Uniformly Observable and Globally Lipschitzian Nonlinear Systems Admit Global Finite-Time Observers

There exist semi-global and finite-time converging observers for nonlinear systems that are uniformly observable and globally Lipschitzian. This was achieved with local finite-time stability theory, together with application of the technique of high-gain observers (the gain is constant). Under the same conditions, it is shown that these systems admit global finite-time observers. The proposed finite-time observers are based on a modified version of high-gain observer (now the gain is an exponential function with arbitrary growth rate). Design procedures are worked out for such observers, and a numerical example is presented to show the effectiveness of the proposed method.      

An approach to design semi-global finite-time observers for a class of nonlinear systems

In this paper, the problem of designing semi-global finite-time observers for a class of nonlinear systems is investigated. Based on the theories of finite-time stability, an approach to designing semi-global finite-time observers for the nonlinear systems is presented. It has been shown that, after the finite time, the designed finite-time observer realizes the accurate reconstruction of the states of the nonlinear system. A numerical example is given to illustrate the effectiveness and validity of the met...     

Finite-time observers for multi-agent systems without velocity measurements and with input saturations

This paper is devoted to the distributed finite-time observers for multi-agent systems, where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback. An effective framework through defining a class of coordinated saturation functions is introduced, under which both a first-order finite-time observer and a high-order finite-time observer are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers. With mild modifications of our control strategies, the foregoing results are then extended to the distributed finite-time containment control problem, where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders. Numerical simulations are presented to demonstrate the efficiency of our methods.     

Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems

This paper considers the problem of designing globally finite-time convergent observers for a class of nonlinear systems with time-varying and output-dependent coefficients, which make the existing design approaches inapplicable. To solve this problem, a bottom-up design approach is first employed to recursively construct a finite-time convergent observer with time-varying coefficients for the nominal system. Then, using the homogeneous domination approach, we scale the finite-time convergent observer with an appropriate choice of gain for the original nonlinear system satisfying a Hölder condition. In addition, we show that the Hölder condition imposed on the nonlinearities can be removed for nonlinear systems with bounded trajectories.     

Robust finite-time containment control for high-order multi-agent systems with matched uncertainties under directed communication graphs

In this paper, we study the robust finite-time containment control problem for a class of high-order uncertain nonlinear multi-agent systems modelled as high-order integrator systems with bounded matched uncertainties. When relative state information between neighbouring agents is available, an observer-based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite-time containment control problem under general directed communication graphs. When only relative output information is available, robust exact differentiators and high-order sliding-mode controllers are employed together with the distributed finite-time observers. It is shown that robust finite-time containment control can still be achieved in this situation. An application in the coordination of multiple non-holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies.     

Smooth sliding-mode observers for specific growth rate and substrate from biomass measurement

This paper addresses the estimation of specific growth rate and substrate concentration from biomass measurements in fermentation processes. Specifically, sliding-mode observers are proposed, for which finite-time global convergence is demonstrated using Lyapunov stability theory and concepts of variable structure systems. Two observers are developed for specific growth rate estimation, one producing a discontinuous estimation which is used afterwards for substrate estimation, and the other one – based on high-gain observers – that generates a smooth estimation with first-order dynamics and finite-time bounded convergence error. In the case of substrate estimation, an observer that increases the convergence rate to a vicinity of the real substrate concentration while achieving asymptotic convergence despite kinetic model uncertainties in properly excited processes is designed. This observer also exhibits first-order dynamics.     

Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics

In this paper, we discuss the finite-time consensus problem for leaderless and leader–follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader–follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. Rigorous proof is given by using Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.     

Finite-time estimation for linear time-delay systems via homogeneous method

This paper presents a finite-time observer for linear time-delay systems with commensurate delay. Unlike the existing observers in the literature which converge asymptotically, the proposed observer provides a finite-time estimation. This is realised by using the well-known homogeneous technique, and the results are also extended to investigate the estimation problem for linear time-delay systems with unknown inputs. Simulation results are presented in order to illustrate the feasibility of the proposed method.     

多智能体系统的有限时间旋转环绕控制

本文主要研究了多智能体系统的分布式有限时间旋转环绕控制问题，其中每个智能体跟踪一个目标且每个目标被一个智能体跟踪.首先，设计了有限时间环绕跟踪协议，该协议包含对所有目标几何中心的观测器以及目标与其几何中心最大距离的估计器.其次，给出了闭环系统实现有限时间环绕跟踪的充分条件.最后，通过仿真验证了所得结果的有效性.     

Global finite-time control for a class of switched nonlinear systems with different powers via output feedback

This paper is concerned with the problem of global finite-time control for switched nonlinear systems whose nonlinear terms satisfy homogenous growth conditions. At first, we design homogenous output feedback controllers for nominal switched nonlinear systems by adding a power integrator method. Then, we employ the homogeneous domination approach to scale homogeneous observers and controllers to render switched nonlinear systems with lower-triangular homogenous growth condition globally finite-time stable. Finally, the proposed control method can be extended to switched nonlinear systems satisfying with upper-triangular homogeneous growth condition. Two examples are provided to demonstrate the effectiveness of the proposed control scheme.     

带有不匹配干扰的二阶多自主体系统有限时间包容控制

针对多自主体系统群集运动问题,本文研究了带有不匹配干扰的二阶系统有限时间包容控制.运用现代控制理论,设计了非线性观测器,对系统未知状态和干扰进行估计.在状态估计的基础上,构建了基于干扰观测器的多自主体系统的协同控制算法.应用代数图论和齐次性理论等方法,分析了二阶多自主体系统有限时间包容控制.数据仿真中应用基于观测器的包容控制算法,使得系统的运动状态最终都收敛到由多个领导者所围成的目标区域中,验证了本文结果的有效性.     

Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.     

Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers

The distributed consensus output tracking problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances and uncertain nonlinear virtual control coefficients of the subsystems. The systems are under a directed communication graph, where the leader node is the root. The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid direct differentiation. At each step of virtual controller design, a prescribed performance controller is constructed to achieve prescribed transient performance so that the system states remain in the feasible domain. Then each virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the control system are analysed theoretically. It is clarified that the prescribed performance control technique ensures that the system signals stay in the feasible domain, whereas sufficiently small ultimate control errors can be achieved by the finite-time disturbance observers. Finally, the performance of the proposed methods is confirmed by numerical studies.     

Full-order observer design for linear systems with unknown inputs

In this article, a full-order observer without unknown inputs reconstruction is suggested in order to achieve finite-time reconstruction of the state vector for a class of linear systems with unknown inputs. The observer is a simple one, its derivation being direct and easy. It will be shown that the problem of full-order observers for linear systems with unknown inputs can be reduced in this case to a standard one (the unknown input vector will not interfere in the observer equations). The effectiveness of the suggested design algorithm is illustrated by a numerical example (aircraft longitudinal motion), and, for the same aircraft dynamics, we make a comparison between our new observer and other already existing observers from the existence conditions and dynamic characteristics’ point of view; the superiority of the new designed observer is demonstrated.     

线性描述系统有限时间函数观测器设计及存在性讨论

本文针对线性描述系统研究了其有限时间函数观测器的设计方法和存在条件.首先,通过构造两个结构上完全相同的渐近收敛观测器得到了一个新的有限时间函数观测器,它可以在任意给定的时间内达到对目标函数的精确估计,且估计精度和收敛时间不依赖于原系统的初始条件.随后,对该函数观测器的存在条件进行了详细讨论,给出了函数观测器存在的充分必...     

Finite-time control of mobile robot systems with unmeasurable angular and linear velocities via bioinspired neurodynamics approach

This paper addresses the stability analysis and adaptive robust finite-time bioinspired neurodynamics control for a class of mobile robot systems with unmeasurable angular and linear velocities, and time-varying bounded disturbance. The error system of the mobile robot is decomposed into two subsystems based on the system model. The state feedback control laws with observers are designed for the two subsystems, and the adaptive robust finite-time bioinspired neurodynamics controller (ARFBNC) is designed based on the state feedback control laws and two subsystems. The stability conditions in the form of linear matrix inequalities (LMIs) are derived by introducing the Lyapunov–Krasovskii functional. The unmeasurable angular and linear velocities, and time-varying bounded disturbance are estimated effectively by employing the state feedback control laws with observers. The smooth bounded outputs are obtained and the sharp jumps of initial values for the state variables are reduced. The closed-loop system is asymptotically stable and the state errors converge to an adjustable bounded region by introducing the Lyapunov–Krasovskii functional. The simulations are performed to show the effectiveness of the proposed methods.     

Command filter-based finite-time adaptive tracking control for MIMO dynamic systems with external disturbances and prescribed performance constraints

This paper investigates command filter-based finite-time stability of multi-input multi-output (MIMO) dynamic systems with prescribed performance constraints and external disturbances. A novel finite-time differentiator is introduced into command filter-based control scheme, which improves transient performance of each subsystem. Meanwhile, disturbance observers are utilized to eliminate negative effects on control system caused by external disturbances. Furthermore, featured with a selected performance function, it can be guaranteed that tracking errors remain in prescribed performance region. Stability analysis of the proposed controller is presented by using a Lyapunov function including transformed filter errors, parameter errors of neural networks, and observed errors of lumped disturbances. Effectiveness of proposed control method is verified by a numerical example and a practical system of inverted pendulums, respectively.     

Finite-time stabilization of output-constrained planar switched systems via output feedback

Finite-time stabilization (FTS) problem of output-constrained planar switched systems via output feedback is investigated in this paper. State feedback control laws are constructed in a systematic way by combining the revamped adding a power integrator technique (APIT) with the elaborately designed logarithm-type barrier Lyapunov function (BLF). By merging the constructed variable-gain switched observers, finite-time output-feedback stabilization, then, is achieved with the output constraint meets too. At the end, simulations are presented to show the effectiveness of the proposed method.     

Finite-time path following control for a stratospheric airship with input saturation and error constraint

This paper addresses the finite-time path following control problem for an under-actuated stratospheric airship with input saturation, error constraint, and external disturbances. To handle the adverse effect of input saturation, anti-windup compensators are employed and finite-time convergence of the saturated control solution is established. Error constraints of airship position and attitude are handled by incorporating a tan-type barrier Lyapunov function (TBLF) in guidance and attitude control schemes. Backstepping design is presented with the anti-windup compensators, the TBLF, and nonlinear disturbance observers which estimate the external disturbances. Stability analysis shows that the tracking errors of the airship position converge into a small set around zero within finite-time, the constrained requirements on the airship position and attitude are not violated during operation, and all closed-loop signals are guaranteed to be uniformly ultimately bounded. Compared with the conventional control scheme, simulation results illustrate that the proposed finite-time controller offers a faster convergence rate and a higher path following accuracy for the stratospheric airship.     

New finite-time stability conditions of linear switched singular systems with finite-time unstable subsystems

ABSTRACT

This paper addresses the finite-time stability problem of linear switched singular systems with finite-time unstable subsystems. Dynamic decomposition techniques are used to transform such systems into equivalent one that is a reduced-order switched normal systems. Based on the mode-dependent average dwell time (MDADT) switching signal, new sufficient conditions are presented to guarantee the linear switched singular systems with finite-time unstable subsystems being finite-time stability, finite-time bounded and finite-time stabilization. Finally, a numerical example is employed to verify the efficiency of the preceding method.