Adaptive Sliding Mode Control Law Research Articles

Projective Synchronization for Uncertain Fractional Reaction-Diffusion Systems via Adaptive Sliding Mode Control Based on Finite-Time Scheme.

In this article, the projective synchronization of uncertain fractional-order (FO) reaction-diffusion systems is studied for the first time via the fractional adaptive sliding mode control (SMC) method. A FO integral type switching function is designed, and corresponding adaptive SMC laws are derived which ensure the FO sliding mode surface (SMS) is reachable after a finite time interval. The improved version of these control laws which have smaller oscillation and better control performance are also derived. A new lemma for proving the finite-time reachability of the FO SMS is developed. At last, numerical examples are provided to verify the effectiveness of our theories.

Sensorless Control Strategy of PMSM with Disturbance Rejection Based on Adaptive Sliding Mode Control Law

Sensorless Control Strategy of PMSM with Disturbance Rejection Based on Adaptive Sliding Mode Control Law

Adaptive sliding mode control for uncertain nonlinear switched system under probabilistic replay attacks: The output feedback approach

SummaryThis article investigates the output‐feedback‐based adaptive sliding mode control problem for a class of switched systems with probabilistic nonlinearities and replay attacks. The adversary might attack the system during the communication transmissions. The objective of the problem addressed is to design a new output‐feedback‐based adaptive sliding mode control law by utilizing the actual measured output information such that the impacts of immeasurable states and probabilistic replay attacks are compensated. In addition, the input‐to‐state stability in probability of closed‐loop switched system and the reachability analysis of the specified sliding surface are discussed, where the sufficient conditions are established accordingly. Finally, two simulations are provided to illustrate the effectiveness of the proposed sliding mode control method.

Dissipative Sliding-Mode Synchronization Control of Uncertain Complex-Valued Inertial Neural Networks: Non-Reduced-Order Strategy

This study investigates the dissipative synchronization of uncertain complex-valued inertial neural networks with external disturbances using sliding mode control (SMC). In the absence of both variable substitution as well as the equivalent transformations of real- and complex-valued systems, this study focuses directly on the original complex-valued inertial system. First, a suitable integral switching surface (SS) function is proposed. Second, by constructing innovative Lyapunov-Krasovskii functionals and applying the Wirtinger-based integral inequality and reciprocally convex approach, a synchronization criterion is derived on the basis of the linear matrix inequality technique to ensure that the sliding mode dynamics are stable and dissipative. Then, an SMC law and an adaptive SMC law are designed, and the accessibility analysis of the predefined SS is provided. Numerical verifications as well as the superiority and practicality analysis of the proposed approach are provided through four examples.

Adaptive control of T-S fuzzy systems with Markov switching parameters through observer-based sliding mode approach

This paper addresses the problem of observer-based adaptive sliding mode control (SMC) for nonlinear Markov jump systems (MJSs), using a Takagi-Sugeno (T-S) fuzzy model with the premise variables of fuzzy rules depend on system state. Firstly, an integral sliding surface is designed based on fuzzy observer system; Secondly, sufficient conditions for stochastic stability and $ H_{\infty} $ perturbation attenuate level are provided for the obtained sliding mode dynamics and error systems using linear matrix inequality techniques. Furthermore, an adaptive SMC law is combined with the observed state variables to ensure finite time reachability of the sliding surface. Lastly, the theory is validated with simulations based on a practical example.

