Neural Adaptive Backstepping Control of a Robotic Manipulator With Prescribed Performance Constraint

Prescribed performance dynamic surface control based on dual extended state observer for 2-dof hydraulic cutting arm

In tunnel section forming operations, the boom-type roadheader tracking target trajectory with high precision is greatly significant in avoiding over and under excavation and improving excavation efficiency. However, there exist complex cutting loads, measurement noise, and model uncertainties, seriously degrading the tracking performance of traditional nominal model-based controllers. Hence, this study first fully analyzes the kinematics of all members of the cutting mechanism and establishes its complete multi-body dynamic model using the Lagrange method. Furthermore, a dual extended state observer is designed to estimate the mechanical system's angular velocity and unmodeled disturbances and actuators' uncertain nonlinearities. In particular, introducing a nonlinear filter replaces the traditional first-order filter in dynamic surface technology, overcoming the "explosion of complexity" while attenuating the conservatism of gains tuning. Then, a dual extended state observer-based prescribed performance dynamic surface controller is developed for roadheaders for the first time. Simultaneously, integrating an improved error transformation function into controller design effectively avoids the online computational burden caused by traditional logarithmic operations. Utilizing Lyapunov theory, the cutting system's prescribed transient response and steady-state performance are guaranteed. Finally, the proposed controller's effectiveness is verified by comparative experiments on the roadheader.

Reinforcement Learning-Based Fractional-Order Adaptive Fault-Tolerant Formation Control of Networked Fixed-Wing UAVs With Prescribed Performance

This article investigates the fault-tolerant formation control (FTFC) problem for networked fixed-wing unmanned aerial vehicles (UAVs) against faults. To constrain the distributed tracking errors of follower UAVs with respect to neighboring UAVs in the presence of faults, finite-time prescribed performance functions (PPFs) are developed to transform the distributed tracking errors into a new set of errors by incorporating user-specified transient and steady-state requirements. Then, the critic neural networks (NNs) are developed to learn the long-term performance indices, which are used to evaluate the distributed tracking performance. Based on the generated critic NNs, actor NNs are designed to learn the unknown nonlinear terms. Moreover, to compensate for the reinforcement learning errors of actor-critic NNs, nonlinear disturbance observers (DOs) with skillfully constructed auxiliary learning errors are developed to facilitate the FTFC design. Furthermore, by using the Lyapunov stability analysis, it is shown that all follower UAVs can track the leader UAV with predesigned offsets, and the distributed tracking errors are finite-time convergent. Finally, comparative simulation results are presented to show the effectiveness of the proposed control scheme.

Realizing asynchronous finite-time robust tracking control of switched flight vehicles by using nonfragile deep reinforcement learning

In this study, a novel nonfragile deep reinforcement learning (DRL) method was proposed to realize the finite-time control of switched unmanned flight vehicles. Control accuracy, robustness, and intelligence were enhanced in the proposed control scheme by combining conventional robust control and DRL characteristics. In the proposed control strategy, the tracking controller consists of a dynamics-based controller and a learning-based controller. The conventional robust control approach for the nominal system was used for realizing a dynamics-based baseline tracking controller. The learning-based controller based on DRL was developed to compensate model uncertainties and enhance transient control accuracy. The multiple Lyapunov function approach and mode-dependent average dwell time approach were combined to analyze the finite-time stability of flight vehicles with asynchronous switching. The linear matrix inequalities technique was used to determine the solutions of dynamics-based controllers. Online optimization was formulated as a Markov decision process. The adaptive deep deterministic policy gradient algorithm was adopted to improve efficiency and convergence. In this algorithm, the actor-critic structure was used and adaptive hyperparameters were introduced. Unlike the conventional DRL algorithm, nonfragile control theory and adaptive reward function were used in the proposed algorithm to achieve excellent stability and training efficiency. We demonstrated the effectiveness of the presented algorithm through comparative simulations.

Lower Limb Joint Torque Prediction Using Long Short-Term Memory Network and Gaussian Process Regression

The accurate prediction of joint torque is required in various applications. Some traditional methods, such as the inverse dynamics model and the electromyography (EMG)-driven neuromusculoskeletal (NMS) model, depend on ground reaction force (GRF) measurements and involve complex optimization solution processes, respectively. Recently, machine learning methods have been popularly used to predict joint torque with surface electromyography (sEMG) signals and kinematic information as inputs. This study aims to predict lower limb joint torque in the sagittal plane during walking, using a long short-term memory (LSTM) model and Gaussian process regression (GPR) model, respectively, with seven characteristics extracted from the sEMG signals of five muscles and three joint angles as inputs. The majority of the normalized root mean squared error (NRMSE) values in both models are below 15%, most Pearson correlation coefficient (R) values exceed 0.85, and most decisive factor (R2) values surpass 0.75. These results indicate that the joint prediction of torque is feasible using machine learning methods with sEMG signals and joint angles as inputs.

