Nonsingular Terminal Sliding Mode Manifold Research Articles

Adaptive Robust Time-Varying Formation Control of Quadrotors under Switching Topologies: Theory and Experiment

This paper investigates a practical time-varying formation control method for quadrotors subjected to disturbances, uncertainties, and switching-directed topologies. A fully distributed formation control scheme is proposed using a linear-velocity independent position controller (LVIPC) and a nonsingular terminal sliding mode attitude controller (NTSMAC). A distributed observer is adopted to eliminate the measurement of linear-velocity states, and only local neighbor states are needed to realize formation flight. A time-varying nonsingular terminal sliding mode manifold is designed to suppress the reaching phase and ensure the finite-time convergence. Adaptive estimators are employed to remove the reliance on the prior knowledge of the upper bound of lumped uncertainties. It is then proven that all the closed-loop signals are bounded under the proposed method. Comparative experimental results based on a practical outdoor hardware solution are presented to confirm the effectiveness of the suggested control algorithm.

Event-triggered fixed-time distributed output feedback sliding mode cooperative control for multiple surface vessels with input saturation

Aiming at the problems of cooperative control for multiple surface vessels (MSVs), such as unknown environmental disturbances, unavailable velocities, model uncertainties, actuator saturation, and limited action times of the actuator, an event-triggered fixed-time distributed output feedback sliding mode cooperative control method with input saturation is proposed. The scheme ensures the practical fixed-time stability of the cooperative control system. First, a fixed-time extended state observer (FxESO) is designed to provide the estimations of velocities and lumped disturbances including unknown environmental disturbances and model uncertainties. Second, to deal with the actuator saturation, a fixed-time auxiliary dynamic system is designed. Third, a fixed-time non-singular terminal sliding mode manifold (FxNTSMM) is introduced to effectively eliminate singularity and improve chattering of the system. Finally, an event-triggered distributed controller based on FxNTSMM and FxESO is proposed. An event-triggered condition can avoid unnecessary actions of the actuator, and Zeno phenomenon is avoided by theoretical proof. In addition, the upper bound of the convergence time is independent of the initial state. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.

Adaptive nonsingular terminal sliding mode control of robot manipulator based on contour error compensation

To achieve accurate contour tracking of robotic manipulators with system uncertainties, external disturbance and actuator faults, a cross-coupling contour adaptive nonsingular terminal sliding mode control (CCCANTSMC) is proposed. A nonsingular terminal sliding mode manifold is developed which eliminates the singularity completely. In order to avoid the demand of the prior knowledge of system uncertainties, external disturbance and actuator faults in practical applications, an adaptive tuning approach is proposed. The stability of the proposed control strategy is demonstrated by the finite-time stability theory. Then, the developed controller combines adaptive nonlinear terminal sliding mode control (ANTSMC) of joint trajectory tracking and proportion–differentiation control of end-effector contour tracking by introducing the coupling factor between multiple axes based on Jacobian. Moreover, a unified framework of cross-coupling contour compensation and reference position pre-compensation is built. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control strategy.

Nonsingular Terminal Sliding Mode-Based Distributed Cooperative Event-Triggered Control for Multiple Surface Vessels Under Actuator Faults With Input Saturation

In this paper, a fixed-time distributed cooperative control under actuator faults with input saturation scheme is designed for multiple surface vessels (MSVs). Firstly, a fixed-time disturbance observer (FxDO) is introduced to observe unknown environmental disturbances and actuator faults (AF). Secondly, to deal with the actuator saturation, an improved nonlinear antiwindup compensator is introduced to compensate for the saturation effect of the actuator. Thirdly, a fixed-time fault-tolerant event-triggered control law with the actuator saturation is applied to cooperative control based on a fixed-time nonsingular terminal sliding mode manifold (FxNTSMM), and their cooperative errors can converge within fixed time. At the same time, the upper bound of convergence time is independent of the initial state. Finally, the stability analysis of the cooperative control system is given to prove that the system can realize the practical fixed time stability, and Zeno phenomenon is avoided by theoretical proof. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.

