Global Finite-time Stabilization Research Articles

Global Finite-Time Stabilization of First-Order Systems With Bounded Controls

This paper addresses the global finite-time stabilization problem for systems with bounded controls. First, based on the bounded functions of tanh(∙) and arctan(∙), two classes of bounded global finite-time controllers are proposed to stabilize single integrator systems and the saturation level of the control input can be prescribed. In addition, for each proposed controller, the upper-bound estimate for closed-loop settling time is provided explicitly, which is closely related to a parameter reflecting the initial state location. Finally, the effectiveness of the proposed controllers is verified through simulation.

Global Finite-Time Stabilization of Spacecraft Attitude With Disturbances via Continuous Nonlinear Controller

In this paper, a robust continuous controller is investigated to solve the global finite-time attitude stabilization problem of rigid spacecraft system subject to multiple disturbances. The system order is firstly increased by derivation and the derivative of the actual torque is regarded as the virtual control law to be designed. Then, a super-twisting differentiator is constructed to provide finite-time angular acceleration estimations. Finally, based on the estimated angular accelerations, a discontinuous set stabilization control law is designed as the virtual controller. The actual continuous controller is obtained by integrating the discontinuous one. Rigorous proof and stability analysis are presented based on Lyapunov analysis. Compared with most of the existing finite-time control approaches in spacecraft systems, the proposed continuous control scheme guarantees the finite-time set stability of the closed-loop system. Moreover, the system states can converge to the equilibria even in the presence of derivative-bounded disturbances. Simulation studies of the proposed controller are illustrated to demonstrate the strong disturbance rejection ability, fast convergence rate, and high steady-state precision.

Global Finite-Time Stabilization for Uncertain Systems With Unknown Measurement Sensitivity.

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

Correction to: Global finite-time set stabilization of spacecraft attitude with disturbances using second-order sliding mode control

Correction to: Global finite-time set stabilization of spacecraft attitude with disturbances using second-order sliding mode control

Global finite-time set stabilization of spacecraft attitude with disturbances using second-order sliding mode control

The performance of attitude stabilization control algorithms for rigid spacecraft can be limited by disturbances. In this paper, the global finite-time attitude stabilization problem with disturbances is investigated and handled by constructing a second-order sliding mode controller. Firstly, a virtual controller based on set stabilization idea is constructed to globally finite-time stabilize the system. Then, a relay polynomial second-order sliding mode controller is constructed to guarantee that the tracking error toward the virtual controller will converge to zero in finite-time. Finite-time Lyapunov theory is applied to support the proof and stability analysis. The global finite-time stability holds even with bounded disturbances. The effectiveness and feasibility of the controller are illustrated by the numerical simulations.

Finite-time stabilization with arbitrarily prescribed settling-time for uncertain nonlinear systems

This paper considers global finite-time stabilization with arbitrarily prescribed settling-time for nonlinear systems with unknown control directions and other serious uncertainties. In view of the challenge of the problem and the scarcity of available methods, several motivating facts are offered by elaborating examples and counterexamples. The facts disclose the potential obstructions in pursuing continuous controllers and force us to resort to powerful discontinuous feedbacks. By combining the method of adding a power integrator, homogeneous approach and desingularization technique, a state-feedback controller with design parameters is first proposed. Then a switching logic is proposed to tune the parameters online, wherein two types of switching sequences are involved to suppress serious uncertainties and to guarantee arbitrarily prescribed settling-time, respectively. Also, fixed-time stabilization is considered as a special case, aiming at the trade-off between arbitrary rapidness and high control cost. Two examples are provided to demonstrate the effectiveness of the proposed strategy.

Global Finite-Time Output-Feedback Stabilization of Nonlinear Systems Under Relaxed Conditions

This article presents a first constructive solution to the global finite-time output feedback stabilization of a large class of lower triangular nonlinear systems under relaxed conditions. The key idea is to introduce a switching strategy in the control design scheme. Unlike the previous literature, the nonlinearities of the systems are assumed to satisfy a general Hölder continuous condition, which include Lipschitz continuous nonlinearities as a special case. Global finite-time stability of the closed-loop observer-controller systems is proved by means of innovative Lyapunov-based analytical techniques. A benchmark practical example of controlling the single-link robotic manipulator coupled to a dc motor is adopted to illustrate the proposed method.