Predefined-Time Hierarchical Coordinated Neural Control for Hypersonic Reentry Vehicle

This paper investigates the predefined-time hierarchical coordinated adaptive control on the hypersonic reentry vehicle in presence of low actuator efficiency. In order to compensate for the deficiency of rudder deflection in advantage of channel coupling, the hierarchical design is proposed for coordination of the elevator deflection and aileron deflection. Under the control scheme, the equivalent control law and switching control law are constructed with the predefined-time technology. For the dynamics uncertainty approximation, the composite learning using the tracking error and the prediction error is constructed by designing the serial-parallel estimation model. The closed-loop system stability is analyzed via the Lyapunov approach and the tracking errors are guaranteed to be uniformly ultimately bounded in a predefined time. The tracking performance and the learning accuracy of the proposed algorithm are verified via simulation tests.

Neural Adaptive Dynamic Surface Asymptotic Tracking Control of Hydraulic Manipulators With Guaranteed Transient Performance

In this article, a novel neural network (NN)-based adaptive dynamic surface asymptotic tracking controller with guaranteed transient performance is proposed for n -degrees of freedom (DOF) hydraulic manipulators. To fulfill the work, the entire manipulator system model, including hydraulic actuator dynamics, is first established. Then, the neural adaptive dynamic surface controller is designed, in which the NN is utilized to approximate the unknown joint coupling dynamics, while the approximation error and uncertainties of the actuator dynamics are addressed by the nonlinear robust control law with adaptive gains. In addition, a modified funnel function that ensures the joint tracking errors remains within a predefined funnel boundary and is skillfully incorporated into the adaptive dynamic surface control (ADSC) design to achieve a guaranteed transient tracking performance. The theoretical analysis reveals that both the guaranteed transient tracking performance and asymptotic stability can be achieved with the proposed controller. Contrastive simulations are performed on a 2-DOF hydraulic manipulator to demonstrate the superiority of the proposed controller.

Neural network-based adaptive second-order sliding mode control for uncertain manipulator systems with input saturation

In order to solve the trajectory tracking problem for robotic manipulators with dynamic uncertainty, external disturbance and input saturation, a novel second-order sliding mode control scheme based on neural network is proposed in this paper. First of all, a model-based second-order non-singular fast terminal sliding mode controller (SONFTSMC) is designed to overcome the chattering problem under the consideration of uncertain parameters. Then attention is focused on the scenario that all those nonlinear uncertainties are unknown, and a new fuzzy wavelet neural network (FWNN) is designed to estimate those unknown uncertainties via lumping them into one compounded uncertainty. In addition, all parameters in FWNN are adjusted autonomously by using an adaptive method. The proposed second-order non-singular fast terminal sliding mode (SONFTSM) control method not only improves the convergence speed and tracking accuracy of the robotic manipulator, but also enhances its robustness. Finally, the advantages of SONFTSM control strategy over existing sliding mode control methods are verified with comparative simulations.

Broad learning control of a two-link flexible manipulator with prescribed performance and actuator faults

In this paper, we present a broad learning control method for a two-link flexible manipulator with prescribed performance (PP) and actuator faults. The trajectory tracking errors are processed through two consecutive error transformations to achieve the constraints in terms of the overshoot, transient error, and steady-state error. And the barrier Lyapunov function is employed to implement constraints on the transition state variable. Then, the improved radial basis function neural networks combined with broad learning theory are constructed to approximate the unknown model dynamics of flexible robotic manipulator. The proposed fault-tolerant PP control cannot only ensure tracking errors converge into a small region near zero within the preset finite time but also address the problem caused by actuator faults. All the closed-loop error signals are uniformly ultimately bounded via the Lyapunov stability theory. Finally, the feasibility of the proposed control is verified by the simulation results.

