Problem Of Fixed-time Stabilization Research Articles

Adaptive fixed-time stabilization for high-order uncertain nonlinear systems with unknown measurement sensitivities

This paper investigates the adaptive fixed-time stabilization problem for a class of uncertain high-order nonlinear systems with unknown measurement sensitivities and unknown control magnitude. Compared to existing practical fixed-time control approaches, our control strategy is capable of driving all states of uncertain high-order systems to the origin within a fixed time, rather than just ensuring their boundedness. Additionally, this study relaxes the restrictions on the nonlinear functions of the system, while overcoming challenges such as unknown control magnitude and unknown measurement sensitivity without prior boundaries. To achieve the control objectives, our control strategy consists of two main steps. Firstly, we divide the initial value of the high-order system into two cases, and construct adaptive controllers separately for each case by adding a power integral technique and backstepping method. Subsequently, the reliance of the stability time of the closed-loop high-order system on the initial value is eliminated by designing an appropriate controller switching mechanism. Finally, we provide a simulation example to validate the effectiveness of our control strategy.

Fixed-time Lyapunov criteria of stochastic nonlinear systems revisited and its applications

In all the references on stochastic fixed-time stability, the customary treatment of the stochastic noise in the worst-case sense is that it is treated as the unfavorable factor for system stability. Consequently, stochastic fixed-time Lyapunov-type conditions are rather restrictive. Realizing this limitation, we revisit stochastic fixed-time stability and present a generalized fixed-time stability theorem for stochastic differential equations. This theorem completely removes the assumption in these references that the differential operator of the Lyapunov function must be strictly negative, and reveals a positive role of the stochastic noise in stochastic fixed-time stability. As the application of this theorem and its corollary, we solve the problem of fixed-time stabilization for stochastic nonlinear systems with high-order and low-order nonlinearities.

Fixed-time cooperative output regulation for second-order nonlinear multiagent systems with an unknown exosystem

This paper investigates the fixed-time cooperative output regulation (FTCOR) problem with unknown exosystem of second-order nonlinear multiagent systems. To solve this problem, it is necessary to ensure that each agent can obtain the reference trajectory originating from an unknown exosystem and reconstruct the solution of the regulator equation containing the exogenous signal and unknown parameter vectors within a fixed time, and the unknown exosystem makes it difficult to solve these two problems with existing tools. By using auxiliary filtering variables, we propose a fixed-time adaptive distributed observer (FTADO) and design a fixed-time distributed internal model (FTDIM) based on this FTADO. These two new tools ensure the solvability of the two problems just mentioned. Then, based on these two tools, we transform the problem into a fixed-time stabilization problem of a so-called augmented system. Through the backstepping technique, we propose a distributed controller that solves this fixed-time stabilization problem while relaxing the assumptions of similar references.

Adaptive Fixed-Time Stabilization for a Class of Uncertain Nonlinear Systems

This paper studies the problem of fixed-time stabilization for a class of nonlinear systems with parametric uncertainties, where the nonlinear functions are constrained by an unknown linear growth condition. By establishing a new adaptive fixed-time stability analysis criterion, it is proved that the closed-loop system is fixed-time stable and all the states can be regulated to zero. In addition, the singularity problem caused by the backstepping method under fixed-time control can be avoided. Finally, the effectiveness of the control strategy is verified by a simulation example.

Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

This paper addresses the fixed-time stability problem of chaotic systems with internal uncertainties and external disturbances. To this end, new sliding-mode surfaces are introduced to design fixed-time controllers for the stabilization of perturbed chaotic systems. First, the required conditions for deriving fixed-time stability are determined. Then, using the obtained stability theorems and sliding mode techniques, the controllers are synthesized. The proposed controller enables the convergence of the trajectories of the chaotic system to the origin in finite time, independently of the initial conditions. The performance of the proposed approach is assessed using a simulation study of a PMSM system and the Matouk system. Among the advantages of the proposed controller are its robustness to external disturbances and the boundedness of the settling time to a constant value for any initial condition.

Fixed-time stabilization of periodic linear systems and its application to the elliptical spacecraft rendezvous

A smooth periodic delayed feedback (SPDF) control scheme is proposed for the fixed-time stabilization problem of linear periodic systems subject to input delay. By investigating the monodromy matrix of the periodic system, it is proved that the SPDF controller can achieve the fixed-time stabilization of linear periodic systems with arbitrarily long yet bounded input delays under the condition that the original system is uniformly completely controllable. The proposed controller is continuously differentiable and smooth. The SPDF control scheme is then applied to the elliptical spacecraft rendezvous problem. The effectiveness of the established method is verified on numerical simulations.