Neural network based adaptive sliding mode tracking control of autonomous surface vehicles with input quantization and saturation

The autonomous surface vehicle (ASV) is supposed to be able to adapt unknown environments without human interference. This paper investigates the problem of trajectory tracking control for ASVs in the present of parameter uncertainties, disturbances, input quantization and actuator saturation. The neural network (NN) approximation and an adaptive sliding mode control (SMC) strategy are combined for the ASVs with a priori unknown upper bound of parameter uncertainties, external disturbances and saturation errors. The NN is adopted to approximate the unknown continuous uncertainties and disturbances in the system. The adaptive law for the SMC parameter can guarantee no overestimation of the robust control parameter with respect to unknown upper bounds of the NN approximation errors and the saturation error. By adding the NN approximation into the adaptive SMC laws, the robust control parameter and the chattering can be reduced. Uniformly ultimately bounded (UUB) for sliding variables and tracking errors can be guaranteed by Lyapunov proof. Simulation examples are given to illustrate the improved performance with the proposed approach. The comparisons on the proposed control method with other algorithms are given by using the integrated absolute error (IAE) and integrated time absolute error (ITAE).

Design of memory-based adaptive integral sliding-mode controller for fractional-order T-S fuzzy systems and its applications

This study investigates the passivity analysis of fractional-order Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and nonlinear perturbations under an adaptive integral sliding mode control (AISMC) methodology. To better accommodate the features of the T-S fuzzy dynamical model, a novel fractional-order memory-based integral-type sliding manifold function is defined, which is different from the existing sliding manifold function. With the help of Caputo fractional-order derivative properties and quadratic Lyapunov functional, some linear matrix inequality (LMI)-based sufficient criteria are derived to ensure the asymptotic stability conditions of resulting sliding mode dynamics with passive performance index. Besides that, an adaptive sliding mode control law is designed for the addressed systems to guarantee the system state variables onto the predefined integral sliding manifold. Finally, the effectiveness of the proposed controller is validated based on derived sufficient conditions with two practical models, such as fractional-order interconnected power systems and fractional-order permanent-magnet synchronous generator (PMSG) model, respectively.

Observer‐based adaptive sliding‐mode control under dynamic event‐triggered scheme with actuator and communication faults

AbstractThe adaptive technique and sliding‐mode algorithm (SMA) for observer‐based fault tolerant control is discussed with dynamic event‐triggered scheme (DETS) in this article. Both the actuator and communication faults are considered, which implies that the inputs of system and controller are unreliable. Moreover, the switched DETS for controller‐actuator channel is proposed to reduce bandwidth usage and actuator action frequency, which is different from the traditional event‐triggered strategies. To deal with communication faults, which can be described as packet losses, the closed‐loop system is modeled as a stochastic system. The SMA‐based observer is designed to estimate system states, which lays the foundation for the design of control algorithm to mitigate the effects of faults and DETS. Then, a novel observer‐based adaptive sliding‐mode control (SMC) law based on hyperbolic tangent function is proposed to guarantee the stochastic globally uniformly ultimately boundedness and reduce chattering. At last, the proposed DETS and observer‐based adaptive SMC law are applied into a robotic arm to illustrate the validity.

Hybrid extended state observer-based integral sliding mode control of the propulsion for a hydraulic roofbolter

For a propulsion system with dead-zone, time-varying parameters and sudden disturbances, the existing hybrid control methods based on sliding-mode and extended state observer still face challenges such as chattering, high-frequency switching of controller, and low anti-disturbance ability. To solve the problems, this paper proposes an integral sliding-mode controller based on hybrid extended state observer (ISM-HESO), which includes a transition process, an Observer unit, a sliding-mode control (SMC) unit and a parameter adaptation law. Taking dead-zone, time-varying parameters and disturbances into consideration, the propulsion system of a hydraulic roofbolter is modeled after compensating for dead-zone. Based on this, a transition process is introduced to transform the reference propulsion of step input into a continuous one, with the purpose of improving the response speed and avoiding overshoot. Then, in Observer unit, a hybrid extended state observer is designed to effectively estimate the dynamic disturbances. SMC unit provides a continuous and effective sliding-mode control law for the propulsion system, with the purpose of speeding up the response and eliminating the chattering. In SMC unit: (1) A novel integral sliding-mode surface is presented to eliminate the negative effect of disturbance estimation error and avoid high-frequency switching of ISM-HESO; (2) A novel sliding-mode reaching law with a Saturation function is developed, with the purpose of enhancing robustness, improving reaching speed and eliminating chattering; (3) An adaptive sliding-mode control law is presented based the above two strategies, which aims to provide an effective and continuous control signal. Moreover, a parameter adaptation law is designed to tune the estimations of time-varying parameters and improve control performance. Finally, the effectiveness of ISM-HESO is verified by comparative experiments. The experimental results show that ISM-HESO has better dynamic and steady-state performance.