Synchronized control of multiple electrohydraulic systems with terminal sliding mode observer under parametric uncertainty and external load

The leader-following synchronization control strategy is proposed for multiple electro-hydraulic systems (MEHS) to realize all the follower outputs of electrohydraulic systems synchronized to a virtual leader demand. Due to existed lumped uncertainties generated by some uncertain errors of hydraulic parameters and unascertainable external load disturbance, the synchronization control performance of MEHS will be degraded by using many common controllers. In this study, a terminal sliding mode observer (TSMO) is adopted in the MEHS to estimate the lumped uncertainties such that guarantees uncertainty estimated errors convergence to zero in a finite time. Then a synchronized controller of MEHS is designed by backstepping iteration and Lyapunov technique to guarantee the output cylinder position of every EHS tracking the virtual leader demand. Finally, the feasibility and effectiveness of the designed TSMO and the proposed synchronized control strategy are verified via simulation and experiment.

Robust Control Based on Adaptive Neural Network for the Process of Steady Formation of Continuous Contact Force in Unmanned Aerial Manipulator

Contact force control for Unmanned Aerial Manipulators (UAMs) is a challenging issue today. This paper designs a new method to stabilize the UAM system during the formation of contact force with the target. Firstly, the dynamic model of the contact process between the UAM and the target is derived. Then, a non-singular global fast terminal sliding mode controller (NGFTSMC) is proposed to guarantee that the contact process is completed within a finite time. Moreover, to compensate for system uncertainties and external disturbances, the equivalent part of the controller is estimated by an adaptive radial basis function neural network (RBFNN). Finally, the Lyapunov theory is applied to validate the global stability of the closed-loop system and derive the adaptive law for the neural network weight matrix online updating. Simulation and experimental results demonstrate that the proposed method can stably form a continuous contact force and reduce the chattering with good robustness.

A comparative study of linear and nonlinear optimal control of a three-tank system

In this work, a laboratory scaled industrial interconnected nonlinear Multi-Input|Multi-Output (MIMO) three-tank system, was modelled to control the liquid levels. Ensuing the tradition in the process industry to apply linear controller to most control processes, a linear control scheme was developed for this system. However, since linear schemes are proximate to actual process models, they may not be adequate, especially for highly nonlinear systems. Therefore, a nonlinear control scheme was also developed and compared with the linear scheme. Specifically, optimal linear and nonlinear controllers were designed. In summary, the results of the two control schemes showed adequate performance. However, the linear controller had more robust control and required lesser computational demand compared to the nonlinear scheme. To enhance the computational demand of the nonlinear scheme, a third-party MATLAB toolbox, Automatic Control and Dynamic Optimization (ACADO) toolbox, that interfaces MATLAB with C++ to speed up computations was also utilised, and its results compared, and tentatively validate the earlier solved nonlinear control scheme.

Saturation-Tolerant Prescribed Control for a Class of MIMO Nonlinear Systems

This article proposes a saturation-tolerant prescribed control (SPC) for a class of multiinput and multioutput (MIMO) nonlinear systems simultaneously considering user-specified performance, unmeasurable system states, and actuator faults. To simplify the control design and decrease the conservatism, tunnel prescribed performance (TPP) is proposed not only with concise form but also smaller overshoot performance. By introducing non-negative modified signals into TPP as saturation-tolerant prescribed performance (SPP), we propose SPC to guarantee tracking errors not to violate SPP constraints despite the existence of saturation and actuator faults. Namely, SPP possesses the ability of enlarging or recovering the performance boundaries flexibly when saturations occur or disappear with the help of these non-negative signals. A novel auxiliary system is then constructed for these signals, which bridges the associations between input saturation errors and performance constraints. Considering nonlinearities and uncertainties in systems, a fuzzy state observer is utilized to approximate the unmeasurable system states under saturations and unknown actuator faults. Dynamic surface control is employed to avoid tedious computations incurred by the backstepping procedures. Furthermore, the closed-loop state errors are guaranteed to a small neighborhood around the equilibrium in finite time and evolved within SPP constraints although input saturations and actuator faults occur. Finally, comparative simulations are presented to demonstrate the feasibility and effectiveness of the proposed control scheme.

Active Disturbance Rejection Contouring Control of Robotic Excavators with Output Constraints and Sliding Mode Observer

This paper proposes an active disturbance rejection contouring control scheme for robotic excavators suffering from model uncertainties, external disturbances, and unmeasurable states. A sliding mode observer (SMO) is firstly designed to precisely estimate both joint velocities and lumped uncertainties and disturbances. These estimations are then fed back into the main controller which is constructed based on the task coordinate frame (TCF) approach. Furthermore, to meet the requirements of high-accuracy control performance, the barrier Lyapunov function (BLF) is utilized in the control design together with the previous techniques, which guarantees the stability of the whole system. Finally, numerical simulation is conducted with a high-reliability excavator model to verify the effectiveness of the proposed control algorithm under various operating conditions. In future work, further practical problems will be conducted to realize the application of robotic excavators in construction.

