Adaptive Finite-time Stabilization Research Articles

Adaptive finite-time stabilization for uncertain nonlinear systems with unknown control coefficients

Finite-time control owns the advantages of precision and rapidness, preferred by many applications with high performance requirements. Its realization calls for subtle treatments, e.g., the Lyapunov method with low-order terms and homogeneity with negative degree. However, the methods available for finite-time control are based on some basic exclusions and essential restrictions to system uncertainties and nonlinearities. This paper addresses for the first time unknown control coefficients without any known bound, and meanwhile extends system nonlinearities, within the framework of continuous adaptive feedback. The success is typically due to several sets of disparate powers in control design and analysis. Specifically, the nonidentical power-type parameters are introduced in high-gain dynamics, instead of an identical one in the literature, to ensure the stabilizing terms have lower powers than the terms containing uncertainties, enabling finite-time convergence. Thus an adaptive finite-time controller is achieved. New integral-type functions are exploited to make up the important Lyapunov function, which are equipped with different powers to make possible the anticipated performance analysis. The effectiveness of the proposed controller is demonstrated by a simulation example.

Practical adaptive finite-time stabilization for a class of second-order systems

This paper considers the practical adaptive finite-time stabilization problem for a class of second-order systems. Based on the adding a power integrator technique and the adaptive method, a novel adaptive control strategy is presented to assure the trajectories of the closed-loop systems converge to a small neighborhood of the origin in a finite time. Under the adaptive control strategy, the dynamical change of control gain is dependent on the cases whether the state trajectories enter or leave a pre-designed domain or not. In addition, the practical finite-time stability (PFTS) of systems is testified via utilizing the Lyapunov method and adaptive mechanism. Last of all, the validity of the obtained practical adaptive finite-time algorithm is verified via simulation results.

Adaptive finite-time stabilisation of output-constrained low-order uncertain nonlinear systems with time-varying powers

This paper investigates adaptive finite-time stabilisation for a class of output-constrained low-order nonlinear systems with unknown time-varying powers, parametric and dynamic uncertainties. Due to low-order nonlinear systems being merely continuous but not smooth, and the presence of time-varying powers and multiple unknowns, all the existing control methods of output-constrained nonlinear systems are inapplicable. By characterising unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), applying finite-time stability theory and introducing the tan-type barrier Lyapunov function, low-power and high-power terms into control design, a unified adaptive state-feedback controller, which can deal with both constrained and unconstrained systems, is constructed. It is proved that all the closed-loop signals are uniformly bounded, the output constraint is not violated, and system states converge to zero in a finite time. Finally, a simulation example is given to illustrate the effectiveness of this control scheme.

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.

Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation

In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.

Adaptive neural finite-time stabilisation for a class of p-normal form nonlinear systems with unknown virtual control coefficients

The adaptive neural finite-time stabilisation problem is studied for a class of p-normal form nonlinear systems in this paper. An adaptive neural finite-time controller is designed by combining the adding a power integrator technique with Lyapunov finite-time stability theory. And the stability of the closed-loop system is analysed. The designed controller can guarantee that all the states in the closed-loop system are finite-time asymptotic stable. In the design, a new assumption for unknown nonlinear terms is proposed, which is looser than the existed works. A combination vector method is adopted to avoid the effect of the approximation errors of neural networks. The maximal value of norms of the combination vectors is taken as an adaptive parameter, so that the complexity of the design method is reduced. And the settling-time can be adjusted by changing a design parameter. Finally, three simulation examples demonstrate the effectiveness of the proposed control method.

Global adaptive finite-time control for uncertain nonlinear systems with actuator faults and unknown control directions

In this paper, the global adaptive finite-time stabilization problem is investigated for a class of uncertain nonlinear systems with actuator faults and unknown control directions. The lower bounds of the actuation effectiveness, the upper bounds of the disturbance and the stuck faults are not required to be known a prior. By adopting adding a power integrator technique, a switching-type adaptive finite-time controller is designed and a modified switching mechanism is also proposed. It is proven that the global finite-time stability can be guaranteed by the proposed controller. A simulation example is provided to verify the effectiveness of the proposed method.

Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode

This article presents a novel adaptive finite-time stabilization technique based on global sliding mode for disturbed chaotic flow with a single unstable node. The considered chaotic flow has unusual characteristics containing attractor merging, symmetry breaking, attracting tori and different forms of multi-stability. A nonlinear function is employed in the global sliding surface to modify damping ratio and improve the transient performance. The damping ratio of the closed-loop system is improved when the states converge to the origin. Using the new chattering-free controller, the reaching mode is removed and the sliding behavior is presented right from the first instant. The adaptive finite-time tuning law eliminates the requirement of the information about the disturbances’ bounds. Illustrative simulations are provided to display the efficiency of the proposed scheme.

Adaptive Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems via Logic-Based Switchings

In this paper, global adaptive finite-time stabilization is investigated by logic-based switching control for a class of uncertain nonlinear systems with the powers of positive odd rational numbers. Parametric uncertainties entering the state equations nonlinearly can be fast time-varying or jumping at unknown time instants, and the control coefficient appearing in the control channel can be unknown. The bounds of the parametric uncertainties and the unknown control coefficient are not required to know a priori . Our proposed controller is a switching-type one, in which a nonlinear controller with two parameters to be tuned is first designed by adding a power integrator, and then a switching mechanism is proposed to tune the parameters online to finite-time stabilize the system. An example is provided to demonstrate the effectiveness of the proposed result.

Adaptive finite-time stabilisation of a class of high-order nonlinear systems with inverse dynamics

ABSTRACTThis paper investigates the adaptive finite-time stabilisation of a class of high-order nonlinear systems with inverse dynamics and time-varying control coefficients. Under the assumptions that the inverse dynamics of the subsystem are input-to-state stable , and nonlinear terms depend upon the inverse dynamics, the states and unknown parameters, we present a systematic design procedure for an adaptive finite-time state-feedback control law by using a recursive design approach. It is shown that under the proposed adaptive control law, the state of the closed-loop system is finite-time convergent. Two examples are provided to show the effectiveness of the proposed method.

Adaptive Finite-Time Controller Design for T-S Fuzzy Systems.

This paper studies the adaptive finite-time stabilization problem for a class of nonlinear systems described by Takagi-Sugeno (T-S) fuzzy dynamic models with parametric uncertainties. A novel adaptive state feedback control scheme for the T-S fuzzy systems is proposed, and the scheme is developed based on finite-time Lyapunov theorem and adaptive backstepping-like method. Augmented dynamics are introduced in the design of finite-time stabilization controllers to construct suitable finite-time Lyapunov functions. It is shown that finite-time convergence of the closed-loop adaptive control system can be achieved, and the potential controller singularity problem caused by the augmented dynamics can be avoided. In addition, constructive procedures to obtain such an adaptive finite-time controller are given. Convergence time as a transient performance specification is also taken into account, and a finite upper bound on the convergence time is estimated. Finally, two numerical examples are provided to illustrate the effectiveness and practicality of the proposed adaptive control approach.

Adaptive finite-time stabilisation of high-order uncertain nonlinear systems

ABSTRACTThis paper studies the problem of finite-time stabilisation of more general high-order nonlinear systems with dynamic and parametric uncertainties. By characterising the unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), skillfully combining Lyapunov function, sign function, backstepping, adaptive control and FTISS approaches, and using finite-time stability theory, an adaptive state feedback controller is designed to guarantee high-order uncertain nonlinear systems globally finite-time stable.

