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PurposeThis paper aims to study the issues of adaptive fuzzy control for a category of switched under-actuated systems with input nonlinearities and external disturbances.Design/methodology/approachA control scheme based on sliding mode surface with a hierarchical structure is introduced to enhance the responsiveness and robustness of the studied systems. An equivalent control and switching control rules are co-designed in a hierarchical sliding mode control (HSMC) framework to ensure that the system state reaches a given sliding surface and remains sliding on the surface, finally stabilizing at the equilibrium point. Besides, the input nonlinearities consist of non-symmetric saturation and dead-zone, which are estimated by an unknown bounded function and a known affine function.FindingsBased on fuzzy logic systems and the hierarchical sliding mode control method, an adaptive fuzzy control method for uncertain switched under-actuated systems is put forward.Originality/valueThe “cause and effect” problems often existing in conventional backstepping designs can be prevented. Furthermore, the presented adaptive laws can eliminate the influence of external disturbances and approximation errors. Besides, in contrast to arbitrary switching strategies, the authors consider a switching rule with average dwell time, which resolves control problems that cannot be resolved with arbitrary switching signals and reduces conservatism.

This paper studies the adaptive neural fault-tolerant control (FTC) problem of a class of switched nonstrict-feedback nonlinear systems (NFNSs) via adopting the hierarchical sliding mode control (HSMC) method and the average dwell time (ADT) switching strategy. First, the original system is transformed into a new system with unknown compound nonlinear functions. Then, by utilizing the robust approximation capability of neural networks (NNs), the compound nonlinear functions are identified online. Furthermore, a novel hierarchical sliding mode surface-based adaptive neural fault-tolerant controller is designed, in which the denominator singular issue is successfully handled by using a modified projection algorithm. By means of the Lyapunov stability theory, it is proved that the proposed control method can ensure the boundedness of all signals of the considered NFNS. Eventually, a practical continuous stirred tank reactor example is given to verify the validity of the proposed HSMS-based adaptive neural FTC method.

In order to stabilize underactuated robotic systems with external disturbances, an adaptive hierarchical sliding mode control strategy based on extended state observer is proposed. The extended state observer is designed to estimate the joint states and lumped disturbance composed of matched and unmatched disturbances. The underactuated robotic system is divided into two subsystems. For each subsystem, a sub-sliding mode surface is constructed to obtain the first layer sliding mode surface and the second layer sliding mode surface is derived from the first layer sliding mode surface. Then the hierarchical sliding mode controller is designed with the estimated state obtained from the observer to compensate the lumped disturbance and an adaptive law is designed to adjust the switching gain. The stability of the system is proved by Lyapunov theory and the effectiveness of the proposed control strategy is verified by comparative simulations. With the proposed control, the tracking performance of the underactuated robotic system is effectively improved and the convergence time of the system is reduced.

In this paper, a new adaptive hierarchical sliding mode control scheme for a 3D overhead crane system is proposed. A controller is first designed by the use of a hierarchical structure of two first-order sliding surfaces represented by two actuated and un-actuated subsystems in the bridge crane. Parameters of the controller are then intelligently estimated, where uncertain parameters due to disturbances in the 3D overhead crane dynamic model are proposed to be represented by radial basis function networks whose weights are derived from a Lyapunov function. The proposed approach allows the crane system to be robust under uncertainty conditions in which some uncertain and unknown parameters are highly difficult to determine. Moreover, stability of the sliding surfaces is proved to be guaranteed. Effectiveness of the proposed approach is then demonstrated by implementing the algorithm in both synthetic and real-life systems, where the results obtained by our method are highly promising.

This research presents three major contributions to the nonlinear control of underactuated systems. First, the identification and characterization of a 2.5 Hz oscillatory phenomenon in the low-cost inverted pendulum system, addressing challenges from mechanical elasticity and electrical delays, is reported. Second, the Hierarchical Sliding Mode Control (HSMC) framework is developed to control this underactuated system considering its unwanted oscillatory phenomenon. This HSMC control system is used to achieve superior disturbance rejection, maintaining cart position within ± 0.05 m compared to PD-LQR's ± 0.35 m under pure oscillatory disturbances, while reducing energy consumption by 32%. Third, a comprehensive Hardware-in-the-Loop (HIL) implementation using the F28379D microcontroller, which provides real-time parameter adjustment capabilities, is established. The stability of the system is theoretically validated through Lyapunov analysis and homoclinic orbit characterization. Experimental results demonstrate the effectiveness of the HSMC controller in maintaining pendulum angular oscillations within ± 2.5°, significantly outperforming PD-LQR's ± 5° range under combined disturbances.