New Results on Fixed-Time Stabilization of Switched Uncertain Nonlinear Systems in p-Normal Form

In this article, the global fixed-time stabilization problem is addressed for a class of switched uncertain nonlinear systems in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -normal form. Different from the existing results, the bounds of the unknown system parameters, including dead-zone parameters and control coefficients, are not required to be known. By combining the adding a power integrator technique with the common Lyapunov function method, a novel adaptive controller is proposed and a dynamic controller parameter is introduced to cope with the unknown system parameters. Besides, an effective common regulate rule is designed based on the improved fixed-time stability framework. Furthermore, it is shown that the controller parameter can be regulated online by the switching mechanism to compensate the unknown system parameters and the system states can converge to zero in fixed time under arbitrary switchings. The effectiveness of the proposed method is verified by a simulation example.

An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach

&lt;abstract&gt;&lt;p&gt;In this brief, we propose a class of generalized memristor-based neural networks with nonlinear coupling. Based on the set-valued mapping theory, novel Lyapunov indefinite derivative and Memristor theory, the coupled memristor-based neural networks (CMNNs) can achieve fixed-time stabilization (FTS) by designing a proper pinning controller, which randomly controls a small number of neuron nodes. Different from the traditional Lyapunov method, this paper uses the implementation method of indefinite derivative to deal with the non-autonomous neural network system with nonlinear coupling topology between different neurons. The system can obtain stabilization in a fixed time and requires fewer conditions. Moreover, the fixed stable setting time estimation of the system is given through a few conditions, which can eliminate the dependence on the initial value. Finally, we give two numerical examples to verify the correctness of our results.&lt;/p&gt;&lt;/abstract&gt;

Fixed-Time Stabilization for Nonlinear Systems With Low-Order and High-Order Nonlinearities via Event-Triggered Control

This paper investigates the fixed-time stabilization problem for a class of nonlinear systems via event-triggered control. The event-triggered mechanism can be applied to the nonlinear system with the coexistence of low-order and high-order nonlinearities. In order to deal with these low-order and high-order terms as well as achieve the objective of fixed-time stabilization, the initial value of the system is divided into two cases, and then the event-triggered controller is designed, respectively. By switching control theory, it is proved that the nonlinear system is globally fixed-time stable under the designed controller and the Zeno behavior can be excluded. Finally, two simulations show that the proposed technology is effective.

Fixed-Time Fractional-Order Global Sliding Mode Control for Nonholonomic Mobile Robot Systems under External Disturbances

The present study addresses the problem of fixed-time stabilization (FTS) of mobile robots (MRs). The study’s distinguishing aspects are that the system under examination is subjected to external disturbances, and the system states are pushed to zero in a finite time. This paper suggests new control techniques for chained-form nonholonomic systems (CFNS) subjected to disturbances. First, a switching fractional-order (FO) control approach is proposed for a first-order subsystem (FOS) of an MR under complex disturbances. Secondly, an FO generic global sliding mode control approach is designed for the second-order system (SOS) of the MR in the presence of disturbances. The suggested sliding manifold for the SOS of the MR guarantees global system stability and reduces the chattering problem during control operations. A conventional quadratic Lyapunov function (QLF) is used to converge to the origin in a finite time (FnT). Through this study, a stabilizer for an MR in the presence of disturbances based on an FO switching time-varying controller that can stabilize immeasurable states in a fixed time is proposed. Finally, three case simulations are provided to demonstrate the efficacy of the control strategy proposed in this work against external disturbances.

Finite-time and fixed-time stabilization of multiple memristive neural networks with nonlinear coupling.

This brief presents the finite-time stabilization and fixed-time stabilization of multiple memristor-based neural networks (MMNNs) with nonlinear coupling. Under the retarded memristive theory, the generalized Lyapunov functional method, extended Filippov-framework and Laplacian matrix theory, we can realize both the finite-time stabilization and fixed-time stabilization problem of MMNNs by designing novel state-feedback controller and the corresponding adaptive controller with regulate parameters. Moreover, we assess the bounds of settling time for the both two kinds of stabilization respectively, and we deeply analyze the influence of initial desiring values and the linear growth condition of the controller on the system. Finally, the benefits of the proposed approach and the experimental analysis are demonstrated by numerical examples.

Stochastic adaptive fixed-time stabilization of chaotic systems with applications in PMSM and FWS

This investigation addresses the problem of fixed-time stabilization of the chaotic systems influenced by environmental noise. An adaptive control scheme is employed so that it is not necessary to set the related control gains in advance. Specifically, the adaptive control is integrated with fixed-time control protocol successfully for guaranteeing the stability of chaotic systems. In the light of stochastic fixed-time stability theory, the criteria are deduced to ensure the (fixed-time) stabilization of chaotic systems, and the upper bound time is estimated, which is irrelevant to the initial states of the systems. For validating the correctness and effectiveness of theoretical analysis, two representative application cases of permanent magnet synchronous motor (PMSM) and food web system (FWS) are selected at last.

