Fixed-time Stability Research Articles

Event-based fixed-time synchronization of neural networks under DoS attack and its applications

In this paper, the fixed-time synchronization control for neural networks with discontinuous data communication is investigated. Due to the transmission blocking caused by DoS attack, it is intractable to establish a monotonically decreasing Lyapunov function like the conventional analysis of fixed-time stability. Therefore, by virtue of recursive and reduction to absurdity approaches, novel fixed-time stability criteria where the estimated upper bound of settling-time is inherently different from existing results are presented. Then, based on the developed conditions, an event-triggered control scheme that can avoid Zeno behavior is designed to achieve synchronization of master–slave neural networks under DoS attack within a prescribed time. For comparison, the established control scheme is further discussed under the case without DoS attack, and the circumstance that there is no attack or event-triggered mechanism, respectively. Simulation results are finally provided to illustrate the significant and validity of our theoretical research. Especially, in terms of encryption and decryption keys generated from the synchronization behavior of chaotic networks, we specifically discuss the application of the proposed fixed-time synchronization scheme to image and audio encryption.

A novel fixed-time stability lemma and its application in the stability analysis of BAM neural networks.

In this paper, we put forward an interesting fixed-time (FXT) stability lemma, which is based on a whole new judging condition, and the minimum upper bound for the stability start time is obtained. In the new FXT stability lemma, the mathematical relation between the upper bound of the stability start time and the system parameters is very simple, and the judgment condition only involves two system parameters. To indicate the usability of the new FXT stability lemma, we utilize it to study the FXT stability of a bidirectional associative memory neural network (BAMNN) with bounded perturbations via sliding mode control. To match the developed FXT stability lemma, novel sliding mode state variables and a two-layer sliding mode controller are designed. According to the developed FXT stability lemma, the perturbed BAMNN can achieve FXT stability under the devised sliding mode controller. The upper bound of the stability start time can be calculated easily by virtue of the control parameters, and the sufficient conditions guaranteeing that the perturbed BAMNN can achieve FXT stability have also been derived. Last, we provide some confirmatory simulations.

Fuzzy Disturbance Observer-Based Fixed-Time Sliding Mode Control for Hypersonic Morphing Vehicles With Uncertainties

This work focuses on the attitude control problem for hypersonic morphing vehicles(HMVs) with uncertainties. A span-morphing HMV model is firstly established with lumped disturbances. Based on fixed-time technique, a disturbance observer with fuzzy logic system(FLS) is proposed to enhance the robustness by estimating the unmodelled dynamics and external disturbances in fixed settling time. The multivariable fixed-time sliding mode manifold is applied to the transformed control system, which guarantees a direct control input design from attitude command and decent tracking performance. Then, the control system degenerates into an autonomous system, and the closed-loop fixed-time stability is ensured via Lyapunov synthesis and homogeneity theory. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Fixed-Time Stable Proximal Dynamical System for Solving MVIPs

In this paper, a novel modified proximal dynamical system is proposed to compute the solution of a mixed variational inequality problem (MVIP) within a fixed time, where the time of convergence is finite and is uniformly bounded for all initial conditions. Under the assumptions of strong monotonicity and Lipschitz continuity, it is shown that a solution of the modified proximal dynamical system exists, is uniquely determined, and converges to the unique solution of the associated MVIP within a fixed time. Furthermore, the fixed-time stability of the modified projected dynamical system continues to hold, even if the assumption of strong monotonicity is relaxed to that of strong pseudomonotonicity. Finally, it is shown that the solution obtained using the forward-Euler discretization of the proposed modified proximal dynamical system converges to an arbitrarily small neighborhood of the solution of the associated MVIP within a fixed number of time steps, independent of the initial conditions.

Predefined-Time Average Consensus Control for Heterogeneous Nonlinear Multi-Agent Systems

This paper is primarily devoted to the predefinedtime average consensus of heterogeneous nonlinear leaderless multi-agent systems(MASs). Firstly, the predefined-time stability for a class of fixed-time stable systems is studied, which greatly improves the overestimation for the settling time of the fixed-time stability. Moreover, compared with the classical conclusions, our results are more suitable for the control of nonlinear MASs. Then, on the basis of the proposed stability analysis, a simple control algorithm is designed for ensuring the predefined-time average consensus of the system under consideration. With this predefined-time approach, any desired settling time can be achieved by adjusting the control gain. Finally, numerical simulation is shown to support the theoretical analysis.