Adaptive Sliding Mode Control for Quadrotor UAVs With Input Saturation

In this article, a novel adaptive sliding mode control strategy is presented for attitude and altitude stabilization of a quadrotor unmanned aerial vehicle (UAV), where the input saturation is taken into consideration. The nonlinear dynamic model of quadrotor UAV subject to system uncertainty and external disturbance is first derived using the Euler–Lagrange mechanical equation. To ensure system stability, as well as eliminating the negative effects of saturation features, a saturated adaptive sliding mode control law (ASMCSAT) is proposed, which takes advantages of the sliding mode control and the adaptive control. Compared with conventional control strategies, better tracking performance and disturbance and uncertainty rejection can be achieved with the root mean square of the tracking error being reduced by 34.91% in vertical takeoff and 30.11% in trajectory tracking. Simulations and experiments are provided to verify the effectiveness and practicability of the proposed control method.

Adaptive Sliding Mode Control Anticipating Proportional Degradation of Actuator Torque in Uncertain Serial Industrial Robots

The paper focuses on faulty actuator problems in an industrial robot using servomotors, and provides an adaptive sliding mode control law to overcome this circumstance. Because of multifarious reasons, robot actuators can undergo a variety of failures, such as locked or stuck joints, free-swinging joints, and partial or total loss of actuation effectiveness. The robot behavior will become worsen if the system controller has not been designed with adequate faulty tolerance. The proportional degradation of actuator torque at unknown degrees of loss, which is one type of partial loss of actuation effectiveness, is considered in this study to design a suitable controller. The robot model is constructed with uncertain parameters and unknown friction, whereas the controller uses only the approximate parameters. Symmetry and skew-symmetry give important contributions in robot modeling and transformation, as well as in the process of proving the system stability. An adjustable coefficient vector of the proposed controller can adaptively reach the upper bounds of an uncertain parametric vector, which guarantees the criterion of Lyapunov stability. In the numerical simulation stage, the selected industrial robot is a Serpent 1 robot with three degrees of freedom. A quasi-physical model based on MATLAB/Simscape Multibody for the robot is built and used in order to increase the reliability of the simulation performance closer to reality. Simulation results illustrate the efficiency of the proposal control methodology in the presence of the mentioned failure. The controller can still deliver satisfactory responses to the robot system under reasonable levels of actuator torque degradation.

Adaptive sliding mode-based active disturbance rejection control for vehicle suspension control

This article presents an adaptive sliding mode-based active disturbance rejection control strategy for the quarter car active suspension control. The suspension system is problematic for its nonlinearities from the dampers, springs, and irregular excitation from the road surface. This study considers this complex behavior and nonlinear characteristics of the suspension system and uses an adaptive sliding mode control law and an extended state observer to estimate and eliminate them from the controlled system. The central concept is to combine the advantages of adaptive sliding mode control to accurately track the reference trajectory with the ability of active disturbance rejection control to reject the parameter uncertainties and external disturbances. The proposed control scheme is verified in simulation studies with parameter uncertainties, nonlinearities, and external disturbances. The simulation results show that the proposed control scheme can significantly improve vehicles’ ride comfort and road-handling ability, owing to the extended state observer’s estimation capability. A comparison of the proposed strategy is also presented with a linear active disturbance rejection control and a conventional proportional–integral–derivative controller. Simulation results show that adaptive sliding mode-based active disturbance rejection improves the robustness against modeling errors, nonlinearities, and disturbances.