Fixed-time stabilization for interconnected high-order nonlinear systems with dead-zone input and output constraint

This paper deals with the problem of fixed-time stabilization for a class of high-order nonlinear systems with time-varying output constraint (also known as p-normal form systems). Compared with the existing results, the order of the systems can be less than 1, which is more relaxed. Moreover, each subsystem is with the dead-zone input and interconnected nonlinearity. We design a new decentralized fixed-time controller based on the recursive design method by revamping the technique of adding a power integrator and using the tan-type barrier Lyapunov function. The proposed controller is also effective for the systems with asymmetric output constraints. Based on Lyapunov stability theory, it is proved that the decentralized controller can realize that the outputs are strictly constrained within predefined boundaries and all state variables converge to zero in a fixed time, where the bound of reaching time is independent of the initial conditions. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.

Fixed-time stabilization of fuzzy neutral-type inertial neural networks with time-varying delay

This paper addresses the problem of fixed-time stabilization for a class of fuzzy neutral-type inertial neural networks (FNTINNs) with time-varying delay. By using a novel fixed-time stability theorem for dynamical systems, two different feedback control laws are designed to ensure the fixed-time stabilization of FNTINNs with time-varying delay. The proposed theoretical results can lead to a better upper settling-time estimation compared to existing results. Finally, three simulation examples are provided to illustrate the validity of the proposed theoretical results.

Impulsive effect on fixed-time control for distributed delay uncertain static neural networks with leakage delay

Abstract In this paper, the problem of fixed-time stabilization (FXTSB) for an uncertain impulsive distributed delay static neural networks (UIDSNNs) with leakage delay is investigated. Firstly, a new memory controller distinct from the existing ones is build. Besides, by using new Lyapunov function which include a new vectorial function, some new criteria are established to deal with the impulsive effect on FXTSB of UIDSNNs with leakage. Under the proposed memory fixed-time controller, the average impulsive interval(AII)-dependent settling-time is established and the controller parameters can be expressed in the form of linear matrix inequalities (LMIs). Finally, some numerical examples with graphical illustrations are provided to demonstrate the effectiveness of our theoretical main results.

Fixed-time stability of positive nonlinear systems

This paper studies the fixed-time stability problem for positive nonlinear systems defined by cooperative vector fields. A criterion is derived to ensure fixed-time stabilization of the positive nonlinear systems using Lyapunov method. In addition, a sufficient condition is also presented for fixed-time stability of switched positive nonlinear systems under arbitrary switching. Simulation examples are provided to demonstrate the obtained results.

Nonlinear mapping-based fixed-time stabilization of uncertain nonholonomic systems with time-varying state constraints

In this paper, the problem of fixed-time stabilization (FxTS) is addressed for a type of uncertain chained-form nonholonomic systems. Remarkably, the study possess two important features: one is that the system under investigation is subject to time-varying state constraints (that are equal to the space constraints of mobile robot or other nonholonomic mechanical systems), and the other is that the design control laws can render the closed-loop system (CLS) states to zero in any prescribed finite time. A novel nonlinear mapping (NM) is introduced to cope with time-varying state constraints. With the help of the adding a power integrator technique and the reasonable switching control strategy, this paper proposes a fixed-time state feedback controller, and completes the performance analysis based on the construction of integral Lyapunov function. Finally, a simulation example is presented to confirm the effectiveness of control strategy.

Barrier Lyapunov functions-based fixed-time stabilization of nonholonomic systems with unmatched uncertainties and time-varying output constraints

The fixed-time stabilization problem is addressed in this paper for a kind of nonholonomic systems in chained form with unmatched uncertainties and time-varying output constraints. A novel tan-type barrier Lyapunov function is introduced to deal with time-varying output constraints. Under the unified framework of the considered system with and without output constraints, a state feedback controller is designed with the aid of adding a power integrator technique and switching control strategy. It is shown that the suggested controller ensures the states of closed-loop system to zero in a given fixed time without disobeying the constraints. Finally, simulation results are given to confirm the efficacy of the presented control scheme.

A Novel Approach to Fixed-Time Stabilization for a Class of Uncertain Second-Order Nonlinear Systems

This paper is concerned with the problem of fixed-time stabilization for a class of uncertain second-order nonlinear systems. By delicately introducing extra manipulations in the feedback domination and revamping the technique of adding a power integrator, a new approach is developed, by which a state feedback controller, together with a suitable Lyapunov function, which is critical for verifying fixed-time convergence, can be explicitly organized to render the closed-loop system fixed-time stable. The major novelty of this paper is attributed to a subtle strategy that offers a distinct perspective in controller design as well as stability analysis in the problem of fixed-time stabilization for nonlinear systems. Finally, the proposed approach is applied to the attitude stabilization of a spacecraft to demonstrate its merits and effectiveness.

Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

In this paper, fixed-time stability problem of nonlinear system is investigated. Firstly, a new fixed-time stability theorem is established, and a higher precise estimate of settling time is provided. Secondly, by theoretical deduction, the provided estimate is compared with the ones in existing fixed-time stabiity theorems. It is shown that our estimate is less conservative and more accurate than existing results. Moreover, as a practical application, fixed-time stabilization problem of general neural networks is studied. By developing a framework of protocol and applying the new fixed-time stability theorem, some new criteria are derived to solve fixed-time stabilization problem of general neural networks systems. Finally, two simulation examples are provided to verify the validity of our theoretical results.