Fixed-time synchronization of delayed BAM neural networks via new fixed-time stability results and non-chattering quantized controls

In this paper, in order to obtain a smaller estimation of settling time, reduce chattering caused by sign function and improve network communication efficiency, the fixed-time (FXT) synchronization of delayed BAM neural networks is analyzed based on some new FXT stability results and non-chattering quantized controllers. Firstly, by comprehensively discussing the conditions of power laws in differential inequalities, a new FXT stability lemma is presented and a smaller upper bound of settling time is estimated. Then, unlike previous controllers with sign functions, a non-chattering quantized state feedback control and a non-chattering quantized pinning control are designed, and some sufficient conditions are derived to ensure FXT synchronization of the established system. Finally, two numerical simulations are given to verify the effectiveness of the theoretical results. The results show that compared with the previous researches, this paper provides a smaller upper bound. However, the convergence time of the uncontrolled nodes is indirectly affected by the coupling of the controlled nodes and is much longer than the estimated upper bound.

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.

Adaptive fractional tracking control of robotic manipulator using fixed-time method

This paper proposes an adaptive fractional-order sliding mode controller to control and stabilize a nonlinear uncertain disturbed robotic manipulator in fixed-time. Fractional calculus is used to construct a fractional-order sliding mode controller (FtNTSM) that suppresses chattering to help the robotic manipulator converge to equilibrium in a fixed-settling time based on fixed-time stability theory. Then, adaptive control is introduced and combined with FtNTSM to overcome the unknown system dynamics. The convergence time of the proposed fixed-time fractional-order sliding mode controller (AFtNTSM) is independent of beginning circumstances and can be precisely assessed, unlike the finite-time control approach. Finally, numerical simulations show that the adaptive fractional-order sliding mode controller outperforms finite-time sliding mode controller.

A novel control system for synchronizing chaotic systems in the presence of communication channel time delay; case study of Genesio-Tesi and Coullet systems

Time delay is one of the challenges that may occur in the communication channels. The control of chaotic systems due to time delay is a challenging purpose. This paper defines a synchronization system where the Genesio-Tesi is the master, and the Coullet is the slave system. A suitable observer-based sliding mode controller is designed for the goal of synchronization with the communication channel’s time delay. The proposed control system consists of state and disturbance observers and a controller. The state, disturbance observers, and controller are designed to synchronize the chaotic systems. The state observer estimates the master system states, the disturbance observer estimates the model of the uncertainties and external disturbances, and the controller uses the information from the state and disturbance observers in real time. These state and disturbance observers and controller work simultaneously. The proposed controller is based on the Sliding Mode Control (SMC) method and fixed-time stability concepts. This control system is compared with finite-time and asymptotical control systems by defining three performance criteria IAE, ITAE, and ISV. The proposed control method is robust against uncertainties and external disturbances and chattering-free. The MATLAB/Simulink software simulates the control systems and compares their results.

Load following control of a PWR with load-dependent parameters and perturbations via fixed-time fractional-order sliding mode and disturbance observer techniques

This paper is concerned with the fixed-time fractional-order sliding mode control (FTFOSMC) approach using fixed-time disturbance observer (FTDO) for the load following problem of a pressurized water reactor (PWR), in the presence of load-dependent parameters and perturbations. First, by integrating the merits of the fixed-time stability theory and the disturbance observer technique, an FTDO which can ensure fixed-time convergence is constructed to estimate perturbations induced by model uncertainties, external disturbances, and unmeasured states. Then, an FTFOSMC strategy with the help of the disturbance observer is proposed to achieve strong robustness against perturbations and high-precision load following performance. The fixed-time stability of the closed-loop system is theoretically demonstrated by Lyapunov’s theorem. Finally, comparative simulation results are presented to illustrate the superiority of the overall proposed control strategy.

Fixed-time periodic stabilization of discontinuous reaction–diffusion Cohen–Grossberg neural networks

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction–diffusion Cohen–Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction–diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction–diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.