Sliding mode control for memristor-based variable-order fractional delayed neural networks

In this paper, we investigate the sliding mode control of variable-order fractional memristor-based neural network with time delay. Two different types of sliding mode controllers for the undisturbed system and an adaptive sliding mode control law for the system with uncertainty, external disturbance and periodical signal order function are designed to realize the asymptotical stability of memristor-based variable-order fractional delayed neural network. By means of the fractional stability criteria in the sense of Mittag-Leffler, the stability of the proposed system has been proved. Finally, the corresponding numerical simulations are shown to verify the feasibility and efficiency of the proposed controllers.

Appointed Fixed Time Observer-Based Sliding Mode Control for a Quadrotor UAV Under External Disturbances

In this article, a study of the appointed fixed time control problem is presented for the quadrotor unmanned aerial vehicle attitude control system subject to external disturbances. Based on the appointed fixed time sliding mode variable and the adaptive technique, a novel sliding mode observer is first established to estimate the external disturbances within the appointed settling time. Subsequently, an appointed fixed time controller is proposed to track the desired attitude regardless of the initial states. To circumvent the singularity problem of the above controller, a novel improved adaptive sliding mode control law is designed by employing a nonlinear function and a modified sliding mode observer. Moreover, the chattering phenomenon is attenuated by replacing the sign function with hyperbolic tangent function. The appointed practical fixed time stability of the closed-loop attitude control system is proved and analyzed rigorously utilizing the Lyapunov theory. Finally, the effectiveness and fine performance of the proposed schemes are illustrated by numerical simulation results.

Event-triggered secure control of discrete systems under cyber-attacks using an observer-based sliding mode strategy

This paper is concentrated on the event-triggered adaptive sliding mode control (SMC) issue for a class of discrete uncertain nonlinear systems subject to false data injection attack (FDIA). The considered control input undergoes the loss of effectiveness (LE) and FDIA in a unified framework. Furthermore, in order to cater the engineering reality, the event-triggered mechanism is introduced in the sensor to observer (S-O) channel and observer to controller (O-C) channel with hope to reduce the communication load. By introducing a novel scheme, sufficient conditions are provided to ensure the asymptotic stability of resultant sliding mode dynamics with prescribed H∞ performance. Subsequently, to reduce the communication burden, an optimal strategy is proposed which can guarantee the stability simultaneously through choosing suitable weighting matrices. Moreover, a projection-based adaptive SMC law is designed to compensate the effects caused by the LE and FDIA, which can force the system state to be attracted into the pre-defined sliding manifold. Finally, some comparison simulations are presented to illustrate the validity of the provided control method.

Adaptive sliding mode control for persistent dwell-time switched nonlinear systems with matched/mismatched uncertainties and its application

In this paper, the adaptive sliding mode control issue for switched nonlinear systems with matched and mismatched uncertainties is addressed, where the persistent dwell-time switching rule is introduced to describe the switching of parameters. Besides, considering the case that the upper bound of the matched uncertainty is unknown, the purpose of this paper is to utilize an adaptive control method to estimate its upper bound parameters. To begin with, a linear sliding surface is constructed, and then the reduced-order sliding mode dynamics can be obtained through a reduced-order method. Next, sufficient conditions can be derived based on the Lyapunov stability and the persistent dwell-time switching analysis techniques ensuring that the reduced-order sliding mode dynamics is globally uniformly exponentially stable. Moreover, a switched adaptive sliding mode control law is designed, which can not only ensure the reachability of the sliding surface but also estimate the upper bound parameters of the matched uncertainty. Finally, a numerical example and a circuit model are introduced to verify the effectiveness of the proposed method.

