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This paper studies neural network-based tracking control of underactuated systems with unknown parameters and with matched and mismatched disturbances. Novel adaptive control schemes are proposed with the utilization of multi-layer neural networks, adaptive control and variable structure strategies to cope with the uncertainties containing approximation errors, unknown base parameters and time-varying matched and mismatched external disturbances. Novel auxiliary control variables are designed to establish the controllability of the non-collocated subset of the underactuated systems. The approximation errors and the matched and mismatched external disturbances are efficiently counteracted by appropriate design of robust compensators. Stability and convergence of the time-varying reference trajectory are shown in the sense of Lyapunov. The parameter updating laws for the designed control schemes are derived using the projection approach to reduce the tracking error as small as desired. Unknown dynamics of the non-collocated subset is approximated through neural networks within a local region. Finally, simulation studies on an underactuated manipulator and an underactuated vibro-driven system are conducted to verify the effectiveness of the proposed control schemes.

By relying on the input–output feedback linearization approach, a novel adaptive controller for flexible joint robots is proposed in this work. First, a model‐based controller is developed to get a structure that is useful in the development of the adaptive controller. The adaptive version is developed by using two techniques. To stabilize the output function, an adaptive neural network controller is used, which approximates the non‐linear function that contains the uncertainties. The desired rotor position required by the input–output feedback linearization controller is defined with the structure of a link dynamics adaptive regressor‐based controller. The main reason to adopt the mentioned structure in the definition of the desired rotor link position is to guarantee its differentiability. Real‐time experiment comparisons among the model‐based controller, a model‐based controller with desired compensation, an adaptive controller based on joint torque feedback, and an adaptive neural network‐based controller are carried out. Experimental results support the theory reported in this document and the accuracy of the proposed approach.

Synthetic biology involves trying to create new approaches using design-based approaches. A controller is a biological system intended to regulate the performance of other biological processes. The design of such controllers can be based on the results of control theory, including strategies. Integrated feedback control is central to regulation, sensory adaptation, and long-term effects. In this work, we present a study of a cubic functional integral equation with a general and new constraint that may help in investigating some real problems. We discuss the existence of solutions for an equation that involves a control variable in the class of bounded continuous functions BC(R+), by applying the technique of measure of noncompactness on R+. Furthermore, we establish sufficient conditions for the continuous dependence of the state function on the control variable. Finally, some remarks and discussion are presented to demonstrate our results.

Variable-order fractional operators were conceived and mathematically formalized only in recent years. The possibility of formulating evolutionary governing equations has led to the successful application of these operators to the modelling of complex real-world problems ranging from mechanics, to transport processes, to control theory, to biology. Variable-order fractional calculus (VO-FC) is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes. Recognizing this untapped potential, the scientific community has been intensively exploring applications of VO-FC to the modelling of engineering and physical systems. This review is intended to serve as a starting point for the reader interested in approaching this fascinating field. We provide a concise and comprehensive summary of the progress made in the development of VO-FC analytical and computational methods with application to the simulation of complex physical systems. More specifically, following a short introduction of the fundamental mathematical concepts, we present the topic of VO-FC from the point of view of practical applications in the context of scientific modelling.

In this work we present a lower limb haptic exoskeleton suitable for patient rehabilitation, specifically in the presence of illness on postural equilibrium. Exoskeletons have been mostly conceived to increase strength, while in this work patient compliance with postural equilibrium enhancement is embedded. This is achieved with two hierarchical feedback loops. The internal one, closing the loop on the joint space of the exoskeleton offers compliance to the patient in the neighborhood of a reference posture. It exploits mechanical admittance control in a position loop, measuring the patient’s Electro Miographical (EMG) signals. The problem is solved using multi variable robust control theory with a two degrees of freedom setting. A second control loop is superimposed on the first one, operating on the Cartesian space so as to guarantee postural equilibrium. It controls the patient’s Center of Gravity (COG) and Zero Moment Point (ZMP) by moving the internal loop reference. Special attention has been devoted to the mechanical multi-chain model of the exoskeleton which exploits Kane’s method using the Autolev symbolic computational environment. The aspects covered are: the switching system between single and double stance, the system’s non-holonomic nature, dependent and independent joint angles, redundancy in the torque controls and balancing weight in double stance. Physical experiments to validate the compliance method based on admittance control have been performed on an elbow joint at first. Then, to further validate the haptic interaction with the patient in a realistic situation, experiments have been conducted on a first exoskeleton prototype, while the overall system has been simulated in a realistic case study.

