Adaptive Neural Network Control of a Robotic Manipulator With Time-Varying Output Constraints

Tracking control via time-varying feedback for an uncertain robotic system with both output constraint and dead-zone input

This paper is devoted to the tracking control for an uncertain robotic system with both output constraint and dead-zone input. Remarkably, the distinctive characters of the system are reflected by system uncertainties and output constraint. First, more serious uncertainties are involved since unknown nonlinear dynamic matrices, external disturbance and the dead-zone input (see unknown slopes and break points therein) are simultaneously considered, but those of the related literature are not. Second, weaker conditions on the output constraint are allowed since the constraint functions considered are only first but not more order continuously differentiable while any their time derivatives are not necessarily available for feedback. This leads to the incapability of the traditional control schemes on this topic. To solve the control problem, a novel control framework is proposed based on time-varying feedback which overcomes the serious system uncertainties while relaxes the conditions on output constraints. Specifically, a state transformation with a time-varying gain is first introduced to derive a new system. Then, by using the traditional backstepping method with the introduction of the time-varying gain in the estimations of some uncertain terms, a time-varying feedback controller is explicitly designed, which ensures that all the states of the resulting closed-loop system are bounded while system output asymptotically tracks the reference signal without any violation of the output constraint. Finally, simulation results for two practical examples are provided to validate the effectiveness of the proposed theoretical results, and moreover, a comparison with PID method is given to show the superiority of the proposed method on tracking accuracy and robustness.

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.

Backstepping control based on adaptive neural network and disturbance observer for reconfigurable variable stiffness actuator

Reconfigurable variable stiffness actuator (RVSA) has attracted increasing attention in robotics due to its safety, compliance, and robustness. However, the control of the RVSA is challenging due to nonlinear factors such as high-order nonlinear dynamic, model uncertainties, time-varying model parameters, and disturbances. In this paper, firstly, a lightweight RVSA structure with both passive and active nonlinear variable stiffness characteristic is developed. Secondly, a dynamic surface backstepping control method based on a radial basis neural network and disturbance observer (DSBC-RBFNN-DOB) is proposed to achieve position control of the lightweight RVSA with matched and unmatched uncertainties. To address solve the "complexity explosion" and noise problems in traditional backstepping control, the dynamic surface backstepping control (DSBC) method is used to design the controller. Then, a method based on radial basis neural network (RBFNN) and disturbance observer (DOB) are used to compensate for the matched and unmatched uncertainties in the link and motor. In this method, the matched uncertainties are compensated using RBFNN, and the DOB is integrated to compensate RBFNN approximation errors and unmatched uncertainties. Through Lyapunov stability analysis, the semi-global boundedness of the controller is proven. Finally, the proposed method is simulated and actually implemented, verifying the effectiveness of the method. Simulation and experimental results show that the root mean square error (RMSE) of the proposed method is only 0.97277° and 0.6418°, respectively. Compared with PID, DSBC, and DSBC-RBFNN, the error reduction percentages in simulation (experiment) are 85.6 % (88.9 %), 49.4 % (88.4 %) and 36.1 % (80.0 %) respectively.

Disturbance Rejection Event-Triggered Robust Model Predictive Control for Tracking of Constrained Uncertain Robotic Manipulators

A novel hierarchical control framework combining computed-torque-like control (CTLC) with disturbance-observer-based event-triggered robust model predictive control (DO-ET-RMPC) is proposed for the trajectory tracking control of robotic manipulators with bounded disturbances and state and control input constraints. The CTLC approach is first used to cancel the exact nonlinear dynamics of the original tracking error system to obtain a set of decoupling linear tracking error subsystems, thus reducing the optimization complexity of model predictive control (MPC). The composite DO-ET-RMPC scheme is then developed based on the so-called dual-mode MPC approach to robustly stabilize the tracking error subsystems, which could improve the robustness of MPC and save its computational resources simultaneously. The continuous-time theoretical properties of the DO-ET-RMPC scheme, considering disturbances and state and control input constraints simultaneously, are provided for the first time, including the avoidance of Zeno behavior, robust constraint satisfaction, recursive feasibility, and stability. In the end, the superiorities of the proposed control scheme are verified by the comparative simulations.

