Stabilization For High-order Nonlinear Systems Research Articles

Prescribed-time stabilization for high-order nonlinear systems with a pre-specified asymmetric output constraint

This article considers the problem of prescribed-time stabilization for a class of uncertain high-order nonlinear systems (i.e., systems in the p-normal form) with a pre-specified asymmetric output constraint. A core ingredient, tangent-type barrier function, is proposed first by skillfully excavating and assimilating the inherent properties of system nonlinearities. Based on the barrier function, as well as a serial of nested signum functions, the celebrated technique of adding a power integrator is renovated finely to establish a new design approach by which a continuous state feedback prescribed-time stabilizer, along with a tangent-type asymmetric barrier Lyapunov function, can be constructed in a systematic fashion, thereby guaranteeing the performance of prescribed-time state convergence and ensuring the fulfillment of pre-specified output constraints surely. Benefiting from the composite characteristics of the presented tangent-type barrier Lyapunov function and the signum functions, the proposed approach further offers a unified nature in design enabling us to organize a prescribed-time stabilizer that is simultaneously valid and executable for the system undergone or free from output constraints, without the need of changing the controller structure. The effectiveness and superiority of the developed approach are illustrated by a numerical example.

Fixed-time stabilization of high-order nonlinear systems with an asymmetric output constraint

Fixed-time stabilization of high-order nonlinear systems with an asymmetric output constraint

Global stabilization of high-order constrained nonlinear systems: An unbounded time-varying scaling based approach

Global stabilization of high-order nonlinear systems is studied with an asymmetric output constraint. A novel approach is raised by incorporating the unbounded time-varying scaling idea into the barrier Lyapunov function method. This is also suitable for systems with symmetric output constraints and without output constraints simultaneously. By the recursive design algorithm, a time-varying controller is established to ensure that state asymptotically converges to zero and output is always keeping in the given asymmetric domain. Finally, the feasibility of the control scheme is shown with an example.

Robust Stabilization of High-Order Nonlinear Systems With Unknown Sensitivities and Applications in Humanoid Robot Manipulation

This article is concerned with the improvement of robust control methodology and its application in stabilizing a class of high-order nonlinear systems with multiple unknown time-varying sensitivities, and discusses how to use the proposed control strategy on humanoid robot manipulation. The novel design approach successfully breaks through the limitation of the neural network technique; that is, state variables must be located in some compact sets. The remarkable feature of the systems under investigation lies in the presence of measurement sensitivities and higher powers, which makes the nonlinear systems essentially different from the related works. By reductio and the introduction of a modified tuning function, an appropriate controller is constructed to render that all the state variables belong to a predetermined bounded set. Finally, an example is provided to illustrate the effectiveness of the proposed control strategy.

A unified approach to finite-time stabilization of high-order nonlinear systems with an asymmetric output constraint

The problem of finite-time stabilization for a class of high-order nonlinear systems (also known as p-normal form systems) with an asymmetric output constraint is investigated in this paper. A novel design approach is proposed by delicately revamping the technique of adding a power integrator with the introduction of a distinctive asymmetric barrier Lyapunov function and performing a skillful manipulation of sign functions. By using the present method, a continuous state feedback finite-time stabilizer can be recursively constructed while achieving the requirement of the asymmetric output constraint. The novelty of the proposed approach is that it is a unified manner that enables us to simultaneously tackle the problem of finite-time stabilization for high-order nonlinear systems with and without asymmetric output constraints, without changing the controller structure.

Fast finite-time partial state feedback stabilization of high-order nonlinear systems with output constraint and dynamic uncertainties

This paper focuses on the problem of finite-time stabilization for a class of high-order nonlinear systems with output constraint and zero dynamics. The systems under investigation possess two remarkable features: the output is restricted in a pre-specified region arising from the demand of practical operation, and inherent nonlinearities include nonlinear growth rate of high-order and low-order together with unmeasurable dynamic uncertainties. This paper proposes a continuous controller by means of a new tangent function and a serial of nonnegative integral functions with sign functions, and the controller ensures the adjustability of convergent speed of system state, which is faster than the counterpart of traditional finite-time stabilizers. The novelty is attributed to a perspective to applying the fast finite-time stability in partial state feedback control design in the case when the output is restricted. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical result.

Stabilisation of high-order nonlinear systems with full-state constraints and input saturation

ABSTRACT This paper investigates the semi-global stabilisation problem of high-order nonlinear systems with full-state constraints and input saturation. By constructing the high-order barrier Lyapunov function (BLF) and auxiliary subsystem, a state feedback controller is designed without state and input constraints violation. It is proved that all the closed-loop signals are bounded in the semi-global sense, error signals converge to a small neighbourhood of the origin, and full-state constraints and input saturation are not violated. Two simulation examples are presented to show the feasibility and advantage of this method.

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.

Global fast finite-time partial state feedback stabilization of high-order nonlinear systems with dynamic uncertainties

This paper is concerned with the problem of finite-time stabilization for a class of high-order nonlinear systems with zero dynamic. As a significant feature, the systems considered suffer from both the unmeasurable dynamic uncertainties and inherent nonlinearities, including high-order and low-order nonlinear growth rates. On the basis of integral Lyapunov functions equipped with sign functions and the notion of input-to-state stability, a partial state feedback stabilizer is proposed to provide a faster finite-time state convergence compared to traditional finite-time one. The novelty of this paper lies in a distinct perspective to applying the concept of fast finite-time stability developed recently in partial state feedback control design, which has been previously regarded as a rather difficult problem.