Actor-critic learning based coordinated control for a dual-arm robot with prescribed performance and unknown backlash-like hysteresis

In this paper, we focus on the tracking problem of a dual-arm robot (DAR) with prescribed performance and unknown input backlash-like hysteresis. Considering this problem, adaptive coordinated control with actor-critic (AC) design is proposed. Motivated by the increasing control requirements, prescribed performance is imposed on the DAR system to guarantee the tracking performance. In order to improve the self-learning ability and handle the problems caused by the input backlash-like hysteresis and system uncertainty, AC learning (ACL) algorithm is introduced. Through the cost function about tracking errors, a critic network is adopted to judge the control performance. An actor network is adopted to obtain the control input based on the critic result, where the system uncertainty and unknown part of the input backlash-like hysteresis are approximated by neural networks (NNs). In addition, the system stability is proven by the Lyapunov direct method. Numerical simulation is finally conducted to further testify the validity of the proposed coordinated control with AC design for the DAR system.

A Novel Trajectory Adjustment Mechanism-Based Prescribed Performance Tracking Control for Electro-Hydraulic Systems Subject to Disturbances and Modeling Uncertainties

This paper proposes a novel active disturbance compensation framework for exactly positioning control of electro-hydraulic systems (EHSs) subject to parameter deviations, unknown dynamics, and uncertain external load without velocity measurement mechanism. In order to accurately estimate and then actively compensate for the effects of these uncertainties and disturbances on the system dynamics, a combination between an extended sliding mode observer (ESMO) and a linear extended state observer (LESO) is firstly established for position control of EHSs. In addition, an inherited nonlinear filter-based trajectory planner with minor modifications is utilized to overcome the barriers of inappropriate desired trajectories which do not consider the system kinematic and dynamic constraints. Furthermore, for the first time, the command filtered (CF) approach and prescribed performance control (PPC) are successfully coordinated together and dexterously integrated into the backstepping framework to not only mitigate the computational cost significantly and avoid the “explosion of complexity” of the traditional backstepping design but also satisfy the predetermined transient tracking performance indexes including convergence rate, overshoot, and steady-state error. The stabilities of the observers and overall closed-loop system are rigorously proven by using the Lyapunov theory. Finally, comparative numerical simulations are conducted to demonstrate the advantages of the proposed approach.

Fault Detection Filter Design and Optimization for Switched Systems with All Modes Unstable

This problem of intelligent switched fault detection filter design is investigated in this article. Firstly, the mode-dependent average dwell time (MDADT) method is applied to generate the time-dependent switching signal for switched systems with all subsystems unstable. Afterwards, the switched fault detection filter is proposed for the generation of residual signal, which consists of dynamics-based filter and learning-based filter. The MDADT method and multiple Lyapunov function (MLF) method are employed to guarantee the stability and prescribed attenuation performance. The parameters of dynamics-based filter are given by solving a series of linear matrix inequalities. To improve the transient performance, the deep reinforcement learning is introduced to design learning-based filter in the framework of actor-critic. The output of learning-based filter can be viewed as uncertainties of dynamics-based filter. The deep deterministic policy gradient algorithm and nonfragile control are adopted to guarantee the stability of algorithm and compensate the external disturbance. Finally, simulation results are given to illustrate the effectiveness of the method in the paper.

Optimal full-state feedback observer integrated backstepping control of chemical processes with unknown internal dynamics

This paper studies the estimation and control problems of chemical processes with unknown internal dynamics. An observer with optimal full-state feedback characteristics for estimating the state variables and unknown dynamics is presented. Unlike other observers that need to know the frequency characteristics of the system, the pole of the proposed observer is determined automatically in a LQR formulation and the observer stability is also inherently ensured. In order to suppress the unknown internal dynamics, the proposed observer is then applied to the control design leading to an observer integrated backstepping control method. The proposed method does not depend on the detailed mathematical model of the system while the stability of the closed-loop system is guaranteed. The stability of the closed-loop system is proven in the Lyapunov sense. Extensive numerical simulations are presented to validate the proposed method.