Event-based adaptive tracking control for robotic systems with deferred position constraints and unknown backlash-like hysteresis

This paper proposes an event-based adaptive tracking control scheme for the n-link robotic systems in the presence of unknown backlash-like hysteresis (BLH) and deferred position constraints. By combining a transformation error with an asymmetric Lyapunov function, the devised control tactic achieves that the position constraints of robotic systems are not violated after user pre-specified time. In contrast to the results of robotic systems with position constraints, this paper removes a common assumption condition generated by the conventional barrier Lyapunov function method. Then, the adverse effect of unknown BLH can be offset by the Nussbaum function. Meanwhile, an event-triggered mechanism is designed to economize on the network bandwidth resources. Finally, based on the Lyapunov theory, an event-based adaptive tracking control tactic is proposed to ensure that all the signals of robotic systems are bounded under unknown BLH and deferred position constraints. Some simulation results proof that the devised control scheme is valid.

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.

Adaptive prescribed settling time periodic event-triggered control for uncertain robotic manipulators with state constraints

In this paper, an adaptive prescribed settling time periodic event-triggered control (APST-PETC) is investigated for uncertain robotic manipulators with state constraints. In order to economize network bandwidth occupancy and reduce computational burden, a periodic event-triggered control (PETC) strategy is proposed to reduce the update frequency of the control signal and avoid unnecessary continuous monitoring. Besides, considering that the maneuverable space of the actual robotic manipulators is often limited, the barrier Lyapunov function (BLF) is applied to deal with the influence of the constraint characteristics on the robotic manipulators. Further, based on the one-to-one nonlinear mapping function of the system tracking error, an adaptive prescribed settling time control (APSTC) is designed to ensure that the system tracking error reaches the predetermined precision residual set within the prescribed settling time. Finally, theoretical analysis and comparative experiments are given to verify its feasibility.

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.

Secure Control of Networked Control Systems Using Dynamic Watermarking

We here investigate the secure control of networked control systems developing a new dynamic watermarking (DW) scheme. First, the weaknesses of the conventional DW scheme are revealed, and the tradeoff between the effectiveness of false data injection attack (FDIA) detection and system performance loss is analyzed. Second, we propose a new DW scheme, and its attack detection capability is interrogated using the additive distortion power of a closed-loop system. Furthermore, the FDIA detection effectiveness of the closed-loop system is analyzed using auto/cross-covariance of the signals, where the positive correlation between the FDIA detection effectiveness and the watermarking intensity is measured. Third, the tolerance capacity of FDIA against the closed-loop system is investigated, and theoretical analysis shows that the system performance can be recovered from FDIA using our new DW scheme. Finally, the experimental results from a networked inverted pendulum system demonstrate the validity of our proposed scheme.

Robust adaptive fault detection and diagnosis observer design for a class of nonlinear systems with uncertainty and unknown time-varying internal delay

This paper introduces a novel robust adaptive fault detection and diagnosis (FDD) observer design approach for a class of nonlinear systems with parametric uncertainty, unknown system fault and time-varying internal delays. The conditions for the existence of the proposed FDD are obtained based on the well-known Linear Matrix Inequalities (LMI) technique. Using Lyapunov stability theory, the adaptation laws for updating the observer weights and unknown faults estimation are derived based on which the convergence of the state estimation error to zero and asymptotic stability of the error dynamics are proven. Toward this, a new structural algorithm for FDD observer design is also derived based on LMIs. The performance of the proposed method is also investigated while applying to some industrial systems. Simulation results illustrate superior performance of the proposed method for the systems subject to time-varying unknown delays on states, uncertainty in nonlinear system modeling and unknown system faults.

DSC-based RBF neural network control for nonlinear time-delay systems with time-varying full state constraints

The presented control scheme in this paper aims at stabilizing uncertain time-delayed systems requiring all states to change within the preset time-varying constraints. The controller design framework is based on the backstepping method, drastically simplified by the dynamic surface control technique. Meanwhile, the radius basis function neural networks are utilized to deal with the unknown items. To prevent all state variables from violating time-varying predefined regions, we employ the time-varying barrier Lyapunov functions during the backstepping procedure. Moreover, appropriate Lyapunov-Krasovskii functionals are used to cancel the influence of the time-delay terms on the system's stability. Under the presented control laws and Lyapunov analysis, it is proven that constraints on all state variables are not breached, good tracking performance of desired output is achieved, and all signals in the closed-loop systems are bounded. The effectiveness of our control scheme is confirmed by a simulation example.