Fixed-Time Output Feedback Distributed Cooperative Event-Triggered Control for Multiple Surface Vessels With Prescribed Performance Constraints

This paper studies the distributed cooperative control problem for multiple surface vessels (MSVs) subject to unknown environmental disturbances, model uncertainties, unavailable velocities and prescribed performance constraints. Firstly, a fixed-time extended state observer (FxESO) is designed to provide the estimations of velocities and lumped disturbances (including unknown environmental disturbances and model uncertainties). Secondly, to improve the convergence performance of the MSVs, a hyperbolic cosecant prescribed performance function is incorporated into the cooperative control algorithm. Thirdly, a fixed-time event-triggered control law with prescribed performance constraint is applied to cooperative control based on a fixed-time nonsingular terminal sliding mode manifold (FxNTSMM), and the cooperative errors can converge within fixed time. Finally, by employing Lyapunov function theory, the stability of the closed-loop system is analyzed. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.

Barrier Function-based adaptive fast non-singular terminal sliding mode tracking control for marine vessels

In this paper, finite-time trajectory tracking problem of the marine vessels (MVs) disturbed by highly coupled nonlinearities and unknown ocean current is solved by developing a barrier function-based adaptive fast non-singular terminal sliding mode control (BFAFNTSMC) method. Salient features are as follows: (1) The defined fast non-singular terminal sliding mode manifold (FNTSM) which introduces the finite-time ocean current observer (OCO) is proposed to guarantee the finite-time sliding motion for mismatched disturbance attenuation. (2) By devising a novel log-type barrier function adaptive sliding mode reaching law (BFARL) based on single switching logic, the synovial variable will converge to and maintain in a predefined neighborhood of zero in a finite time, without overestimating the control gain. (3) Finite-time convergence of trajectory tracking errors to the predefined neighborhood of zero can be guaranteed, independently of the boundaries of the lumped nonlinearities. The proposed method exhibits the satisfied properties of tracking performance as well as chattering alleviation. Simulation results and comparisons are further presented to illustrate remarkable effectiveness of the proposed approach.

Time-Varying Nonsingular Terminal Sliding Mode control of Autonomous Surface Vehicle with predefined convergence time

This paper addresses the problem of trajectory tracking control of an Autonomous Surface Vehicle (ASV) with the presence of uncertainties and disturbances. First, a Time-Varying Nonsingular Terminal Sliding Mode (TV-NTSM) manifold is designed by incorporating a piecewise-defined function of time into a nonsingular terminal sliding mode (NTSM) manifold. As a result, the reaching phase that exists in traditional sliding mode is totally suppressed as well as the avoidance of the singularity problem. Then, a TV-NTSM controller is proposed to guarantee the convergence of the tracking errors to the origin in finite-time and to ensure the global robustness of the system with respect to large uncertainties and unknown environmental disturbances. To meet the mission requirement, an adequate method is given for the parameters system selection to guarantees the convergence of the tracking errors to the origin in prespecified time. Furthermore, an adaptive tuning law is introduced to estimate the unknown upper bounds of the lumped uncertainty, which is convenient for practical implementation. The stability of the closed-loop system is verified by Lyapunov theory and simulation results are carried out to prove the effectiveness of the proposed control algorithm.

Time‐varying nonsingular terminal sliding mode control for uncertain second‐order nonlinear systems with prespecified time

AbstractThis article proposes a time‐varying nonsingular terminal sliding mode (TSM) control for a class of uncertain second‐order nonlinear system and its application to n‐links rigid robotic manipulators. First, a time‐varying nonsingular terminal sliding manifold is developed by incorporating a piecewise‐defined function of time into a nonsingular TSM manifold. As a result, the singularity problem is avoided and the reaching phase existing in conventional TSM control is totally suppressed which ensures the global robustness of the system against uncertainties and disturbances. Moreover, adaptive tuning laws are developed to omit the requirement of prior knowledge of the upper bound of the lumped uncertainty. In particular, an effective method is provided for the parameters selection to meet a prespecified convergence time. Hence, the convergence time to the origin of the tracking errors can be specified in advance according to the mission requirements. The formulation of the controllers and the stability analysis are verified by Lyapunov theory. Simulation results and comparative studies are presented to demonstrate the effectiveness and the superiority of the proposed algorithms.

