Adaptive Integral Sliding Mode Control Research Articles

Synchronization and Antisynchronization of Identical 4D Hyperchaotic Financial System with External Perturbation via Sliding Mode Control Technique

In this article, complete synchronization and antisynchronization in the identical financial chaotic system are presented. The proposed control strategies depend on first‐order sliding mode and adaptive integral sliding mode for complete synchronization and antisynchronization of the identical financial chaotic system. In the primary case, the system parameters should be known, and first‐order sliding mode control is utilized for synchronization and antisynchronization while in the second case, the system parameters are considered unknown. An adaptive integral sliding mode control strategy is utilized for synchronization and antisynchronization of the system considering the parameters unknown. The error system is changed into a particular structure containing a nominal part and several unknown terms to utilize the adaptive integral sliding mode control. Then, this error system is stabilized using integral sliding mode control. The stabilizing controller is usually developed based on the nominal part plus the compensator control part. To suppress the high‐frequency oscillation (chattering) phenomenon, smooth continuous compensator control can be used rather than conventional discontinuous control. The compensator controller along with the adapted law is derived such that the time derivative of the Lyapunov function becomes strictly negative. The effectiveness of the proposed method was tested through computer simulations. The proposed control strategies are verified for that Identical 4D hyperchaotic financial system to attain complete synchronization and antisynchronization along with the improved performance.

High-Performance Adaptive Attitude Control of Spacecraft With Sliding Mode Disturbance Observer

A new disturbance observer-based control method is presented in this paper to address the attitude tracking problem of rigid-body spacecraft in the presence of external disturbances and parameter uncertainties. Particularly, a sliding mode disturbance observer (SMDO) is designed. The most important feature of this SMDO is the relaxation of the assumption that external disturbances must be constants or changing at a slow rate, which is a typical assumption required in these classes of problems concerning disturbance observer (DO) design but hard to guarantee from the standpoint of practical engineering. In addition, a special adaptive integral sliding mode controller is combined with the SMDO to ensure system state convergence. The proposed control scheme’s primary advantage is the enhanced robustness against system parameter uncertainties and external disturbances. Stringent closed-loop system stability analysis is performed using Lyapunov-based stability theory. Numerical simulations are carried out on nonlinear model of spacecraft to validate the proposed control scheme’s efficiency compared to the existing methods in the literature.

Investigation of chaos behavior and integral sliding mode control on financial risk model

<abstract> <p>This paper reports the finding of a new financial chaotic system. A new control law for completely synchronizing the new financial chaotic system with itself has been established using adaptive integral sliding mode control. We also find that the new financial chaotic system has fascinating traits including symmetry, equilibrium points, multistability, Lyapunov exponents and bifurcation diagrams. We illustrate all the main results of this research work using MATLAB phase plots. The Lyapunov characteristic exponents and analysis using bifurcation diagrams have resulted in a new financial chaos system showing chaos phenomena in the intervals of parameters 0 < <italic>a</italic> < 15, and parameters 0 < <italic>b</italic> < 0.25. The results of this study can be used to predict if there is chaos in financial risk. Chaotic systems have many applications in engineering like cryptosystems and secure communication systems.</p> </abstract>

Adaptive Integral Terminal Sliding Mode Control for the Nonlinear Active Vehicle Suspension System under External Disturbances and Uncertainties

Suspension system is one of the most effective vehicle components that play an essential role in the stability and comfort of the vehicle. The passive suspension can not fully meet a car's stability and comfort requirements. Instead, an active suspension system has been proposed to improve these challenges. Active suspension minimizes the vibrations entering the body using a closed-loop control system. To this end, in this research, an integral terminal sliding mode control (integral TSMC) for an active nonlinear car suspension system under external disturbances and uncertainties is designed. First, the integral TSMC is designed to deal with the uncertainties and the external disturbances in the system when the upper bound is known. Next, an adaptation law is recommended to estimate the upper bound of uncertainties and external disturbances. The results show that the proposed integral TSMC improves the convergence rate and tracking error of the closed-loop system. The stability of the nonlinear control system is investigated and proven using Lyapunov's stability theory. The numerical results indicate a good robust performance and stability for the proposed controller for the nonlinear suspension system with different road profiles in the presence of uncertainties and external disturbances. From the results, it can also be understood that important measures such as ride comfort, road holding, and mechanical structural limitations are met using the proposed approach.