Global stabilization of high-order nonlinear systems under multi-rate sampled-data control

This paper studies the sampled-data control problem for a class of high-order nonlinear systems. Based on exact discrete-time equivalent model of the sampled-data system, a multi-rate sampled-data controller with the form of a power series expansion is designed to achieve the global asymptotic stability of the closed-loop system under some assumptions. Approximate solutions of the proposed controller are proved to be effective by a theoretical analysis. The results show that, compared with the emulated control scheme, the approximate controllers allow considering larger sampling periods and enlarge the domain of attraction for a given sampling period. Finally, a simulation example is given to show the effectiveness of the proposed control scheme.

Output feedback stabilization of high-order nonlinear systems with polynomial nonlinearity

In this paper, the problem of output feedback stabilization for high-order nonlinear systems with more general low-order and high-order nonlinearities multiplied by a polynomial-type output-dependent growth rate is studied. By constructing the novel Lyapunov function and observer, based on the homogeneous domination and adding a power integrator methods, an output feedback controller is developed to guarantee that the equilibrium of the closed-loop system is globally uniformly asymptotically stable.

Global output-feedback stabilization for high-order nonlinear systems with unknown growth rate

Summary This paper considers the global stabilization via time-varying output-feedback for a class of high-order uncertain nonlinear systems with rather weak assumptions. Essentially different from the existing literature, the systems under investigation simultaneously have more serious nonlinearities, unknowns, immeasurableness, and time-variations, which are indicated from the unknown time-varying control coefficients and the higher-order and lower-order unmeasured states dependent growth with the rate of unknown function of time and output. Recognizing that adaptive technique is quite hard to apply, a time-varying design scheme is proposed by combining time-varying approach, certainty equivalence principle and homogeneous domination approach. One key point in the design scheme is the selection of the design functions of time, in order to compensate/capture the serious unknowns and serious time-variations, and another one is the design of a time-varying observer to rebuild the unmeasured system states. With the appropriate choice of the involved design functions, the designed controller makes all the signals of the closed-loop system globally bounded and ultimately converge to zero. Copyright © 2016 John Wiley & Sons, Ltd.

Global output feedback stabilisation of high-order nonlinear systems with low-order and high-order nonlinearities

In this paper, we study the global output feedback stabilisation of a class of high-order nonlinear systems with more general low-order and high-order nonlinearities. By constructing the novel Lyapunov function and observer, based on the homogeneous domination theory together with adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed-loop system globally uniformly asymptotically stable.

Global output feedback stabilisation of high-order nonlinear systems with multiple time-varying delays

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

Global output-feedback stabilization for high-order nonlinear systems with unknown control coefficients

This paper is concerned with the global stabilization via time-varying outputfeedback for a class of high-order uncertain nonlinear systems. The remarkable feature of the systems, that is, the unknown time-varying control coefficients and the unmeasured states dependent growth with unknown time-varying rate, makes the existing control design methods unapplicable. By skillfully combining time-varying approach and certainty equivalence principle, a time-varying output-feedback control design scheme is proposed in the paper. It is worth mentioning that the serious unknowns and time-variations in the systems are compensated by introducing time-varying design functions, rather than employing adaptive approach. With the appropriate choices of the design functions, all the states of the closed-loop system are globally bounded and converge to zero.

Further results on global state feedback stabilization of high-order nonlinear systems with time-varying delays

This paper considers the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. Comparing with the existing relevant literature, the systems under investigation allow more uncertainties, to which the existing control methods are inapplicable. By introducing sign function and necessarily modifying the method of adding a power integrator, a state feedback controller is successfully constructed to preserve the equilibrium at the origin and guarantee the global asymptotic stability of the resulting closed-loop system. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

Global state feedback stabilization of high-order nonlinear systems with multiple time-varying delays

This paper studies the global stabilization problem for a class of high-order nonlinear systems with low-order and high-order nonlinearities, and multiple time-varying delays. Systems become more general due to both low-order and high-order in nonlinearities taking values in certain intervals. By introducing a novel Lyapunov–Krasovskii functional, a state feedback controller based on the Lyapunov–Krasviskii theorem together with the adding a power integrator and sign function methods is designed to guarantee the globally uniformly asymptotic stability of the closed-loop system.

Global stabilisation of high-order nonlinear systems with multiple time delays

This paper focuses on the stabilisation for a class of high-order nonlinear systems with multiple time delays. Growth restriction on system nonlinearities is further relaxed. Design procedures of a continuous controller are provided by the method of adding a power integrator, and the stability of the resulting closed-loop system is rigorously proven with the help of the elegant choice of a Lyapunov–Krasovskii functional. Finally, a simulation example is provided to demonstrate the validness of the proposed approach.

Global Adaptive Stabilization of High-order Nonlinear Systems with Zero Dynamics

This paper investigates the global adaptive stabilization for a class of high-order nonlinear systems with uncertain control coefficients and unmeasurable zero dynamics. Compared with the existing works, restriction on zero dynamics is further relaxed, and the dynamic order of a continuous adaptive state-feedback controller is reduced to be minimum (only one dimensional) through delicately defining an appropriate unknown parameter. The design procedures of the controller are provided by flexibly incorporating the method of adding a power integrator with the related adaptive technique and the idea of changing supply functions. Finally, a simple example is given to demonstrate the effectiveness of the control scheme.

Correction to "Homogeneous Observers, Iterative Design, and Global Stabilization of High-Order Nonlinear Systems by Smooth Output Feedback"

Correction to "Homogeneous Observers, Iterative Design, and Global Stabilization of High-Order Nonlinear Systems by Smooth Output Feedback"