Robust adaptive finite-time stabilization control for a class of nonlinear switched systems based on finite-time disturbance observer

The problem of adaptive global finite-time stabilization control for a class of nonlinear switched systems in the presence of external perturbations and arbitrary switchings has been addressed in this research study. The proposed scheme has been designed based on a finite-time estimation technique in which during the control procedure, unknown imposed perturbations are accurately estimated by means of the designed finite-time disturbance observer (FTDO). Due to the exact estimation of the external disturbances within a given finite time, the encountered complications and adversities from loss of information in the Lyapunov parameter estimation (LPE) methods have been solved which are caused by the persistent switchings in the system. Furthermore, a new solution for the problem of chattering phenomenon in nonlinear switched systems has been presented by utilizing the designed FTDO, which can counteract the malfunctioning responses of the system caused by external disturbances and unmodeled dynamics. In this paper, an acknowledged class of nonlinear switched systems has been taken into account which is in the general form of canonical structure. In addition, the established design strategy is formulated for the control of perturbed nonlinear switched systems with one and only input and assures that the system states through the finite-time convergence characteristic, reach the equilibrium point of origin. Finally, numerical simulations are carried out on a mass-spring-damper (MSD) dynamical system to indicate advantages and superior efficiency of the suggested method.

Robust Finite Time Passivity and Stabilization of Uncertain Switched Nonlinear System

This paper studies the robust finite time passivity, feedback robust finite time passification and global finite time stabilisation of the switched nonlinear systems with structural uncertainties. First, a concept of robust finite time passivity is proposed. Each subsystem is not required to be robust finite time passive. Namely, each active subsystem is finite time passive, even if there exists uncertainties in the switched system. Based on this finite time passivity concept, the finite time stability is obtained for switched nonlinear systems. Second, the robust finite time passivity criterion of switched system is established by the design of a state-dependent switching law. Third, a state-dependent switching law and a set of state feedback controllers are designed to render the closed loop system finite time passive. Finally, the robust finite time passivity property is preserved for the feedback interconnected uncertain switched systems. A numerical example is given to verify the effectiveness of our results.

Finite-time stabilization of an overhead crane with a flexible cable submitted to an affine tension

The paper is concerned with the finite-time stabilization of a coupled PDE–ODE system describing the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is described by the wave equation with a variable coefficient which is an affine function of the curvilinear abscissa along the cable. Using several changes of variables, a backstepping transformation, and a finite-time stable second-order ODE for the dynamics of a conveniently chosen variable, we prove that a global finite-time stabilization occurs for the full system constituted of the platform and the cable. The kernel equations and the finite-time stable ODE are numerically solved in order to compute the nonlinear feedback law, and numerical simulations validating our finite-time stabilization approach are presented.

Global finite-time stabilization of switched high-order rational power nonlinear systems

This works is concerned with the finite-time optimal stabilization problem for a class of switched non-strict-feedback nonlinear systems whose powers are possibly different positive odd rational numbers in the sense the powers of each subsystem might differ from others. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping method successfully developed for low-order systems fail to work. To this purpose, the nested saturation homogeneous controller is constructively devised to achieve global finite-time stability. Furthermore, the corresponding design parameters are optimized by minimizing a well-defined cost function, and thus an optimal controller being independent of switching signals is obtained. Simulation results are eventually provided to validate the effectiveness of the proposed control scheme.

Global finite-time stabilisation for a class of nonlinear systems in the p-normal form via output feedback

In this paper, a finite-time output feedback control scheme is presented for a class of nonlinear systems in the p-normal form. The nonlinear functions in the systems are assumed to be bounded by both low-order and high-order nonlinearities multiplied by a polynomial-type output-dependent growth rate, which are able to cover a more general ones. A reduced-order observer is constructed to estimate unmeasurable states, and a finite-time output feedback controller is proposed for the considered system by constructing a new Lyapunov function and using the adding a power integration technique. Two simulation examples are given to verify the effectiveness of the proposed scheme.

On the global finite-time stabilization of bilinear systems by homogeneous feedback laws. Applications to some PDE's

In this paper, the problem of global finite-time stabilization of bilinear control systems by means of homogeneous feedback law is investigated. We prove under some reasonable assumptions on the operators A and B that continuous bounded and discontinuous unbounded feedbacks stabilize globally in finite-time the closed loop system. For illustrative, the examples of heat, Schrödinger and transport equations are considered where homogeneous stabilizing feedback is built for these systems.