Composite nonlinear feedback–based adaptive integral sliding mode control for a servo position control system subject to external disturbance

This paper presents a composite nonlinear feedback–based adaptive integral sliding mode controller with a reaching law (CNF-AISMRL) for fast and accurate control of a servo position control system subject to external disturbance. The proposed controller exploits the advantages of composite nonlinear feedback (CNF) and sliding mode control (SMC) schemes to improve the transient performance and increase the robustness of the closed-loop system. An integral sliding mode combined with a quick reaching law is designed to eliminate the effect of disturbances, which mitigates chattering and achieves finite-time convergence of the sliding mode. An adaptation tuning approach is utilized to deal with unknown but bounded system uncertainties and disturbances. When considering the model uncertainties and disturbances, the stability of the closed-loop system is verified based on the Lyapunov theorem. Numerical simulations are investigated to the effectiveness of the proposed scheme. The transient performance of load disk position to step signal with disturbances using CNF, composite nonlinear feedback based integral sliding mode control (CNF-ISM), and the proposed CNF-AISMRL schemes is given. The simulation results indicate that, without acquiring the knowledge of bounds on system disturbances, the proposed control scheme has superior performance in the presence of time-varying disturbances.

Adaptive integral sliding mode controller for solid state transformer based on generalized averaged model and T‐S fuzzy method

The integrated converter between distributed renewable source and main grid has been widely applied. Although the independent control strategies regarding each submodule of solid state transformer (SST) have been studied, the integrated control based on overall model has not been proposed. To this end, this paper proposes an adaptive integral sliding mode control strategy based on T-S fuzzy method for the single-phase SST to regulate the output voltage and guide the power transmission. First, the overall state-space model based on generalized average method is first built through quasi-Fourier series. It can capture switching ripple compared with conventional model. Furthermore, the built model with uncertainties and nonlinear components is switched as the linear time invariant system through T-S fuzzy method. Meanwhile, the system order can also be reduced, which reduces the complexity of the controller design. Based on this model, an integral sliding mode control approach with rapid dynamic response and strong robustness against perturbations or model uncertainties is proposed. Finally, several simulation and experimental results are provided to validate the performance of the proposed control approach.

Adaptive quantized sliding mode attitude tracking control for flexible spacecraft with input dead-zone via Takagi-Sugeno fuzzy approach

This paper addresses the sliding mode control design problem for the flexible spacecraft attitude tracking control system with Takagi-Sugeno fuzzy model based method. In this design, the external disturbance and actuator input dead-zone are considered simultaneously, and the signals between sensors and controller are quantized before transmission over digital communication channels. A quantized adaptive integral sliding mode control law is proposed to ensure that the sliding motion is globally asymptotically stable, and the effects of unknown external disturbances, actuator nonlinearity and quantization errors are compensated via the online adaptive mechanism simultaneously. Moreover, under the proposed digital control law the finite-time reachability of the designed sliding surface can be guaranteed strictly. Finally, simulation results are presented to illustrate the feasibility and effectiveness of the developed quantized spacecraft attitude control method.

Fault-tolerant control of flexible satellite with infinite-dimensional model

Fault-tolerant control (FTC) strategy based on adaptive integral sliding mode (AISM) is proposed to stabilize a flexible satellite, subject to inertia uncertainties, external disturbances, and actuator faults. Using Hamilton’s principle, the satellite dynamics is presented as a coupled Ordinary Differential Equation (ODE) and Partial Differential Equation (PDE). The control scheme is based on the infinite-dimensional model of the flexible satellite with no discretization, so the spillover instability phenomenon is eliminated. This is the most important advantage of the proposed control scheme over the previous FTC schemes that have been used for the flexible satellite. Stabilization and vibration suppression are performed using control torque that is applied to the rigid center, and there is no need to implement in-domain actuators on panels to stabilize their vibration. First, a novel nominal controller based on the infinite-dimensional model of the satellite is designed for a healthy system. Then, an integral sliding surface, including angular velocities, internal reaction torques, and nominal control, is proposed. Finally, an AISM controller with an adaptive estimator is designed to accommodate actuator faults and other uncertainties. System stability is guaranteed for small changes in a neighborhood around the sliding surface with simultaneous vibration damping. Numerical simulations illustrate the effectiveness of the proposed control strategy.