Tracking control of tendon-driven manipulators has become a prevalent research area. However, the existence of flexible elastic tendons generates substantial residual vibrations, resulting in difficulties for trajectory tracking control of the manipulator. This paper proposes the radial basis function neural network adaptive hierarchical sliding mode control (RBFNNA-HSMC) method, which combines the dynamic model of the elastic tendon-driven manipulator (ETDM) with radial basis neural network adaptive control and hierarchical sliding mode control technology. The aim is to achieve trajectory tracking control of ETDM even under conditions of model inaccuracy and disturbance. The Lyapunov stability theory demonstrates the stability of the proposed RBFNNA-HSM controller. In order to assess the effectiveness and adaptability of the proposed control method, simulations and experiments were performed on a two-DOF ETDM. The RBFNNA-HSM method shows superior tracking accuracy compared to traditional model-based HSM control. The experiment shows that the maximum tracking error for ETDM double-joint trajectory tracking is below 2.593×10 -3 rad and 1.624×10 -3 rad, respectively.

This paper presents a new spherical robot with a cable transmission mechanism. Cable transmission mechanism replaces conventional gear train to eliminate the influence of gear backlash, reduce the robot mass, lower the costs on mechanical customization and can be arranged flexibly. By projection method, the 3D robot dynamic model with structural asymmetry is decoupled into balance subsystem and velocity subsystem, and the kinetics equations are established based on Newton-Euler’s law. For the balance control, an adaptive law is designed to estimate the upper bound instead of the exact value of the uncertainty caused by the structural asymmetry online firstly, then a finite-time adaptive hierarchical sliding mode control (FAHSMC) strategy is proposed based on the estimation result to minimize the convergence time. For the velocity control, a hierarchical sliding mode controller (HSMC) and a tracking differentiator (TD)-based nonlinear disturbance observer are designed, leading to enhanced disturbance rejection capability and a reduced steady-state error. Simulations and experiments on a real spherical robot are conducted to demonstrate the efficacy of the proposed control strategies.

This paper studies the stabilization problem for a class of underactuated systems in the presence of unknown disturbances. Due to less number of control inputs with respect to the degrees of freedom of the system, closed-loop asymptotic stability is a challenging issue in this field. In this paper, anti-swing controllers are designed for nominal and disturbed systems. In the case of the nominal system, the proposed two-loop controller is a combination of collocated partial feedback linearization and hierarchical sliding mode control (HSMC) theories. Then, due to the importance of robustness in control of physical systems, the proposed controller is developed for underactuated mechanical systems in the presence of additive disturbances. One of the main advantages of the proposed design method is that it does not need any switching algorithm. Finally, to illustrate the performance of the proposed controllers, they are applied to two underactuated mechanical systems: a pendubot and a Furuta pendulum. In addition, the practicality of the proposed approach is also verified experimentally using a quadrotor stand.

This paper presents a study on controlling a rotary inverted pendulum (RIP) system using a hierarchical sliding mode control (HSMC) approach. The objective is to swing up and stabilize the pendulum at a desired position. The proposed HSMC controller addresses the underactuation challenge through a hierarchical structure of sliding surfaces. The particle swarm optimization (PSO) algorithm is used to optimize the controller parameters. Simulations were performed to evaluate the performance of the HSMC controller at different initial pendulum angles, demonstrating its effectiveness in achieving swing-up and stabilization. The integration of the PSO algorithm enhances the controller’s adaptability and robustness, emphasizing the benefits of combining optimization algorithms with controller parameter tuning for underactuated systems like the RIP.

The paper addresses a problem of efficiently controlling an autonomous underwater vehicle (AUV), where its typical underactuated model is considered. Due to critical uncertainties and nonlinearities in the system caused by unavoidable external disturbances such as ocean currents when it operates, it is paramount to robustly maintain motions of the vehicle over time as expected. Therefore, it is proposed to employ the hierarchical sliding mode control technique to design the closed-loop control scheme for the device. However, exactly determining parameters of the AUV control system is impractical since its nonlinearities and external disturbances can vary those parameters over time. Thus, it is proposed to exploit neural networks to develop an adaptive learning mechanism that allows the system to learn its parameters adaptively. More importantly, stability of the AUV system controlled by the proposed approach is theoretically proved to be guaranteed by the use of the Lyapunov theory. Effectiveness of the proposed control scheme was verified by the experiments implemented in a synthetic environment, where the obtained results are highly promising.