On novel distributed fixed-time formation tracking of multiple hypersonic flight vehicles with collision avoidance

This paper aims to achieve collision-free formation tracking for multiple hypersonic flight vehicles without introducing conventional approximators such as fuzzy logic systems and neural networks. By relying on the hierarchical control theory, a globally fixed-time distributed formation control protocol with guaranteed tracking behaviors is proposed. Firstly, for the purpose of deriving the virtual control commands in the three-dimensional translational dynamics, a fixed-time consensus control input is presented. Then, by designing a comprehensive performance-preserving feedback control law, the actual control commands are derived, so that the virtual control inputs can be tracked timely and accurately. Meanwhile, with resort to a novel exponential-type artificial potential function, a collision-free control input is proposed to avoid close proximity between adjacent hypersonic flight vehicles. Summarily, the outstanding advantage of the proposed protocol is that it simultaneously realize the collision-free formation tracking, fixed-time stability and performance-preserving control for multiple hypersonic flight vehicles with uncertain dynamics. Lyapunov stability criterion verifies the closed-loop stability, showing that the error signals can attenuate to a tiny region around the origin within a user-specified time. Finally, comparative numerical simulations are performed to further demonstrate the theoretical results.

Observer-based robust impact angle control three-dimensional guidance laws with autopilot lag

Considering an air-based missile intercepting maneuvering target with desired impact angles, robust guidance laws with autopilot lag in three-dimensional coupling space are presented in this paper. First, combining the fixed-time stability theory and adaptive sliding mode control technique, a novel dual-layer adaptive fixed-time sliding mode disturbance observer is proposed to estimate the unknown target maneuver. The proposed disturbance observer releases the requirement of information on either the target maneuver or its derivative. To achieve interception with the desired impact angles, a novel guidance law based on the nonsingular terminal sliding mode (NTSM) with an exponent coefficient is provided. The proposed control framework prevents singular problems and ensures the fixed-time stability of the guidance system. In addition, autopilot dynamics are taken into consideration, and the dynamics surface control (DSC) method is used to address the nonlinear static feedback system. Meanwhile, the improved fixed-time differentiator is used to acquire the derivative of virtual control laws. This prevents the inherent “differential explosion” of the backstepping technique. The uniform boundedness of the closed-loop system is demonstrated via the Lyapunov method. Finally, numerous numerical simulations are carried out, and the simulation results verify the effectiveness of the proposed guidance laws.

Robust fixed-time trajectory tracking control of the dynamic positioning ship with actuator saturation

This paper addresses the fixed-time trajectory tracking control and setpoint regulation problems for dynamic positioning (DP) ships subject to unknown time-varying disturbances, system uncertainties, and actuator saturation. To meet the resistance of the low-frequency disturbances and system uncertainties, a continuous fixed-time disturbance observer (FTDO) based on integral sliding mode and fixed-time control is constructed. A nonlinear auxiliary dynamic system is introduced to mitigate the inconsistency between command forces and actual control forces, in which the feedback of the bias Δτ guarantees the input constraints for the design of the proposed controller. The explosion-of-complexity problem inherent in traditional backstepping is addressed based on a nonlinear first-order filter. Furthermore, a robust fixed-time control law with constraints is developed to track the predefined trajectory and the desired setpoint. Theoretical analyses demonstrate the fixed-time stability of the closed-loop system via Lyapunov analysis. Numerical simulation results illustrate the effectiveness and robustness of the proposed control approach.

Fixed-Time Stabilization of Leakage-Delayed Neural Networks Modeled by Delayed Filippov Systems: Leakage-Delay-Dependent Settling-Time

This paper considers the periodicity and fixed-time stabilization of discontinuous neural networks with time-varying leakage and discrete delays, which is more general. Before considering the stability, the existence of periodic solutions in the sense of Filippov should be proved. So, firstly, based on the set-valued mapping, coincidence theorem, Hölder inequality and supremum-infimum principle, the investigation on the leakage-delay-dependent periodic solutions is obtained, which can not only complement the periodic solutions of leakage-delayed neural networks, but also is absolutely different from the almost-periodic solution results. Secondly, by virtue of the integral inequality, new fixed-time stability lemmas of Filippov systems are established, which involve more relaxed assumptions and do not need to input extra parameters. Thirdly, leakage-delay-dependent results on fixed-time stabilization of the proposed neural networks are established via the new fixed-time stability lemmas under modified non-chattering control laws. It is worth mentioning that the settling-times are relevant to the leakage delays, which have not been reported in the literature. Finally, the validity of the proposed results is demonstrated by two numerical examples.