Design of Decentralized Adaptive Integral Terminal Sliding Mode Controller for Linear Interconnected Mechanical Systems in the Presence of External Disturbance

Design of Decentralized Adaptive Integral Terminal Sliding Mode Controller for Linear Interconnected Mechanical Systems in the Presence of External Disturbance

Adaptive Integral‐Based Robust Q‐S Synchronization and Parameter Identification of Nonlinear Hyperchaotic Complex Systems

This communique presents the Q-S synchronization of two nonidentical complex nonlinear hyperchaotic systems with unknown parameters. An adaptive controller based on adaptive integral sliding mode control and parameter update laws are designed to realize the synchronization and parameter identification to a given map vector. The aforementioned strategy’s employment demands the transformation of a system into a specific structure containing a nominal part and some unknown terms (later on, these unknown terms will be computed adaptively). An integral sliding mode controller is used to stabilize the error system by designing nominal control accompanied by compensator control. For chattering suppression, a continuous compensator of smooth nature is used instead of conventional control. The stability of the proposed algorithm is established in an impressive way, using Lyapunov criteria. A numerical simulation is performed to illustrate the validity of the proposed synchronization scheme.

Adaptive Integral Sliding Mode Control Using Fully Connected Recurrent Neural Network for Position and Attitude Control of Quadrotor.

This article proposes an adaptive integral sliding mode control (ISMC) strategy for quadrotor control that ensures faster and finite-time convergence along with chattering attenuation. Quadrotor dynamics are assumed to be unknown because of the high degree of parametric uncertainties, including external disturbances. The equivalent control law obtained by ISMC consists of quadrotor dynamics and, thus, cannot be applied to the quadrotor. A new fully connected recurrent neural network (FCRNN) controller has been proposed to mimic the equivalent control instead of estimating the Quadrotor dynamics separately. The proposed FCRNN architecture consists of output feedback to the input layer and the hidden layer, which enhances the approximation capability of FCRNN. All hidden layer neurons receive self-feedback and feedback from other hidden layer neurons, which further strengthens FCRNN's potential to capture complex dynamic characteristics. As learning should happen in finite time, the finite-time stability of the overall system has been guaranteed using the Lyapunov stability theory, and the update laws for FCRNN weights in real time are derived using the same. To show the effectiveness of the proposed approach, a comprehensive analysis has been done against existing SMC strategy and against well-known function approximation techniques, e.g., the radial basis function network (RBFN) and RNN.

Fault-tolerant control of flexible satellite with infinite-dimensional model

Fault-tolerant control (FTC) strategy based on adaptive integral sliding mode (AISM) is proposed to stabilize a flexible satellite, subject to inertia uncertainties, external disturbances, and actuator faults. Using Hamilton’s principle, the satellite dynamics is presented as a coupled Ordinary Differential Equation (ODE) and Partial Differential Equation (PDE). The control scheme is based on the infinite-dimensional model of the flexible satellite with no discretization, so the spillover instability phenomenon is eliminated. This is the most important advantage of the proposed control scheme over the previous FTC schemes that have been used for the flexible satellite. Stabilization and vibration suppression are performed using control torque that is applied to the rigid center, and there is no need to implement in-domain actuators on panels to stabilize their vibration. First, a novel nominal controller based on the infinite-dimensional model of the satellite is designed for a healthy system. Then, an integral sliding surface, including angular velocities, internal reaction torques, and nominal control, is proposed. Finally, an AISM controller with an adaptive estimator is designed to accommodate actuator faults and other uncertainties. System stability is guaranteed for small changes in a neighborhood around the sliding surface with simultaneous vibration damping. Numerical simulations illustrate the effectiveness of the proposed control strategy.

