulation results illustrate the efficiency of the resulting synthesis procedure and support analytical results.     

Event‐triggered control via impulses for exponential stabilization of discrete‐time delayed systems and networks

This paper investigates the stabilization issue via event‐triggered controls (ETCs) for discrete‐time delayed systems (DDSs) and networks. Based on the recently proposed ETC scheme for discrete‐time systems without time delays, improved ETC (I‐ETC) and event‐triggered impulsive control (ETIC) are proposed for DDS. The algorithms for ETC, I‐ETC, and ETIC are given respectively to derive criteria of exponential stabilization of DDS. Moreover, the exponential stabilization and stabilization to ISS for discrete‐time delayed networks is achieved by employing the algorithms of ETC and ETIC. The issue of stabilization via ETCs for dynamical networks where different subsystems have different sequences of event instants is solved by introducing the check‐period into ETCs and establishing general ISS estimate of discrete‐time delayed inequality. In order to assess the performances of the control schemes, discussions on nontriviality are given by proposing the concept of rate of control and the function of control cost. Finally, two examples with numerical simulations are presented to demonstrate the effectiveness of theoretical results. From the obtained results on stabilization and the simulations, the ETIC is shown to have clear advantages and well performances than the classical state feedback control, the ETC recently proposed, I‐ETC, and the time‐based impulsive control on aspects of nontriviality, lower rate of control, lower cost of control, and robustness w.r.t. external disturbances.     

Observer‐based finite‐time stabilization for extended Markov jump systems

In this paper, we study the problem of observer‐based finite‐time stabilization for a class of extended Markov jump systems with norm‐bounded uncertainties and external disturbances. The stochastic character under consideration is governed by a finite‐state Markov process, but with only partial information on the transition jump rates. Based on the finite‐time stability analysis, sufficient conditions for the existence of the observer‐based controller are derived via a linear matrix inequality approach such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval. When these conditions are satisfied, the designed observer‐based controller gain matrices can be obtained by solving a convex optimization problem. Simulation results demonstrate the effectiveness of the approaches proposed in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Time‐varying feedback for stabilization in prescribed finite time

This paper provides a time‐varying feedback alternative to control of finite‐time systems, which is referred to as “prescribed‐time control,” exhibiting several superior features: (i) such time‐varying gain–based prescribed‐time control is built upon regular state feedback rather than fractional‐power state feedback, thus resulting in smooth (C^m) control action everywhere during the entire operation of the system; (ii) the prescribed‐time control is characterized with uniformly prespecifiable convergence time that can be preassigned as needed within the physically allowable range, making it literally different from not only the traditional finite‐time control (where the finite settling time is determined by a system initial condition and a number of design parameters) but also the fixed‐time control (where the settling time is subject to certain constraints and thus can only be specified within the corresponding range); and (iii) the prescribed‐time control relies only on regular Lyapunov differential inequality instead of fractional Lyapunov differential inequality for stability analysis and thus avoids the difficulty in controller design and stability analysis encountered in the traditional finite‐time control for high‐order systems.     

基于super-twisting算法的多航天器姿态有限时间分布式协同控制

针对受外界干扰和执行器故障影响的多航天器姿态协同控制问题,本文设计了一种基于干扰观测器的分布式协同supper-twisting滑模控制器.首先,将各航天器的外界干扰和执行器故障看作一个集总干扰,设计自适应滑模干扰观测器对其进行估计.其次,将supper-twisting算法和积分滑模面相结合,设计一种基于多航天器姿态...     

Almost global finite‐time stabilization of rigid body attitude dynamics using rotation matrices

This work considers continuous finite‐time stabilization of rigid body attitude dynamics using a coordinate‐free representation of attitude on the Lie group of rigid body rotations in three dimensions, SO(3). Using a Hölder continuous Morse–Lyapunov function, a finite‐time feedback stabilization scheme for rigid body attitude motion to a desired attitude with continuous state feedback is obtained. Attitude feedback control with finite‐time convergence has been considered in the past using the unit quaternion representation. However, it is known that the unit quaternion representation of attitude is ambiguous, with two antipodal unit quaternions representing a single rigid body attitude. Continuous feedback control using unit quaternions may therefore lead to the unstable unwinding phenomenon if this ambiguity is not resolved in the control design, and this has adverse effects on actuators, settling time, and control effort expended. The feedback control law designed here leads to almost global finite‐time stabilization of the attitude motion of a rigid body with Hölder continuous feedback to the desired attitude. As a result, this control scheme avoids chattering in the presence of measurement noise, does not excite unmodeled high‐frequency structural dynamics, and can be implemented with actuators that can only provide continuous control inputs. Numerical simulation results for a spacecraft in low Earth orbit, obtained using a Lie group variational integrator, confirm the theoretically obtained stability and robustness properties of this attitude feedback stabilization scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

随机系统输出概率密度函数的有限时间镇定

针对一类含有限能量未知扰动的随机动态系统,研究基于随机分布函数的有限时间控制问题.通过B样条逼近建立了输出概率密度函数(PDF)与权值之间的对应关系,利用线性矩阵不等式,给出了基于观测器的PDF有限时间控制器的参数化设计方法.采用该方法设计的控制器,可使系统对所有满足条件的未知扰动是随机有限时间有界和随机有限时间镇定的.仿真实例验证了所提出方法的有效性.     

A dual‐observer design for global output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

This paper employs a dual‐observer design to solve the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are bounded by both low‐order and high‐order terms. We show that the dual‐observer comprised of two individual homogeneous observers, can be implemented together to estimate low‐order and high‐order states in parallel. The proposed dual observer, together with a state feedback controller, which has both low‐order and high‐order terms, will lead to a new result combining and generalizing two recent results (Li J, Qian C. Proceedings of the 2005 IEEE Conference on Decision and Control, 2005; 2652–2657) and (Qian C. Proceedings of the 2005 American Control Conference, June 2005; 4708–4715). Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.