Fixed-time Terminal Sliding Mode Control Research Articles

Cascaded robust fixed-time terminal sliding mode control for uncertain cartpole systems with incremental nonlinear dynamic inversion

This paper proposes a cascaded fixed-time terminal sliding mode controller (TSMC) for uncertain underactuated cartpole dynamics using incremental nonlinear dynamic inversion (INDI). Leveraging partial linearization and prioritizing pole dynamics for internal tracking, the proposed controller achieves efficient stabilization of the cart upon convergence of the pole. Stability analysis is carried out using Lyapunov stability theorem, proving that the proposed controller stabilizes the state variables to an arbitrarily small neighborhood of the equilibrium in fixed-time, along with the suboptimality (steady-state error), existence and uniqueness of the solutions. The INDI is also integrated into TSMC to further improve the robustness while suppressing the conservativeness of conventional TSMC. The stability of INDI is rigorously proved using sampling-based Lyapunov function under sampling-based control realm. The simulation results illustrate the superiority of the proposed method with comparison and ablation studies.

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.

Nonsingular fixed‐time adaptive neural terminal sliding mode control for a class of uncertain second‐order nonlinear systems

AbstractIn this article, the fixed‐time adaptive neural tracking control for a class of second‐order uncertain nonlinear systems is investigated. First, a novel fast fixed‐time stable (FTS) autonomous system with the switched nonlinear term is constructed. Compared with the traditional FTS system (FTSS), the state of the proposed fast FTS system has a faster convergence rate for arbitrary initial state. Then, a fixed‐time terminal sliding mode control (FTSMC) scheme is developed based on the novel fast FTSS, and the tracking error of the closed‐loop system is verified to converge to the origin within a fixed time. The proposed FTSMC scheme not only realizes the upper bound of the settling time independent of the initial conditions but also completely avoids the singularity problem by introducing the switching sliding mode surface. Moreover, an adaptive neural FTSMC scheme is developed for the general uncertain nonlinear systems with the help of the approximation capabilities of neural networks (NNs). The feasibility of the presented control strategy is examined by the simulation of a single‐link robot system.

A nonlinear system of hybrid fractional differential equations with application to fixed time sliding mode control for Leukemia therapy

In this article, a coupled nonlinear problem of hybrid fractional differential equations (HFDEs) is presented for the qualitative work and numerical results. Two types of operators are involved in the research problem. One of them is DβrR which represent Riemann–Liouville's (RL) fractional derivatives while the operator L(DϱrR) is a series operator and DϱrR's are RL operators such that βr,ϱr∈(0,1]. These operators are joined by Φp operator. As a result, we have a nonlinear coupled system of FDEs. The newly established nonlinear system is studied for the existence, uniqueness criteria, stability of the solutions, and numerical computations. For the theoretical results, we take help from the available literature about the fixed point (FP) techniques. Then a computational scheme is developed with the help of Lagrange's interpolation technique. An application of the problem as a particular case is presented in the sense of the Leukemia mathematical model. The model presents the infection propagation. Leukemia can be managed by providing a chemotherapeutic treatment generally accepted to be safe, and a fractional-order fixed-time terminal sliding mode control has been developed to achieve this goal of removing Leukemic cells while keeping a sufficient number of normal cells. In order to evaluate the proposed controller stability, the fixed-time Lyapunov stability theory is employed. To better illustrate the study, comparison simulations are shown, demonstrating that the suggested control approach has higher tracking and convergence performance.

A new fixed-time terminal sliding mode control for second-order nonlinear systems

In this paper, the fixed-time control for a class of second-order nonlinear systems with matched disturbance is addressed by using terminal sliding mode control technique. To improve the control performance of traditional fixed-time control method, a new fixed-time stability theorem is constructed by introducing a simple linear term, and theoretical analysis shows that the proposed control method provides faster convergence speed and more accurate estimate of the upper bound of settling time. Moreover, the practical fixed-time stability is also discussed in details. Based on the proposed fixed-time stability theorem, a fixed-time terminal sliding mode controller for a class of second-order nonlinear system is designed to obtain a bounded settling time independently of the initial conditions of the system. Simulations are carried out to verify the feasibility of the proposed control method.