Adaptive type‐II fuzzy nonsingular fast terminal sliding mode controller using fractional‐order manifold for second‐order chaotic systems

AbstractA novel fuzzy adaptive finite‐time controller is designed for synchronization and control of the Duffing–Holmes and the gyroscope systems in the presence of uncertainty and external disturbance. The fractional‐order fast nonsingular terminal sliding mode manifold is used to ensure the finite‐time control, speed up the convergence rate, and address the singularity problem of the conventional terminal sliding mode controller. Also, the novel control law successfully reduces the chattering phenomenon. Adaptive biased type‐II fuzzy inference system is used to determine the optimal values of the switching control term. The adaptation rules of the novel fuzzy inference system are achieved based on Lyapunov stability theorem. Finally, by using numerical simulations, the effectiveness and superiority of the proposed control scheme are verified against some other methods.

Finite-time tracking control for autonomous underwater vehicle based on an improved non-singular terminal sliding mode manifold

This paper investigates the finite-time tracking problem for autonomous underwater vehicles (AUVs) in the presence of external disturbance and modelling uncertainty. A finite-time tracking control scheme is proposed based on an improved non-singular terminal sliding mode manifold. Firstly, in order to achieve finite-time stability and avoid singular problem, a continuous and smooth non-singular terminal sliding mode manifold is designed based on a piecewise function. And then a continuous control law is designed by indirectly estimating the bound of the general uncertainty, to compensate the external disturbance and modelling uncertainty. Based on the Lyapunov stability analysis, it is verified that the tracking error can converge to a certain range near zero in a finite time. Finally, the proposed control scheme is applied to ODIN AUV and compared with another two finite-time tracking controllers. Simulation results show the effectiveness of the proposed control scheme.

Novel Dynamic-Sliding-Mode-Manifold-Based Continuous Fractional-Order Nonsingular Terminal Sliding Mode Control for a Class of Second-Order Nonlinear Systems

A novel dynamic-sliding-mode-manifold-based continuous fractional-order nonsingular terminal sliding mode control is proposed for a class of second-order nonlinear systems. By designing the parameter in the continuous fractional-order nonsingular terminal sliding mode manifold as an exponential function of the tracking error, a dynamic sliding mode manifold can be obtained by adjusting the parameter online. Even if reference signals change, the parameter does not need repetitive offline optimization. By combining the fast-terminal-sliding-mode-type reaching law, the system states are attracted to the manifold quickly, enhancing the controller’s robustness. When a large initial error exists, the control system can still accelerate response and reduce overshoot simultaneously owing to the dynamic changing characteristic of the manifold. The stability and finite-time convergence of the closed-loop system are proven by the Lyapunov stability theory. Simulation results on SISO and MIMO nonlinear systems show that for different reference signals, the proposed method has a better tracking performance than the general fractional-order nonsingular terminal sliding mode control.

A new finite-time cooperative control algorithm for uncertain multi-agent systems

ABSTRACTIn this paper, the problem of fixed-time consensus tracking control is investigated for multi-agent networks with input uncertain dynamics under the undirected graph. First, a nonsingular terminal sliding mode manifold is proposed, with which the convergence time is globally bounded irrelevant to initial states. Then, with the aid of the observer method and sliding mode technique, the distributed nonsingular controller is designed for the underlying system to ensure that the consensus tracking errors go into sliding mode manifold and converge to origin within a desired time. Finally, examples are presented to verify the validity of the new control strategy.

Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

This paper addresses the kinematically optimal control problem of the mobile manipulators. Dynamic equations of the mobile manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end-effector. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. Such controllers apply a new non-singular Terminal Sliding Mode (TSM) manifold defined by a non-linear integral equality of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, the proposed Jacobian transpose control schemes are proved to be finite-time stable provided that some well-founded assumptions are fulfilled during the mobile manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a mobile manipulator that attains trajectory tracking by the end-effector in a two-dimensional task space and simultaneously minimises some objective function.

Chattering-free full-order recursive sliding mode control for finite-time attitude synchronization of rigid spacecraft

This paper investigates a quaternion-based finite-time cooperative attitude synchronization and tracking of multiple rigid spacecraft with a virtual leader subject to bounded external disturbances. Firstly, the communication network between followers is assumed to be an undirected graph and every follower can get a direct access to the virtual leader, by using two neighborhood attitude error signals, a novel chattering-free recursive full-order sliding mode control algorithm is proposed such that all follower spacecraft synchronize to the virtual leader in finite time. In the proposed algorithm, the sliding mode surface is constructed by two layers of sliding mode surfaces, which are called as the outer and the inner sliding mode surfaces. To achieve finite-time performance of sliding mode dynamics, the outer sliding mode surface is designed as a terminal sliding mode manifold, and the inner one is designed as a fast nonsingular terminal sliding mode manifold, respectively. Then, to reduce the heavy communication burden, a distributed recursive full-order sliding mode control law is designed by introducing a distributed finite-time sliding mode estimator such that only a subset of the group members has access to the virtual leader. Finally, a numerical example is illustrated to demonstrate the validity of the proposed results.

Fixed-time compliant motion/force control of robotic manipulators with environmental constraints

PurposeThe purpose of this paper is to design a new compliant motion/force control strategy for robotic manipulators with environmental constraints in the sense of fixed-time stability.Design/methodology/approachThis paper investigates a novel compliant motion/force control strategy for robotic manipulators with environmental constraints. By using the Lyapunov theory and fixed-time stability theory, a non-singular terminal sliding mode manifold is first established. Then, the compliant motion/force controller is designed, and relevant conditions are given for guaranteeing that the robotic manipulator can track the prescribed constrained trajectory while exerting a desired force to the environment in fixed-time. An illustrative example is presented to show the effectiveness of our proposed control strategy.FindingsBased on fixed-time stability theory, the desired compliant motion/force controller for robotic manipulators with environmental constraints is developed.Originality/valueCompared with most existing literature, the proposed fixed-time compliant motion/force control strategy can provide the upper bound of the settling time independent of the initial conditions in designing procedure and is more practical for the real-world applications.

Prescribed performance slide mode guidance law with terminal line-of-sight angle constraint against maneuvering targets

This paper proposes a new terminal homing guidance law with line-of-sight angle constraint for a missile to intercept a noncooperative maneuvering target by integrating prescribed performance control with sliding mode control. The newly proposed guidance law is derived analytically with a prescribed performance controller in combination with the continuous nonsingular terminal sliding mode manifold and the disturbance observer. The prescribed performance controller is designed with a new prescribed performance function to avoid undesired abrupt change in the derivative of prescribed performance variable. In addition to its robustness and preciseness, this new homing guidance law is able to attenuate a largely abrupt change in guidance commands due to driving the sliding mode variable whose initial derivative is close to zero to a desired residual set at the beginning of the terminal homing phase. Furthermore, the time-varying control gain of the new guidance law is analytically determined by terminal tolerance. Theoretical analysis and numerical simulations are conducted to demonstrate the effectiveness of this new guidance law.