Variable Structure Disturbance Observer Based Dynamic Surface Control of Electrohydraulic Systems with Parametric Uncertainty

This paper focuses on the position tracking control issue of electrohydraulic systems (EHS). The dynamical model of EHS is introduced in the first place, based on which a type of Variable Structure Disturbance Observer (VSDO) is constructed for EHS to estimate the parametric uncertainty the EHS possesses. Then, a backstepping controller is designed under VSDO to realize the high precision position tracking purpose. To avoid the phenomenon of differential explosion, a dynamic surface control method is adopted in this paper, which improved the position tracking control performance of EHS. The proposed theoretical results are verified by numerical simulation and experiment to illustrate the feasibility.

Observer-based adaptive neural tracking control for a class of nonlinear systems with prescribed performance and input dead-zone constraints

This paper investigates the problem of output feedback neural network (NN) learning tracking control for nonlinear strict feedback systems subject to prescribed performance and input dead-zone constraints. First, an NN is utilized to approximate the unknown nonlinear functions, then a state observer is developed to estimate the unmeasurable states. Second, based on the command filter method, an output feedback NN learning backstepping control algorithm is established. Third, a prescribed performance function is employed to ensure the transient performance of the closed-loop systems and forces the tracking error to fall within the prescribed performance boundary. It is rigorously proved mathematically that all the signals in the closed-loop systems are semi-globally uniformly ultimately bounded and the tracking error can converge to an arbitrarily small neighborhood of the origin. Finally, a numerical example and an application example of the electromechanical system are given to show effectiveness of the acquired control algorithm.

Model-Based Design of an Improved Electric Drive Controller for High-Precision Applications Based on Feedback Linearization Technique

This paper presents the design flow of an advanced non-linear control strategy, able to absorb the effects that the main causes of torque oscillations, concerning synchronous electrical drives, cause on the positioning of the end-effector of a manipulator robot. The control technique used requires an exhaustive modelling of the physical phenomena that cause the electromagnetic torque oscillations. In particular, the Cogging and Stribeck effects are taken into account, whose mathematical model is incorporated in the whole system of dynamic equations representing the complex mechatronic system, formed by the mechanics of the robot links and the dynamics of the actuators. Both the modelling procedure of the robot, directly incorporating the dynamics of the actuators and the electrical drive, consisting of the modulation system and inverter, and the systematic procedure necessary to obtain the equations of the components of the control vector are described in detail. Using the Processor-In-the-Loop (PIL) paradigm for a Cortex-A53 based embedded system, the beneficial effect of the proposed advanced control strategy is validated in terms of end-effector position control, in which we compare classic control system with the proposed algorithm, in order to highlight the better performance in precision and in reducing oscillations.

Prescribed Performance Control with Sliding-Mode Dynamic Surface for a Glue Pump Motor Based on Extended State Observers

The actuator of a particleboard glue-dosing system, the glue pump motor, is affected by external disturbances and unknown uncertainty. In order to achieve accurate glue-flow tracking, in this paper, a glue pump motor compound control method was designed. First, the prescribed performance control method is used to improve the transient behaviors, and the error of the glue flow tracking is guaranteed to converge to a preset range, as a result of the design of an appropriate performance function. Second, two extended state observers were designed to estimate the state vector and the disturbance, in order to improve the robustness of the controlled system. To further strengthen the steady-state performance of the system, the sliding-mode dynamic surface control method was introduced to compensate for uncertainties and disturbances. Finally, a Lyapunov stability analysis was conducted, in order to prove that all of the signals are bounded in a closed-loop system, and the effectiveness and feasibility of the proposed method were verified through numerical simulation.

High-precision motion servo control of double-rod electro-hydraulic actuators with exact tracking performance

Comprehensive effects coming from measurement noises, matched and mismatched uncertainties make it difficult for electro-hydraulic servo systems to further attain high-accuracy tracking level. The existing control strategies often consider these control issues one-sidedly. Accordingly, we develop two different control strategies combining integral robust control and direct adaptive control for high-precision position control of double-rod electro-hydraulic systems to account for these control issues concurrently. Specially, by skillfully introducing a filtered error function, a novel desired compensation adaptive control framework will be integrated into the controller design to reduce environmental noises. Moreover, an improved noise-alleviation method is proposed to achieve high-accuracy calculation of the standard sign function in nonlinear integral robust terms. Furthermore, each of the control algorithms can guarantee asymptotic position tracking performance in general. Comparative experiments and simulation results show the evident superiorities of the developed control strategies.