Nonlinear system controlled using novel adaptive fixed-time SMC

<abstract><p>This work introduces a novel adaptive fixed-time control strategy for nonlinear systems subject to external disturbances. The focus pertains to the introduction of the fixed-time terminal sliding mode control (FxSMC) technique. The proposed scheme exhibits rapid convergence, chatter-free and smooth control inputs, and stability within a fixed time. The utilization of an adaptive methodology in combination with the FxSMC yields the proposed strategy. This approach is employed to address the dynamic system in the presence of external disturbances. The results obtained from the Lyapunov analysis will provide insights into the stability of the closed-loop system in a fixed time. In the end, the simulation results are presented in order to assess and demonstrate the effectiveness of the methodology.</p></abstract>

Qualitative analytical results of complex order nonlinear fractional differential equations with robust control scheme

In this manuscript, our work was about a qualitative study for a class of multi-complex orders nonlinear fractional differential equations (FDEs). Our methodology utilized the topological degree theory and studied a novel operator tailored for non-singular FDEs with $ \mathrm{T} $-Riemann-Liouville (T-RL) fractional order derivatives. The primary objective was to prove the existence and uniqueness of solutions for both initial and boundary value problems within the intricated framework. With the help of topological degree theory, we contributed to a wider understanding of the structural aspects governing the behavior of the considered FDE. The novel operator proposing for non-singular FDEs added a unique dimension to our analytical problem, offering a versatile and effective means of addressing the challenges posed by these complex systems for their theoretical analysis. For the practical implications of our theoretical framework, we presented two concrete examples that reinforced and elucidated the key concepts introduced. These examples underscored our approach's viability and highlighted its potential applications in diverse scientific and engineering domains. Through this comprehensive exploration, we aimed to contribute significantly to advancing the theoretical foundation related to the study of multi-complex nonlinear FDEs. Moreover, a fixed-time terminal sliding mode control (TSMC) has been developed. This proposed control strategy for eliminating leukemic cells while maintaining normal cells was based on a chemotherapeutic treatment that was not only effective but also widely acknowledged to be safe. This strategy was evaluated using the fixed-time Lyapunov stability theory, and simulations were included to illustrate its performance in terms of tracking and convergence.

Fixed-time terminal sliding mode control with arbitrary convergence time for a class of chaotic systems applied to a nonlinear finance model

Fixed-time terminal sliding mode control with arbitrary convergence time for a class of chaotic systems applied to a nonlinear finance model

A Model-Free-Based Control Method for Robot Manipulators: Achieving Prescribed Performance and Ensuring Fixed Time Stability

This paper addresses three significant challenges in controlling robot manipulators: improving response time, minimizing steady-state errors and chattering, and enhancing controller robustness. It also focuses on eliminating the need for computing the robot’s dynamic model and unknown functions, as well as achieving global fixed-time convergence and the prescribed performance for the control system. To achieve these objectives, a fixed-time sliding mode function is designed, which uses transformation errors to achieve prescribed control performance, with adjustments made to the maximum overshoot, convergence time, and tracking errors to keep them within predefined bounds. Additionally, a radial basis function neural network (RBFNN) is used to eliminate the need for knowledge of the robot’s dynamical properties and uncertain terms, which also reduces negative chattering. Finally, a novel fixed-time terminal sliding mode control (TSMC) algorithm is developed for robot manipulators without using their dynamical model. The fixed-time stability of the control system is thoroughly demonstrated by applying Lyapunov criteria and conducting simulations on a robot manipulator to showcase its effectiveness.

Fractional-order Fixed-time Non-singular Sliding Mode Control for Nonlinear Robotic Manipulators

In this study, fractional-order non-singular fixed-time terminal sliding mode control (FoFxNTSM) for nonlinear robotic manipulators in the existence of uncertainties and external disturbances is examined. To begin, the concept of fractional-order fixed-time non-singular terminal sliding mode control is introduced. This method combines the benefits of NTSM (which provides fast convergence speed, smooth and singularity-free control inputs) with the advantages of a fractional-order constants (which improves position tracking effectiveness). Lyapunov analysis yields the fixed-time stability of the closed-loop system. To evaluate and illustrate the performance of the proposed strategy, the relevant simulation results are presented.