Adaptive super-twisting sliding mode control for maximum power point tracking of PMSG-based wind energy conversion systems

This paper proposes a super-twisting adaptive sliding mode control law for maximum power point tracking of wind energy conversion systems based on permanent magnet synchronous generators (PMSGs). The employed sliding mode control algorithm can be considered an effective solution, as it retains the robustness properties of classical sliding mode control methods in the presence of disturbances and parameter uncertainties; at the same time, it provides chattering reduction via gain adaptation and generation of second-order sliding modes. In our work, a nonlinear multi-input multi-output tracking control problem is solved to maximize the captured power. Simulation results are presented using real wind speed data, and discussed for the proposed controller and four other sliding mode control solutions for the same problem, in the presence of variations of stator resistance, stator inductance and magnetic flux linkage. The proposed controller achieves the best trade-off between tracking performance and chattering reduction among the five considered solutions: compared to a standard sliding mode control algorithm, it reduces the amount of chattering from two to five orders of magnitude, and the steady-state error on PMSG rotor velocity of one order of magnitude. Also, it reduces the above-mentioned steady-state error of four orders of magnitude with respect to a previously-proposed linear quadratic regulator based integral sliding mode control law for the same system.

Adaptive Sliding Mode Control for a Robotic Manipulator with Unknown Friction and Unknown Control Direction

This paper is aimed at addressing the tracking control issue for an n-DOF manipulator regardless of unknown friction and unknown control direction. In order to handle the above issues, an adaptive sliding mode control (ASMC) is developed with a Nussbaum function. The sliding mode control (SMC) in the proposed control guarantees the tracking problem and fast responses for the manipulator. Additionally, there are adaptive laws for the robust gain in the SMC to deal with the unknown external disturbance and reduce the chattering effect in the system. In practice, the mistakes in the connection between actuators and drivers, named unknown control direction, cause serious damage to the manipulator. To overcome this issue, the Nussbaum function is multiplied by the ASMC law. A Lyapunov approach is investigated to analyze the stability and robustness of the whole system. Finally, several simulations are implemented on a 3-DOF manipulator and their results are compared with those of the existing controllers to validate the advantages of the proposed method.

Exponential Stability of Markovian Jumping Systems via Adaptive Sliding Mode Control

In this paper, the exponential stability in mean square for Markovian jumping systems (MJSs) is discussed. A new dynamic model, which involves parameters uncertainties, nonlinearities, and Lévy noises, is proposed. Moreover, an adaptive sliding mode controller is built to study the stability of such a complex model. First, an integral-type sliding mode surface (SMS) is established to obtain the sliding mode motion dynamics of MJSs. By the generalized Itô formula and the Lyapunov stability theory, some sufficient conditions are obtained to make sure the exponential stability in mean square for the sliding mode motion dynamics. Second, an adaptive sliding mode control law is provided to assure the reachability of the specified SMS. Furthermore, corresponding parameters of the sliding mode controller and the SMS can be got by solving the convex optimization problem. Finally, the validity of the stability results obtained is illustrated by a numerical simulation and a practical simulation.

A Novel Equivalent Input Disturbance-Based Adaptive Sliding Mode Control for Singularly Perturbed Systems

This paper develops a novel equivalent input disturbance (EID)-based adaptive sliding mode control (SMC) method for singularly perturbed systems (SPSs). Firstly, the block diagonalization approach is introduced to decompose the full-order SPSs exactly, and slow and fast subsystems are obtained by solving the upper and lower triangular matrices individually. Secondly, an EID is constructed to estimate the unknown disturbances with the observer gain and error system convergence analyzed. Then, depending on the decoupled reduced-order system models, a Lyapunov equation-based solution is adopted to construct a composite sliding surface. Finally, combined with the EID estimation, an adaptive SMC law is proposed to compensate the adverse effect of disturbances and the reachability condition is proven. The presented control strategy is free of any priori disturbances information while the satisfactory system performance can be guaranteed. Simulation results on two examples illustrate its superiority over the existing methods.