Semi-global finite-time observers for nonlinear systems

It is well known that high gain observers exist for single output nonlinear systems that are uniformly observable and globally Lipschitzian. Under the same conditions, we show that these systems admit semi-global and finite-time converging observers. This is achieved with a derivation of a new sufficient condition for local finite-time stability, in conjunction with applications of geometric homogeneity and Lyapunov theories.     

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.      

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.     

基于预设性能的非仿射非线性系统自适应有限时间控制

针对一类具有死区的非仿射非线性系统,将预设性能控制与有限时间控制相结合,提出一种具有预设性能的自适应有限时间跟踪控制方法.基于Backstepping技术、模糊逻辑系统及有限时间Lyapunov稳定理论,给出使系统半全局实际有限时间稳定(semi-globally practically finite-time stable,SGPFS)的充分条件和设计步骤.该控制策略不仅使系统的输出误差在有限时间内收敛到一个预先设定区域,同时保证其收敛速度、最大超调量和稳态误差均满足预先设定的性能要求.最后通过仿真示例验证了所提出设计方法的有效性.     

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.     

Adaptive Fuzzy Finite-time Dynamic Surface Control for High-order Nonlinear System with Output Constraints

This paper studies the problem of finite-time fuzzy adaptive dynamic surface control (DSC) design for a class of single-input and single-output (SISO) high-order nonlinear systems with output constraint. Fuzzy logic systems (FLSs) are utilized to identify the unknown smooth functions. By adopting Barrier Lyapunov function (BLF), the problem of output constrain is handled. Combining adding a power integrator and adaptive backstepping recursion design technique, a novel fuzzy adaptive finite-time DSC algorithm is proposed. Based on finite-time Lyapunov stable theory, the developed control algorithm means that all the signals of the closed-loop system are semi-global practical finite-time stable (SGPFS) and the tracking error converges to a small neighborhood of origin in finite time. In addition, the output does not violate the given constrain bound. Finally, both numerical and practical simulation examples are given to illustrate the effectiveness of the proposed control algorithm.

     

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.     

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

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.     

Semi-global observer for multi-output nonlinear systems

We present an explicit form of nonlinear observers for a class of multi-input multi-output systems. Observer construction for multi-output nonlinear systems is not a trivial extension of single output case, especially when the global error convergence is of interest. In this paper, we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself, and the overall system has a block triangular form for each subsystem. Hence, the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed. The construction is based on the saturation of some estimates, which is originated by Khalil and Esfandiari for the use of semi-global output feedback control.     

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.     

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.     

Observer with linear error dynamics for nonlinear multi-output systems

Based upon nonlinear state coordinate transformations and a condensed dual Brunovský form for multi-output systems, a method for designing nonlinear state observers with linear error dynamics is presented. Necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained.     

On fault-tolerant observers

The problem of designing asymptotic observers for multioutput systems with one unreliable output measurement is addressed. It is shown that observers designed on the basis of observability indexes are not fault tolerant, and an observer for linear systems which tolerates failures in one a priori known output is given. The results are extended to nonlinear systems with no inputs: it is pointed out that the proposed design procedure may enlarge the class of nonlinear systems for which a nonlinear observer can be obtained     

Finite-time tracking control for robot manipulators with actuator saturation

This paper addresses the finite-time tracking of robot manipulators in the presence of actuator saturation. The commonly-used proportional-derivative (PD) plus dynamics compensation (PD+) scheme is extended by replacing the linear errors in the PD+ scheme with saturated non-smooth but continuous exponential-like ones. Advantages of the proposed controller include semi-global finite-time tracking stability featuring faster transient and high-precision performances and the ability to ensure that actuator constraints are not violated. This is accomplished by selecting control gains a priori, removing the possibility of actuator failure due to excessive torque input levels. Lyapunov's direct method and finite-time stability are employed to prove semi-global finite-time tracking. Simulations performed on a three degree-of-freedom (DOF) manipulator are provided to illustrate the effectiveness and the improved performance of the formulated algorithm.     

一类非线性严格反馈系统基于干扰观测器的抗干扰控制

针对一类带有干扰的非线性严格反馈系统, 研究其抗干扰控制问题. 系统干扰满足不匹配条件, 代表一类部分信息已知的干扰. 通过设计非线性干扰观测器, 提出基于非线性干扰观测器和back-stepping 的抗干扰控制方法来补偿干扰, 该方法可以保证闭环系统所有信号是半全局最终一致有界的. 最后, 通过与现有方法的对比验证了所提出方法的正确性和有效性.

     

Output-feedback finite-time stabilization of disturbed feedback linearizable nonlinear systems

A novel methodology for designing multivariable High-Order Sliding-Mode (HOSM) controllers for disturbed feedback linearizable nonlinear systems is introduced. It provides for the finite-time stabilization of the origin of the state-space by using output feedback. Only the additional assumptions of algebraic strong observability and smooth enough matched disturbances are required. The control problem is solved in two consecutive steps: firstly, designing an observer based on the measured output and, secondly, designing of a full-state controller computed from a new virtual output with vector relative degree. The introduced notion of algebraic strong observability allows recovering the state of the system using the measured output and its derivatives. By estimating the required derivatives through the HOSM differentiator, a finite-time convergent observer is constructed.     

Adaptive consensus tracking of high-order nonlinear multi-agent systems with directed communication graphs

This paper studies the adaptive consensus tracking problem for multi-agent systems modeled as high-order integrators with uncertain nonlinear dynamics under directed communication graphs. By parameterizing the unknown dynamics of the agents and the unknown input of the leader, two decentralized tracking control laws are designed using the state information and only the output information, respectively. With state information, globally uniformly ultimately bounded consensus tracking with arbitrarily small tracking errors can be achieved and when only output information is available, based on high-gain observers, semi-global result can be obtained. Numerical examples are provided to illustrate the effectiveness of the controllers.     

非线性系统的能观性和状态观测器*

本文首先介绍了非线性系统能观性的各种定义,探讨了这些定义的背景,叙述了在各种定义下的研究成果,指出了尚未解决的问题,并介绍了Morse-Smale系统的能观性。其次,叙述了非线性系统设计状态观测器的五种方法,详细介绍了各种方法的假设条件和设计步骤。