Adaptive Fault Tolerant Non-Singular Sliding Mode Control for Robotic Manipulators Based on Fixed-Time Control Law

This paper presents a fault tolerant scheme employing adaptive non-singular fixed-time terminal sliding mode control (AFxNTSM) for the application of robotic manipulators under uncertainties, external disturbances, and actuator faults. To begin, non-singular fixed-time terminal sliding mode control (FxNTSM) is put forth. This control method uses non-singular terminal sliding mode control to quickly reach fixed-time convergence, accomplish satisfactory performance in tracking, and produce non-singular and non-chatter control inputs. Then, without knowing the upper bounds beforehand, AFxNTSM is used as a reliable fault tolerant control (FTC) to estimate actuator faults and unknown dynamics. The fixed-time stability of the closed-loop system is established by the theory of Lyapunov analysis. The computer simulation results of the position tracking, control inputs, and adaptive parameters are presented to verify and illustrate the performance of the proposed strategy.

Approximate continuous fixed-time terminal sliding mode control with prescribed performance for uncertain robotic manipulators

Approximate continuous fixed-time terminal sliding mode control with prescribed performance for uncertain robotic manipulators

Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator

In this paper, fast global fixed-time terminal sliding mode control for the synchronization problem of a generalized class of nonlinear perturbed chaotic systems has been investigated with the application of memristor-based oscillator in the presence of external disturbances and unmodeled dynamics. In the fixed-time control strategy, unlike conventional asymptotic or finite-time approaches, convergence time is not related to the initial conditions. In the designed global fixed-time controller, both the sliding phase and reaching phase have fixed-time convergence characteristics and consequently, via the proposed strategy, precise synchronization of the master-slave systems is accomplished within fixed convergence time. The fast fixed-time synchronization problem of the nonlinear memristor chaotic system (MCS) has been investigated. In the first stage, an in-circuit emulator (ICE) for the considered memristor is utilized in order to apply on the defined MCSs. In the next stage, according to the considered ICE, the dynamical structure of the MCS is formulated along with the fixed-time synchronization problem which is efficiently addressed via the designed controller in the presence of external disturbances and unmodeled dynamics. Finally, the strength and validity of the theoretical outcomes are confirmed through numerical simulations.

Trajectory planning and low-chattering fixed-time nonsingular terminal sliding mode control for a dual-arm free-floating space robot

AbstractThis paper addresses fixed-time trajectory tracking for a dual-arm free-floating space robot (FFSR) with the large initial errors and bounded uncertainty. A wrist-based trajectory planning method is improved by fixed-time stability to fast eliminate the error caused by singularity. Then, a novel low-chattering and global-nonsingular fixed-time terminal sliding mode control strategy is studied by state approaching angle and switching sliding mode; the practical fixed-reachable Lyapunov stability analysis is presented for a mechanical control system. In the end, the proposed trajectory planning method and controller are combined to improve the tracking accuracy of end-effector to the nanoscale. Simulation results validate the effectiveness of the proposed methodologies.

Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control

• The synchronization of second-order chaotic systems is investigated. • A novel fixed-time adaptive sliding mode control scheme is proposed. • A new type of fixed-time nonsingular sliding mode surface is developed. • The semi-global fixed-time stability of the resulting closed-loop system is proved. In this paper, a novel fixed-time adaptive sliding mode control scheme is proposed for the synchronization of second-order chaotic systems with system uncertainties and external disturbances. First, a new type of fixed-time nonsingular sliding mode surface is developed based on the bi-limit homogeneous theory. Then, on the basis of the fixed-time sliding mode surface, the fixed-time adaptive sliding mode controller is designed by integrating the fixed-time terminal sliding mode control with the parametric adaptation technique. Finally, rigorous theoretical analysis for the semi-global fixed-time stability of the resulting closed-loop system is provided. A distinct feature of the proposed controller is that it can guarantee the synchronization tracking errors converge to the arbitrarily small neighbourhood of zero in fixed time even in the presence of lumped disturbances. To the best of the authors’ knowledge, there are relatively few existing controllers can achieve such excellent performance in the same conditions. Two simulation examples are performed to illustrate the effectiveness and benefits of the proposed control scheme.