A new actuator fault‐tolerant control for Lipschitz nonlinear system using adaptive sliding mode control strategy

AbstractThis article proposed a new adaptive integral sliding mode (ISM) based fault‐tolerant control (FTC) strategy to solve the actuator's faults and failures compensation problem for the class of Lipschitz nonlinear systems. A nominal state feedback virtual control law is designed first to stabilize the Lipschitz nonlinear system and to attain the desired nominal performance. To cater for the effect of faults and failures, the control allocation (CA) scheme reorganizes the virtual input signals among the healthy redundant actuators based on actuator's effectiveness level. Then, a nonlinear adaptive integral sliding mode controller (ISMC) is incorporated with the CA scheme to compensate for unknown disturbance and uncertainties effect that arises in the system by virtue of actuator faults/failures and error in fault estimation . An effective synthesis procedure is adopted to ensure the closed‐loop stability condition using linear matrix inequality (LMI) optimization. Finally, the FTC scheme is tested to achieve maneuvering control of coaxial octorotor unmanned aerial vehicle (UAV) system. Simulations are performed on the nonlinear system at different actuator faults/failures combinations. Moreover, the effect of wind‐gust, parameter variations, estimated state feedback and sensor noise are considered in nonlinear simulations. Finally, the results obtained during faults/failures are compared with the nominal condition and fixed ISMC based CA scheme.

Functional observer-based finite-time adaptive ISMC for continuous systems with unknown nonlinear function

This paper is concerned with functional observer-based finite-time adaptive integral sliding mode control (ISMC) for continuous systems with unknown nonlinear function. First, a novel finite-time ISMC framework is established based on the functional observer whose parameters can be directly found. Second, an adaptive compensator is designed to counteract the effect of the unknown nonlinear function such that the composite integral sliding mode controller ensures that the closed-loop system reaches boundedness in a predefined finite time. Moreover, some sufficient conditions in the form of matrix inequalities are proposed to guarantee the finite-time boundedness with H∞ performance (FTB-H∞) over the sliding phase and the reaching phase of the closed-loop system. Then the FTB-H∞ conditions over the whole finite-time interval are also provided. Due to introducing more degrees of freedom in the functional observer, the designed finite-time integral sliding mode controller is more flexible and less conservative. Finally, a simulation example is given to show the validity of the proposed method.

Actuator Fault-Tolerant Control for an Electro-Hydraulic Actuator Using Time Delay Estimation and Feedback Linearization

This article proposes a novel fault-tolerant controller for a double-rod electro-hydraulic actuator whilst the motion control system faces with system disturbances/uncertainties and internal leakage fault. Firstly, taking the advantage of the coordinate transformation, the nonlinear system is converted to a linear system to apply the control design tools in linear control theory. Besides, the matched, mismatched disturbances, and internal leakage fault are integrated into a new lumped uncertainty based on this transformation. Inspired by the great capability of time delay estimation technique, the suggested controller is developed to effectively detect and compensate for the internal leakage fault. To enhance the performance of the control system, an adaptive integral sliding mode control approach is deployed to effectively suppress the lump estimated error, and the effects of fault. The perfect combination of input-output feedback linearization, adaptive integral sliding mode, and time delay estimation is investigated to achieve high-precision tracking control and strong robustness in the presence of matched, mismatched disturbances, and faults, simultaneously. Moreover, the global stability of the suggested control algorithm is demonstrated by the Lyapunov theory. Finally, several tracking performance comparisons of the proposed approach with the existing controllers to demonstrate the efficiency are exhibited through simulation analyses and experiment results.