Event-Based Distributed Fixed-Time Resilient Control for Heterogeneous Vehicular Platoon Against Attack and Disturbances

This article is concerned with the issue of distributed adaptive fixed-time fuzzy resilient control (DAFTFRC) for the heterogeneous connected vehicular platoon (HCVP) system subject to deception attacks and unknown external disturbances. Firstly, an effective fixed-time disturbance observer (FTDO) is introduced to quickly estimate the unknown external disturbance of the platoon. Then, the DAFTFRC framework is designed to satisfy the internal stability and the string stability under the deception attacks in a settling time by introducing the improved event-triggered mechanism (IETM). Correspondingly, by employing the IETM, the inter-event execution intervals are prolonged, and the execution rate of the actuator can also be significantly reduced. Ample and rigorous theoretical analysis proves the internal stability and string stability in sense of the practical fixed-time stability. Finally, the effectiveness of the developed scheme is substantiated by the comparison examples and the SUMO-MATLAB joint simulation platform.

Spiking-free disturbance observer-based fixed-time sliding mode control of maximum power extraction from wind turbine

This paper proposes a new spiking-free fixed-time disturbance observer (DO)-based sliding mode control (SMC) scheme of maximum power extraction for the wind turbine system. First, a fixed-time DO is developed by using uniform robust exact differentiator (URED). Then, an SMC scheme is proposed by using the estimation of fixed-time DO and designing a spiking-free function. The proposed spiking-free fixed-time DO-based SMC scheme exhibits three attractive features: first, compared with existing scheme, the proposed scheme can guarantee the fast convergent performance under different initial system conditions based on the design of fixed-time stability. Second, by designing a novel spiking-free function, the potential spiking problem of fixed-time DO that occurs when observer gain is high and initial estimate states and initial true states are not equal is avoided. Third, the control input of proposed SMC is continuous, thus the undesirable chatter of conventional SMC is avoided. Finally, the attractive features of proposed scheme are illustrated based on simulation.

Prescribed Fixed-Time Adaptive Neural Control for Manipulators with Uncertain Dynamics and Actuator Failures

In this paper, a fixed-time adaptive neural control scheme is proposed to solve the prescribed tracking problem of robot manipulators in the presence of uncertain dynamics, and stuck-type actuator failures which are unknown in time, pattern, and values. Technically, the combination of neural networks and adaptive control is used to handle the uncertainties in system dynamics, an adaptive compensation mechanism is designed to accommodate the failures occurring in actuators, and also a systematic design procedure based on the prescribed performance bounds is presented to establish the conditional inequality for ensuring fixed-time stability. With our scheme, it can be proved rigorously that the tracking errors in joint space can always be kept within the prescribed bounds, and converge to a small region of zero in a bounded settling time, in addition to the closed-loop signal boundedness. The proposed scheme is validated through simulations.

Fixed-time stability of Cohen-Grossberg BAM neural networks with impulsive perturbations

This article concerns the problem of fixed-time stability (FXTS) of a Cohen-Grossberg bidirectional associative memory neural network (CGBAMNN) with destabilizing impulsive effects. A novel sufficient condition for the impulsive dynamical systems (IDSs) to be FXTS for destabilizing impulses is obtained. Different from the usual Lyapunov inequality for FXTS of IDSs, we have applied a new Lyapunov inequality to obtain the results under impulsive perturbations. Based on the average impulsive interval (AII) and the comparison principle, we have derived the results of this paper. Two types of continuous controllers: one with signum terms and another without signum terms, based on a new Lyapunov inequality, FXTS of CGBAMNN have been studied. The settling-time functions obtained in this article depend on the parameters of the impulsive sequences. Finally, two numerical examples, one is a cyber-physical system with deception attacks and another is a neural network, are given to validate the efficiency of our obtained theoretical results.

Fixed-time integral fast nonsingular terminal sliding mode control and its application to chaos suppression in gyros system

This paper proposes a novel control methodology to achieve fixed-time stabilisation for a class of three-order nonlinear systems based on fast nonsingular terminal sliding mode control. In this research, based on the combination of integral fast nonsingular terminal sliding mode (IFNTSM) surface and fixed-time control theory, a novel backstepping fast nonsingular terminal sliding mode (FNTSM) controller is being studied. The interests of this method are that the presented controller can not only maintain the characteristics of integral fast nonsingular terminal sliding mode control (IFNTSMC) but also has the advantages of fixed time convergence and fast transient response. Piecewise function is introduced to solve the singularity problem caused by negative exponential term. Our control strategy achieves the stabilisation performance within finite convergent time being independent of initial condition. The control scheme is applied to the gyros system with chaotic state and suppress its chaotic phenomenon. The theoretical results are supported by simulation results.