Global Adaptive Finite-Time Stabilization of Uncertain Time-Varying $p$-Normal Nonlinear Systems Without Homogeneous Growth Nonlinearity Restriction

The problem of global finite-time stabilization for $p$ -normal nonlinear systems subject to uncertain time-varying control coefficients and vanishing nonlinear uncertainties without homogeneous growth restriction is investigated in this paper. By virtue of the technique of homogeneous domination, a new dual-layer adaptive approach is presented to address the uncertainties and nonlinearities of the system. For one layer of the adaptive mechanism, a nonlinear adaptive parameter estimator is proposed to reconstruct the upper bounds of the unknown uncertainties. For the other, an explicit construction approach of a new adaptive dynamic gain mechanism is presented for the first time to cope with the uncertain time-varying control coefficients of the $p$ -normal nonlinear systems. It is shown that the global boundedness of the systems under consideration is guaranteed by the presented approach, and in addition the time taken to converge to the equilibrium is rendered to be finite time.

Event-Triggered Global Finite-Time Control for a Class of Uncertain Nonlinear Systems

This paper focuses on the problem of global finite-time stabilization for a class of uncertain nonlinear systems with event-triggered inputs. The existing event-based design methods can only partially compensate for the effects of the event-triggered errors and cannot completely counteract them to achieve finite-time control. For this reason, a new method about event triggering mechanism and event-triggered controller codesign is presented based on the idea of backstepping design and the sign function technique. It is proved that the event-triggered control system is the Zeno-free and the newly proposed control strategy ensures the global finite-time stability of the closed-loop systems via Lyapunov analyses and finite-time stability theory, which improves the existing results of only boundedness or asymptotic stability. Finally, two examples are performed to demonstrate the validity of the proposed strategy.

Global finite-time stabilisation of high-order nonlinear systems: a dynamic gain-based approach

ABSTRACTThis paper deals with finite-time stabilisation problem for a class of high-order nonlinear systems. By generalising a dynamic gain design method and adding a power integrator technique, a new state feedback controller is constructed by choosing an appropriate Lyapunov function. It is proved that the corresponding closed-loop system is globally finite-time stable by the constructed controller, and the proposed method can accelerate the convergent speed and decrease the settling time. Finally, a simulation example is given to verify the effectiveness of the proposed scheme.

Fast finite-time stability and its application in adaptive control of high-order nonlinear system

This paper addresses the problem of global finite-time adaptive stabilization for a class of high-order uncertain nonlinear systems. A new finite-time stability result is established to provide a less conservative estimation of convergent time in uncertain situation, and a state feedback stabilizer with an adaptive mechanism is constructed by applying continuous domination to adaptive fashion of the systems to be considered. The main novelty of this paper is the skillful development of an analytic strategy and the delicate selection of Lyapunov functions in searching for the adaptive fast finite-time stabilizer. A benchmark example is given to demonstrate the effectiveness of the proposed strategy.

Reduced-order observer-based saturated finite-time stabilization of high-order feedforward nonlinear systems by output feedback

This paper is concerned with the problem of global finite-time stabilization by output feedback for a class of feedforward (upper-triangular) nonlinear systems in p-normal form. Remarkably, both the high order powers and the saturated input are involved in the system under consideration, that renders the existing output feedback control methods are inapplicable. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a reduced order observer-based saturated finite-time output feedback control scheme is successfully developed. With choosing appropriate design parameters, the proposed controller ensures that the states of the closed-loop system are regulated to zero in a finite time without violation of the input constraint. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed method.

Global finite-time stabilization for switched stochastic nonlinear systems via output feedback

This paper is concerned with the problem of global finite-time stabilization via output feedback for a class of switched stochastic nonlinear systems whose powers are dependent of the switching signal. The drift and diffusion terms satisfy the lower-triangular homogeneous growth condition. Based on adding a power integrator technique and the homogeneous domination idea, output-feedback controllers of all subsystems are constructed to achieve finite-time stability in probability of the closed-loop system. Distinct from the existing results on switched stochastic nonlinear systems, the delicate change of coordinates are introduced for dominating nonlinearities. Moreover, by incorporating a multiplicative design parameter into the coordinate transformations, the obtained control method can be extended to switched stochastic nonlinear systems with nonlinearities satisfying the upper-triangular homogeneous growth condition. The validity of the proposed control methods is demonstrated through two examples.

Global output-feedback finite-time stabilization for a class of stochastic nonlinear cascaded systems

In this paper, the problem of global finite-time stabilization via output-feedback is investigated for a class of stochastic nonlinear cascaded systems (SNCSs). First, based on the adding a power integrator technique and the homogeneous domination approach, a global output-feedback finite-time control law is constructed for the driving subsystem. Then, based on homogeneous systems theory, it is shown that under some mild conditions the global finite- time stability in probability of the driving subsystem implies the global finite-time stability in probability of the whole SNCS. Finally, a simulation example is given to illustrate the effectiveness of the proposed control design approach.