Adaptive Reinforcement Learning Strategy with Sliding Mode Control for Unknown and Disturbed Wheeled Inverted Pendulum

This paper develops a novel adaptive integral sliding-mode control (SMC) technique to improve the tracking performance of a wheeled inverted pendulum (WIP) system, which belongs to a class of continuous time systems with input disturbance and/or unknown parameters. The proposed algorithm is established based on an integrating between the advantage of online adaptive reinforcement learning control and the high robustness of integral sliding-mode control (SMC) law. The main objective is to find a general structure of integral sliding mode control law that can guarantee the system state reaching a sliding surface in finite time. An adaptive/approximate optimal control based on the approximate/adaptive dynamic programming (ADP) is responsible for the asymptotic stability of the closed loop system. Furthermore, the convergence possibility of proposed output feedback optimal control was determined without the convergence of additional state observer. Finally, the theoretical analysis and simulation results validate the performance of the proposed control structure.

On the synthesis of a sliding-mode-observer-based adaptive fault-tolerant flight control scheme

This paper presents an active Fault-Tolerant Control (FTC) framework to accommodate the actuator faults by using a Fault Estimation (FE) module fitted with an adaptive control law. It focuses on the problem of fault estimation based fault tolerant control for linear uncertain system with mitigation of the reconfiguration transients. In this work, a second-order sliding mode observer is designed to reconstruct the Loss of Effectiveness (LoE) of the actuators. The use of a bumpless strategy to cleverly manage the transient behavior where fault estimation is different from the real one due to an abrupt fault occurrence. Signals provided by the FE module are next used by an augmented fault-tolerant control allocation scheme to accommodate the fault. More precisely, the flight state tracking problem has been addressed with a robust adaptive model-reference Integral Sliding Mode (ISM) control law in a state feedback setting. Next, the problem of stability and performance of the overall FTC scheme with taking into account both FE performance and control law is rigorously considered. At the end, simulation examples on an aircraft from a European program are used to illustrate the effectiveness of the proposed approach.

Continuous integral sliding mode control for space manipulator with actuator uncertainties

This paper studies the trajectory tracking control of space manipulator in the presence of actuator uncertainties, such as actuator fault, actuator saturation and the bias control torque. In addition, parametric uncertainty and external disturbances are also taken into consideration. A novel continuous adaptive integral sliding mode controller, which is chattering free and singularity free compared to the traditional terminal sliding mode control, is proposed to achieve the finite-time trajectory tracking control for space manipulator with uncertainties. Lyapunov theory is employed to prove the stability of the closed-loop system. The main advantage of the proposed controller is that it is easy to be implemented with continuous chattering-free control command. Numerical simulations are used to verify the effectiveness of the proposed controller.

Neural adaptive integral sliding mode control for attitude tracking of flexible spacecraft with signal quantisation and actuator nonlinearity

This study investigates the neural adaptive integral sliding mode control for attitude tracking of flexible spacecraft, where unknown actuator nonlinearity, input quantisation and external disturbances are considered simultaneously. In this design, the hysteresis encoder–decoder scheme is employed between the controller and actuator side for signal quantisation. A quantised adaptive integral sliding mode control strategy is developed, where the neural network scheme is applied to approximate the unmeasurable rigid-flexible coupled nonlinear dynamics. The proposed control strategy can compensate for quantisation error, actuator faults, actuator dead-zone as well as external disturbances effectively, and guarantee the trajectory of the attitude tracking error converge to the equilibrium point along the designed sliding surface. Finally, a simulation example is conducted to demonstrate the validness of the developed quantised control strategy for flexible spacecraft attitude tracking problem.

Frequency-shaped sliding mode control of piezoelectric nano-stages with hysteresis estimation

Due to the emerging applications of ultra-high precision scanning in many engineering fields, dynamical tracking of desired reference trajectories for nano-stages has attracted a lot of significant research. An adaptive integral sliding mode control (AISMC) framework in combination with frequency-shaped optimization and hysteresis observer is proposed to improve tracking performance of piezoelectric nano-stages in this article, where hysteresis nonlinearities, undesired high-frequency dynamics and model uncertainties are the major issues that limit high-precision dynamic tracking. The convergence regarding both the observation error of the hysteresis state and the tracking error of the considered system is analyzed. By comparison with representative results in the literature, the experimental studies conducted on an multi-axis nano-stage are used to verify the proposed approach has a substantial improvement in terms of robustness and tracking performance.