Fixed-time terminal sliding mode control of spinning tether system for artificial gravity environment in high eccentricity orbit

In this paper a new strategy is introduced to produce an artificial gravity environment by spinning tether system (STS) in high eccentricity transfer orbit. Compared with other common artificial gravity environment methods, spinning tether system has simple structure, light weight and suitable spin velocity, which is more favorable for the spacecraft to generate the artificial gravity in the weightless space. The mathematical model of the spinning tether system is established by the second type of Lagrangian equation firstly. Then, the tension control law and the tangential thrust control law of tether system are designed. Through the mutual coordination of both control law, a method of Variable Moment-of-Inertia and Angular Momentum is realized which makes the tether system spin along the expected spinning velocity in most of the processes of uniform velocity development by constant tangential thrust. With the end of development, the artificial gravity environment level on the spacecraft also met the expected requirements, and the nominal trajectory curve of STS under the high-eccentricity transfer orbit was obtained. Finally, considering the rapidity of convergence time, a fixed time terminal sliding mode controller is designed to control the closed-loop trajectory curve of the tether system.

Adaptive Fixed-Time Terminal Sliding Mode Control on SE(3) for Coupled Spacecraft Tracking Maneuver

In this paper, a reaching law-based adaptive fixed-time terminal sliding mode control law, which is used for coupled spacecraft tracking maneuver in the presence of large inertia parametric uncertainties and external disturbances, is proposed. The coupled 6-DOF kinematics and dynamics for spacecraft motion are modeled on Lie group SE(3). The relative configuration is expressed by a local coordinate (exponential coordinate) of SE(3). In order to estimate the inertia parameters and external disturbances, we also propose a novel adaptive update law, which can make the control law be applied without the inertia parameters of the spacecraft a priori. Fixed-time convergence property of the closed-loop feedback system is proved in the framework of Lyapunov. Numerical simulations are performed to demonstrate the performances of the proposed control scheme for coupled spacecraft tracking maneuver.

Time-Dependent Global Nonsingular Fixed-Time Terminal Sliding Mode Control-Based Speed Tracking of Permanent Magnet Synchronous Motor

This paper studies global nonsingular fixed-time terminal sliding mode control (GNFTSMC) for a second-order uncertain permanent magnet synchronous motor (PMSM) system to further improve its speed tracking performance. The newly proposed GNFTSMC consists of a time-dependent terminal sliding surface and a piecewise continuous sliding mode control law. By a time-dependent function constructed from the initial conditions of the system and a predefined time, the sliding surface is always reached at the initial instant and forced to a traditional fast terminal sliding surface after the predefined time. Based on Filippov's stability principles, the globally fixed-time stability of the GNFTSMC is proved. Furthermore, a priori time independent of the initial conditions is derived to estimate the boundary of the settling time of the closed control loop. Then, the control law is analyzed to be always nonsingular. Thus, the GNFTSMC-based speed controller for the PMSM speed tracking system is developed. Finally, simulations are conducted for the proposed controller and other terminal sliding mode controllers. The results show that compared to the other controllers, the PMSM system based on GNFTSMC displays improved performance characteristics of faster speed response, smaller chattering and higher current efficiency.

Neural network‐based multivariable fixed‐time terminal sliding mode control for re‐entry vehicles

This study develops a neural network (NN)-based multivariable fixed-time terminal sliding mode control (MFTTSMC) strategy for re-entry vehicles (RVs) with uncertainties. A coupled MFTTSMC scheme is designed for the attitude system on the basis of feedback linearisation. A saturation function is introduced to avoid the singularity problem. Adaptive NNs are employed to approximate the uncertainties in RVs, thus alleviating chattering without sacrificing robustness. The whole closed-loop system is proven to be bounded and tracking errors are fixed-time stable. Simulations verify the effectiveness of the proposed strategy.

Synchronization of single-degree-of-freedom oscillators via neural network based on fixed-time terminal sliding mode control scheme

In this paper, the synchronization problem is investigated for two single-degree-of-freedom oscillators via neural network based on fixed-time terminal sliding mode control. First, a fixed-time terminal sliding mode is constructed. Then, in order to deal with the unknown function in master system, the neural network technique is introduced. Combining fixed-time terminal sliding mode surface and adaptive control scheme plus neural network technique, an adaptive fixed-time terminal sliding mode controller is presented. The stability of the closed-loop system is analyzed. Finally, simulation results are provided to demonstrate the effectiveness of the proposed two control strategies.