Fixed-time Stability Research Articles

Cluster formation tracking of networked perturbed robotic systems via hierarchical fixed-time neural adaptive approach

This paper investigates the fixed-time cluster formation tracking (CFT) problem for networked perturbed robotic systems (NPRSs) under directed graph information interaction, considering parametric uncertainties, external perturbations, and actuator input deadzone. To address this complex problem, a novel hierarchical fixed-time neural adaptive control algorithm is proposed based on a hierarchical fixed-time framework and a neural adaptive control strategy. The objective of this study is to achieve accurate CFT of NPRSs within a fixed time. Specifically, we design a distributed observer algorithm to estimate the states of the virtual leader within a fixed time accurately. By using these observers, a neural adaptive fixed-time controller is developed in the local control layer to ensure rapid and reliable system performance. Through the use of the Lyapunov argument, we derive sufficient conditions on the control parameters to guarantee the fixed-time stability of NPRSs. The theoretical results are eventually validated through numerical simulations, demonstrating the effectiveness and robustness of the proposed approach.

Finite-time and fixed-time stability for nonlinear systems via aperiodically intermittent control

Finite-time and fixed-time stability for nonlinear systems via aperiodically intermittent control

Fixed-time second-order sliding mode output feedback trajectory tracking control for an autonomous surface vehicle with model uncertainties and prescribed performance

This paper investigates the fixed-time trajectory tracking control problem of autonomous surface vehicle system with asymmetric performance constraints. The external disturbances, model uncertainties and the difficulty of velocity measurement are all taken into account in the controller design. Asymmetric performance constraints are firstly studied to improve the transient and steady-state performance of the tracking error system. Next, a fixed-time extended state observer is developed to estimate the unknown velocity and external disturbances. Both the fixed-time first-order and the second-order PID-type sliding surfaces are designed. Further, two continuous output feedback controllers are built to achieve high control accuracy and low energy consumption and to achieve fixed-time stability of the closed-loop system. Finally, abundant simulations for CyberShip II demonstrate the effectiveness of the proposed algorithms.

Second-order DSC-based adaptive fuzzy tracking control for uncertain unmanned helicopter with fixed-time stability

Second-order DSC-based adaptive fuzzy tracking control for uncertain unmanned helicopter with fixed-time stability

Design of fixed-time sliding mode control using variable exponents

This paper proposes the design of a robust fixed-time sliding mode controller for a second-order nonlinear system with matched and unmatched uncertainties. First, a fixed-time stable scalar dynamics with a variable exponent is introduced. We establish the global fixed-time stability results for the proposed dynamics using Lyapunov analysis. The maximum convergence time has been derived in terms of the design parameters, which is independent of the initial conditions. These results are then extended to solve the robust fixed-time stabilization for uncertain nonlinear second-order system. Specifically, we proceed with the sliding mode control design, where the sliding surface and the control law are motivated by the proposed scalar dynamics. Moreover, the proposed design is free from singularity and guarantees fixed-time robust stabilization. Simulation results with comparative analysis has been included. Further, experimental validation on a single link manipulator is provided to demonstrate the performance of the proposed approach.

A fast fixed-time backstepping control method for systems with mismatched disturbances

In this paper, a fast fixed-time backstepping control approach is developed for systems with mismatched disturbances. A novel fast fixed-time disturbance observer (FFTDO), which is convergent within fixed time regardless of initial conditions, is designed to efficiently estimate and compensate the disturbances. On the basis of FFTDO, a novel fast fixed-time backstepping control scheme is proposed, which can guarantee fast fixed-time convergence and high steady-state precision. In addition, a novel fixed-time filter is used to circumvent the problem of “explosion and complexity,” and to ensure overall fixed-time convergence. The fixed-time stability of the closed-loop system under the proposed controller is proved by the Lyapunov stability theory. The simulation results are carried out to confirm the feasibility and superiority of the proposed control strategy.

Adaptive model-free disturbance rejection for continuum robots

This paper presents two model-free control strategies for the rejection of unknown disturbances in continuum robots. The strategies utilize a neural network-based approximation technique to estimate the uncertain Jacobian matrix using position measurements. The first strategy is designed for periodic disturbances and employs an adaptive model-free controller in conjunction with an adaptive disturbance observer. The second strategy is designed for robustness against arbitrary disturbances and employs time-varying input and update law gains that grow monotonically, resulting in the achievement of asymptotic, exponential, and prescribed-time reference trajectory tracking. The notion of fixed-time stabilization in prescribed time is particularly noteworthy, as it allows for the predefinition of a terminal time, independent of initial conditions and system parameters. A formal stability analysis is presented for each strategy, and the strategies are both tested experimentally with a concentric tube robot subject to unknown disturbances.