Robust adaptive nonsingular terminal sliding mode control of MEMS gyroscope using fuzzy-neural-network compensator

To attenuate the effect of time-varying parameters, quadrature errors, and external disturbances and realize finite-time control, a robust adaptive nonsingular terminal sliding mode (NTSM) tracking control scheme using fuzzy-neural-network (FNN) compensator is presented for micro-electro-mechanical systems (MEMS) vibratory gyroscopes in this paper. By introducing a nonsingular terminal sliding mode manifold, a novel terminal sliding mode controller is designed for MEMS gyroscopes, while ensuring the control system could reach the sliding surface and converge to equilibrium point in a finite period of time from any initial state. In the presence of unknown model uncertainties and external disturbances, an adaptive fuzzy-neural-network controller is employed to compensate such system nonlinearities and improve the tracking performance. Online fuzzy-neural-network weight tuning algorithms are derived in the sense of Lyapunov stability theorem to guarantee the network convergence as well as stable control performance. Numerical simulations for a MEMS gyroscope are provided to justify the claims of the proposed adaptive fuzzy-neural-network control scheme and demonstrate the satisfactory tracking performance and robustness.

Chattering-free adaptive fast convergent terminal sliding mode controllers for position tracking of robotic manipulators

The paper documents a new continuous adaptive fast terminal sliding mode control approach for position tracking of robotic manipulators. Combining linear sliding mode and terminal sliding mode, a fast nonsingular terminal sliding mode manifold is presented. Considering the discontinuous property of the sign function, which is often used in traditional sliding mode controller and will result in high-freqsency chattering in the control channel, the proposed controller adopts the continuous saturation function for chattering elimination. Besides the continuous property, convergence to the origin asymptotically and in finite time can be guaranteed in theory with the proposed controller, which is quite different from traditional boundary layer technique, where only bounded motion around the sliding manifold can be ensured. For asymptotic stability, it is only required that the lumped uncertainty is bounded, but the upper bound may be unknown by virtue of the designed adaptive methodology. The obtained results are applied to the problem of position tracking for robotic manipulators. Detailed simulations with some comparisons under various conditions demonstrate the effectiveness of the proposed method.

Smooth second-order nonsingular terminal sliding mode control for reusable launch vehicles

Purpose – The purpose of this paper is to present a sliding mode attitude controller for reusable launch vehicle (RLV) which is nonlinear, coupling, and includes uncertain parameters and external disturbances. Design/methodology/approach – A smooth second-order nonsingular terminal sliding mode (NTSM) controller is proposed for RLV in reentry phase. First, a NTSM manifold is proposed for finite-time convergence. Then a smooth second sliding mode controller is designed to establish the sliding mode. An observer is utilized to estimate the lumped disturbance and the estimation result is used for feedforward compensation in the controller. Findings – It is mathematically proved that the proposed sliding mode technique makes the attitude tracking errors converge to zero in finite time and the convergence time is estimated. Simulations are made for RLV through the assumption that aerodynamic parameters and atmospheric density are perturbed. Simulation results demonstrate that the proposed control strategy is effective, leading to promising performance and robustness. Originality/value – By the proposed controller, the second-order sliding mode is established. The attitude tracking error converges to zero in a finite time. Meanwhile, the chattering is alleviated and a smooth control input is obtained.

Time-varying nonsingular terminal sliding mode control for robot manipulators

In this paper, a time-varying nonsingular terminal sliding mode (T-NTSM) controller is proposed and modified for the rigid robot manipulators with parametric uncertainties and external disturbances. First, in order to eliminate the reaching phase, a novel T-NTSM manifold is proposed by incorporating a piecewise defined function of time into a nonsingular terminal sliding mode manifold. Then a T-NTSM controller is derived from such a sliding surface, by which the robustness is ensured during the entire response of the system, and the convergence time can be chosen in advance. An especially effective method is provided for parameter selection to meet the convergence time requirement. Subsequently, a modified T-NTSM controller is proposed to enhance performance by introducing a time-varying gain in the proposed T-NTSM manifold. The modified controller ensures faster convergence rate and smaller control input amplitude. Finally, the proposed controllers are applied in the control of a two-link manipulator. All of the simulation results demonstrate the effectiveness of the proposed control methods.