Adaptive finite-time control for a class of switched nonlinear systems using multiple Lyapunov functions

ABSTRACTThis paper investigates the problem of global adaptive finite-time stabilisation for a class of switched nonlinearly parameterised systems. Without requiring that each subsystem is globally adaptively finite-time stabilisable, a switched adaptive finite-time control scheme is developed by exploiting the multiple Lyapunov functions method and adding a power integrator technique. By using the parameter separation technique, the unknown parameters are separated from nonlinear functions. On the basis of finite-time Lyapunov stability theory, it is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to the origin in finite time. Finally, an example is given to demonstrate the effectiveness of the proposed method.

Adaptive Finite-Time Stabilization of High-Order Nonlinear Systems with Dynamic and Parametric Uncertainties

Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.

Adaptive finite-time control for non-linear delay systems via non-fragile state feedback

The problem of adaptive finite-time control is addressed in this paper for a class of non-linear delay systems. First, the concepts of adaptive finite-time stability and adaptive finite-time boundedness are defined, respectively. Then, by resorting to the Lyapunov–Krasovskii functional technique, some new delay-dependent criteria guaranteeing adaptive finite-time boundedness and adaptive finite-time stability are developed, respectively. An explicit expression for the desired non-fragile state feedback controller is also presented. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.

Adaptive finite-time stabilization of a class of switched nonlinear systems using neural networks

This paper investigates the adaptive finite-time stabilization of a class of switched nonlinear systems via backstepping technique, where unknown nonlinear functions are only required to be continuous. At each step of backstepping, neural network is used to appropriate the unknown continuous function, an adaptive law and a virtual controller are constructed simultaneously. By using the Lyapunov function method, it is shown that, under the designed controller and adaptive laws, the state of the closed-loop system is semi-globally uniformly finite-time bounded. An example is provided to show the effectiveness of the proposed method.

Adaptive finite-time control for hyperchaotic Lorenz–Stenflo systems

This paper investigates the issue of adaptive finite-time control for hyperchaotic Lorenz–Stenflo systems with parameter uncertainties. Based on finite-time Lyapunov theory, a class of non-smooth adaptive finite time controllers is given to guarantee the adaptive finite-time stability and make the states of the systems converge to the origins within a finite-time. Finally, illustrative examples are presented to verify the effectiveness of the proposed adaptive finite-time controller.

Adaptive neural finite-time control for a class of switched nonlinear systems

This paper investigates the adaptive finite-time stabilization of a class of switched nonlinear systems with unknown nonlinear terms using neural networks. Under the assumption that all the growth conditions for the unknown nonlinear perturbation functions are partially known, the common finite-time controller and adaptive law are constructed by extending the adding-a-power-integrator technique and using the backstepping methodology. The unknown parts of the growth conditions are modeled by the neural networks and the known parts are exploited for the controller design. The bounds of neural network approximation errors are assumed to be unknown and are estimated online. It is shown that the state of the closed-loop system is finite-time stable and the parameter estimations are bounded under arbitrary switching. A simulation example is provided to show the effectiveness of the proposed method.

Adaptive finite-time stabilization for a class of uncertain high order nonholonomic systems

In this paper, the adaptive finite-time stabilization problem is investigated for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts and nonlinear parameterization. By skillfully using finite-time stability theorem, parameter separation technique and adding a power integrator method, an adaptive state feedback controller is obtained. To overcome the obstacle that x-subsystem is uncontrollable when the control input u0=0, a novel switching control strategy is given. Based on this, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. Two illustrative examples are also provided to demonstrate the effectiveness of the proposed controller.

Adaptive finite-time control of chaos in permanent magnet synchronous motor with uncertain parameters

Permanent magnet synchronous motor (PMSM) exhibits chaotic behavior when its parameters are within a certain range which seriously affect the stable work of PMSM. In order to eliminate the chaos, many approaches have been proposed. Most of them considered asymptotic stability of the system, while finite-time stability makes more sense in practice. In addition, parameters of PMSM may be uncertain because of some external factors, then adaptive control is a good method to be considered. In this paper, adaptive finite-time stabilization problem is considered to eliminate the chaos in PMSM system with uncertain parameters. To show the effectiveness of the proposed method, some simulation results are provided.