Fixed-time self-triggered fuzzy adaptive control of N-link robotic manipulators

This paper studies the fixed-time fuzzy adaptive self-triggered control of n-link robotic manipulators. To achieve fixed-time stability, a fuzzy adaptive fixed-time control algorithm is proposed by reconstructing the self-triggered controller and using the singularity-free function, which avoids the singularity problem and obtains fixed-time stability. Meanwhile, the self-triggered mechanism reduces the communication resources between the actuator and the controller, improving the system's transmission efficiency. Through the above thoughts, a kind of fixed-time fuzzy adaptive controller based on the self-triggered mechanism is designed, which guarantees that the tracking error of each joint converges to the prescribed range within a fixed time. Finally, the effectiveness of the proposed algorithm is verified by a simulation example of the two-link robotic manipulator.

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Enhanced tracking control for n-DOF robotic manipulators: A fixed-time terminal sliding mode approach with time delay estimation

This work proposes a fixed-time terminal sliding mode control scheme with time delay estimation (FxTSM-TDE) for unknown nonlinear robotic systems under uncertainties and unknown bounded disturbances. The idea of the fixed-time terminal sliding mode control method (FxTSM) is thoroughly explained and analyzed. The FxTSM approach has been used to achieve nonsingular fixed-time control, non-chatter control inputs, and superior trajectory tracking performance. Then, the proposed approach for estimating the unknown robot dynamics utilizes the TDE approach. The Lyapunov analysis is used to establish the fixed-time stability of the system. The effectiveness of the suggested approach is evaluated, demonstrated, and contrasted with the existing control schemes by illustrating the results of the proposed method's enhanced performance in tracking accuracy, robustness, and convergence speed when implemented in robotic manipulator dynamics. The results indicate that the existing scheme has corresponding root mean square (RMS) error values of 0.0235 and 0.0283, while the proposed scheme has values of 0.0178 and 0.0188, respectively.

Practical fixed-time non-singular sliding mode control of second order nonlinear dynamic systems with chattering and overshooting avoidance

This paper introduces a Practical Fixed-Time Stabilization technique (PFxT) designed for a specific class of nonlinear second-order systems. The closed-loop systems, when appropriately parameterized, exhibit convergence within a predetermined time frame to a confined region near the origin. This outcome is achieved by amalgamating a nonlinear sliding mode approach with a practical fixed-time tracking virtual trajectory. The control algorithmś design incorporates considerations for overshoot reduction and chattering cancellation. Furthermore, the Lyapunov method is employed to establish the practical fixed-time stability of the proposed solution, providing insights into the limits within which the algorithm can be effectively deployed. To complete the algorithm specification, a parameter selection approach is introduced, enabling customization of the desired settling time. Comprehensive simulations are conducted to validate the effectiveness and viability of the proposed PFxT technique.

Fixed-time attitude control for hypersonic morphing vehicles: A dynamic memory event-triggering approach

This paper focuses on achieving fast attitude tracking and resource preservation for hypersonic morphing vehicles (HMVs) in continuous morphing stages. Firstly, the most remarkable feature of an HMV are the morphing wings, leading to dramatic aerodynamic property changes. As a result, fast tracking and excellent adaptation to various morphing statuses are necessary to guarantee the success of flight missions. Thus, this work employs the fixed-time stability theory to establish a high-performance controller, including variable exponent coefficients. Compared to the traditional constant exponent coefficient-based methods, some singularity problems are avoided, and the global fixed-time stability is ensured. Then, in order to implement the control input in a low-resource occupation, the dynamic event-triggering mechanism is presented to provide a flexible updating policy. The proposed event-triggering technology has a more concise and efficient structure than the traditional methods. In this case, the controller and the dynamic variable of the event-triggering method simultaneously adopt the exponent coefficients. Finally, the closed-loop stability is proven via the Lyapunov thesis, and simulation results show the effectiveness and the advantage of the proposed control strategy.

Fixed-time active fault-tolerant control for dynamical systems with intermittent faults and unknown disturbances

In this article, the problem of fixed-time active fault-tolerant control is investigated for dynamical linear systems with intermittent faults and unknown disturbances. Unlike traditional active fault-tolerant control, fixed-time control is taken into account in this article since intermittent faults appear and disappear within a certain period of time. The entire active fault-tolerant control framework is composed of fault detection, fault isolation, fault and state estimation as well as the reconfigurable controller. Using the homogeneity-based observers, states and faults are well estimated and a fault diagnosis scheme is proposed for the sake of detecting and isolating intermittent faults in a fixed time. The fault-tolerant controller, which provides global practical fixed-time stability of the closed-loop system, has two switching states corresponding to the appearance and disappearance of intermittent faults. As a consequence, intermittent faults are compensated via the designed active fault-tolerant control method and the system reaches practical stability with the entire convergence time bounded in a fixed time. Finally, two examples are exploited to demonstrate the effectiveness of theoretical results.

Resilient Neuroadaptive Distributed Fixed-Time Attitude Coordination Control for Multiple Spacecraft.