The nonlinear factors, the external interference, and the coupling between the two hydraulic cylinders in the electro-hydraulic position servo system seriously affect the synchronous control accuracy. In this paper, based on the establishment of the state space equation of double hydraulic cylinders, the cross-coupling control structure was adopted, and the synchronous controller based on dynamic soft variable structure control was designed. The synchronous controller based on sliding mode control was used as a comparison for co-simulation and experimental analysis. The results showed that under the control of two synchronization controllers, the controlled dual cylinders could track the given positioning signal in a short time, and the synchronization error was always within the specified range. The synchronization controller based on dynamic soft variable structure control could shift smoothly without significant impact when the given positioning signal suddenly changes, avoiding the chattering problem in the sliding mode control.

An adaptive sliding mode variable structure control method is proposed for the shipboard cranes in the presence of unknown parameters. The proposed method can solve the problem of frequent controller tuning and effectively reduce the payload pendulation. First, the length change of the rope and unmodeled disturbance are considered in the model, then the model is divided into the actuated and unactuated parts. The error function is induced into the sliding mode surface to design the equivalent control law, and unmodeled disturbance is estimated by the nonlinear extended state observer. Then, the mass of the payload is equal to the estimated parameter, and an adaptive law is designed to eliminate errors of them. Moreover, the asymptotic stability of the closed-loop system is assured by carefully designed Lyapunov techniques. Finally, a comparative study of numerical simulation under different conditions is investigated. The results show that the proposed method can effectively reduce payload swing, which further illustrates the satisfactory performance of the proposed method.

Due to the multiple nonlinear composite disturbance problems such as gap, friction, hydraulic spring force and external load disturbance force in the double closed-loop digital hydraulic cylinder position control system, traditional or single structure controllers have no obvious effect on improving the performance of this complex nonlinear system. In this paper, the high-order state equation is obtained for the existing mathematical model of the double closed-loop digital hydraulic cylinder. Then, using ADRC, the high-order double closed-loop digital hydraulic cylinder control system is equivalent to a second-order integral series control system. Applying sliding mode variable structure control to ADRC, in order to improve the control accuracy of the sliding mode controller and reduce the influence of chattering, utilizing the external disturbance in the ESO observation system in ADRC, a control term f ( x ) in the system, which is an uncertain nonlinear variable due to the time-varying and unknown internal parameters of the system. RBF neural network is used to approximate f ( x ). Based on this, the RBF neural network sliding mode active disturbance rejection control strategy (RBFSMADRC) is proposed. The control law and adaptive law of the system are derived based on the Lyapunov method, and the stability of the whole closed -loop system is ensured by adjusting the size of the adaptive weight. Specifically, the effectiveness of the proposed control method is validated through simulation and experimentation.

This study proposes a method for operating wheeled cross-coupled systems. Wheeled cross-coupled systems are more sensitive to disturbances than other cross-coupled systems. When the slip phenomenon occurs in wheels, it causes synchronous errors between axles, resulting in differences in the controller outputs of the two axles. In the worst case, the two axles can end up competing. To solve this problem, this study introduces base controllers to each axle using a discrete-time variable structure control system with a decoupled disturbance compensator and an auxiliary controller, called a synchronous error compensator (SEC), to minimize synchronous errors arising from differences in the states of the two axles. Experiments are conducted on a verification system with a similar form of overhead hoist transfer (OHT) to demonstrate the effectiveness of the proposed method. Results reveal that the SEC generates control commands to make the control inputs (current command) and state variables (velocity feedback) of the two axles similar.

Aiming at the problems of low control precision, poor anti-interference ability and poor stability of traditional PID controller, the improvement effect of fuzzy control and BP neural network in closed-loop control of PMSM is compared. In the case of variable speed and variable load, the stability, real-time, anti disturbance and robustness of PMSM system with traditional PID controller, fuzzy self-tuning PID controller and BP neural network PID controller as speed regulator are simulated and analyzed. The simulation results show that the fuzzy self-tuning PID controller has more advantages in the response speed of the system, and can make the system quickly recover to the initial state in case of sudden change. The BP neural network PID controller can ensure the relative stability of the system is better, and can restrain the sudden fluctuation.