This work studies the attitude coordination tracking problem for multiple spacecraft with consideration of unintended faults (communication link faults and actuator faults), inertial uncertainties, and external disturbances under a directed communication graph. A resilient neuroadaptive distributed fixed-time control scheme is investigated to solve this challenging problem. First, an improved adaptive distributed observer is established for followers to estimate the states of the leader when considering communication link faults. The proposed observer improves the resilience against communication link faults. Subsequently, to further cope with the problem of actuator faults, inertial uncertainties, and external disturbances, based on the proposed observer and the technique of adding a power integrator, a neuroadaptive distributed fixed-time attitude coordination controller is developed. Unlike the existing controllers, the proposed one requires less information when dealing with faults and lumped uncertainties, and has a lower-computational cost. Moreover, the fixed-time stability of the closed-loop system is ensured under the designed resilient neuroadaptive distributed control scheme. Finally, comparative simulations are carried out to manifest the effectiveness of the investigated coordination control method.

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 fractional-order sliding mode controller with disturbance observer for U-tube steam generator

Water level control of a U-tube steam generator plays a critical and challenging role in ensuring safe and reliable operation for a pressurized-water reactor-type nuclear power plant, as both excessively high and low water level in the U-tube steam generator would affect the normal operation of the nuclear power plant and even lead to unplanned shutdown events. This work presents a fixed-time fractional-order sliding mode water level controller coupled with a fixed-time disturbance observer, aiming to further improve the water level control performance under full operating conditions, considering uncertainties and actuator saturation. The proposed scheme is formulatedbased on the popular Irving water level model with uncertainties and the pre-existing actual water level control framework, while at the same time incorporating the benefits of the state-of-the-art anti-windup techniques, disturbance observer-based feedforward compensation techniques, fractional-order calculus, sliding mode control techniques, and fixed-time stability theorem, such that the transient water level response and steady-state control accuracy can be further enhanced even in the presence of uncertainties and actuator saturation phenomenon. It is theoretically proved that under the proposed scheme, both the estimation error of the uncertainties and the water level control error can be driven to zero within a fixed time regardless of their initial values by Lyapunov’s theorem. Meanwhile, simulation studies, involving the comparisons with a real-world adopted water level controller and a pre-existing integer-order sliding mode water level controller coupled with an uncertainty estimator, reveal the feasibility and superiority of the proposed approach.

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.

Adaptive fixed-time TSM for uncertain nonlinear dynamical system under unknown disturbance.

For nonlinear systems subjected to external disturbances, an adaptive terminal sliding mode control (TSM) approach with fixed-time convergence is presented in this paper. The introduction of the fixed-time TSM with the sliding surface and the new Lemma of fixed-time stability are the main topics of discussion. The suggested approach demonstrates quick convergence, smooth and non-singular control input, and stability within a fixed time. Existing fixed-time TSM schemes are often impacted by unknown dynamics such as uncertainty and disturbances. Therefore, the proposed strategy is developed by combining the fixed-time TSM with an adaptive scheme. This adaptive method deals with an uncertain dynamic system when there are external disturbances. The stability of a closed-loop structure in a fixed-time will be shown by the findings of the Lyapunov analysis. Finally, the outcomes of the simulations are shown to evaluate and demonstrate the efficacy of the suggested method. As a result, examples with different cases are provided for a better comparison of suggested and existing control strategies.

A new fixed-time sliding mode control scheme for synchronization of chaotic systems

Chaotic synchronization is crucial in the field of secure communication, and fixed-time synchronization has realistic application prospects and demands. Aiming at the traditional sliding mode synchronization control method with chattering problem, based on the Lyapunov stability theory and incorporating the continuous time fixed time stability theorem, this paper proposed a new fixed-time sliding mode control scheme for synchronization of chaotic systems. The traditional finite-time sliding mode synchronization is compared with the proposed fixed-time sliding mode synchronization scheme and the results are discussed. The efficacy of the controller is validated using MATLAB simulations, which eliminates the chatter problem in the traditional sliding mode synchronization scheme and has the advantage of short synchronization time. In addition, the parameters of the controller can be set flexibly, which is an advantage of the fixed-time synchronous control scheme.

Internal/Boundary Control-Based Fixed-Time Synchronization for Spatiotemporal Networks.

This article is concerned about fixed-time (FT) synchronization of spatiotemporal networks (STNs) with the Robin boundary condition. Above all, a switching-type FT stability theorem and an integral inequality are established, which provide a novel theoretical tool for the rigorous analysis of FT control in STNs. Subsequently, three kinds of nontrivial power-law controllers are developed which are separately acted on the interior, the boundary, and the whole of the spatial domain. Based on these control schemes and Lyapunov-like method, several flexible criteria are obtained to achieve FT synchronization of STNs, and the upper bound of the synchronization time is explicitly estimated. Note that, the derived results here are also perfectly applicable to STNs with Neumann or Dirichlet boundary condition. Several illustrate examples are presented at final to confirm the developed controllers and criteria.