High-order control barrier functions-based impedance control of a robotic manipulator with time-varying output constraints

This paper focuses on the impedance control for robotic manipulators with time-varying output constraints. High-order control barrier functions (HoCBFs) are firstly proposed for a nonlinear system with high relative-degree time-varying constraints. Then, the HoCBFs are introduced to impedance control for robotic manipulators, where the HoCBFs are employed to avoid the violation of time-varying output constraints in Cartesian space by quadratic program (QP), and the impedance control is designed to achieve compliance for human-robot interaction (HRI). In this way, the desired trajectory within the safety-critical region can be tracked without violating the output constraints due to the controller generated from QP, and the safe HRI can also be achieved because of the usage of impedance control method. Finally, simulation tests are conducted to verify the proposed control design methods.

Optimal Bounded Ellipsoid Identification With Deterministic and Bounded Learning Gains: Design and Application to Euler-Lagrange Systems

This article proposes an effective optimal bounded ellipsoid (OBE) identification algorithm for neural networks to reconstruct the dynamics of the uncertain Euler-Lagrange systems. To address the problem of unbounded growth or vanishing of the learning gain matrix in classical OBE algorithms, we propose a modified OBE algorithm to ensure that the learning gain matrix has deterministic upper and lower bounds (i.e., the bounds are independent of the unpredictable excitation levels in different regressor channels and, therefore, are capable of being predetermined a priori). Such properties are generally unavailable in the existing OBE algorithms. The upper bound prevents blow-up in cases of insufficient excitations, and the lower bound ensures good identification performance for time-varying parameters. Based on the proposed OBE identification algorithm, we developed a closed-loop controller for the Euler-Lagrange system and proved the practical asymptotic stability of the closed-loop system via the Lyapunov stability theory. Furthermore, we showed that inertial matrix inversion and noisy acceleration signals are not required in the controller. Comparative studies confirmed the validity of the proposed approach.

Adaptive Neural Network Control for Full-State Constrained Robotic Manipulator With Actuator Saturation and Time-Varying Delays

This article proposes an adaptive neural network (NN) control method for an n -link constrained robotic manipulator. Driven by actual demands, manipulator and actuator dynamics, state and input constraints, and unknown time-varying delays are taken into account simultaneously. NNs are employed to approximate unknown nonlinearities. Time-varying barrier Lyapunov functions are utilized to cope with full-state constraints. By resorting to saturation function and Lyapunov-Krasovskii functionals, the effects of actuator saturation and time delays are eliminated. It is proved that all the closed-loop signals are semiglobally uniformly ultimately bounded, full-state constraints and actuator saturation are not violated, and error signals remain within compact sets around zero. Simulation studies are given to demonstrate the validity and advantages of this control scheme.

Anti-Saturation-Based Adaptive Sliding-Mode Control for Active Suspension Systems With Time-Varying Vertical Displacement and Speed Constraints

In this article, an adaptive sliding-mode control scheme is developed for a class of uncertain quarter vehicle active suspension systems with time-varying vertical displacement and speed constraints, in which the input saturation is considered. The integral terminal SMC is adopted to improve convergence accuracy and avoid singular problems. In addition, neural networks are used to model unknown terms in the system and the backstepping technique is taken into account to design the actual controller. To guarantee that the time-varying state constraints are not violated, the corresponding Barrier Lyapunov functions are constructed. At the same time, a continuous differentiable asymmetric saturation model is developed to improve the stability of the system. Then, the Lyapunov stability theory is used to verify that all signals of the resulting system are semi globally uniformly ultimately bounded, time-varying state constraints are not violated, and error variables can converge to the small neighborhood of 0. Finally, results of the simulation of the designed control strategy are given to further prove the effectiveness.

Full-state constrained neural control and learning for the nonholonomic wheeled mobile robot with unknown dynamics

The adaptive learning and control are proposed for the full-state(FS) constrained NWMR system with external destabilization. First, the constrained state is reformulated as the unconstrained state. Then, approximating the unknown dynamics in the closed-loop (CL) system is conducted via radial basis function (RBF) NN. Also, a sliding term is designed to deal with the external destabilization and the neural network training error. The derived adaptive neural controller can realize the asymptotic stability of a robot system without violating FS constraints. Moreover, the neural weights are converged so that the unknown dynamics are expressed by the constant weights in the CL system. It is also applicable to other similar control tasks. Lastly, the proposed algorithm is simulated and validated.

Asymptotic Tracking Control of State-Constrained Nonlinear Systems With Time-Varying Powers

This article investigates the asymptotic tracking control problem for full-state-constrained nonlinear systems with unknown time-varying powers. By introducing a nonlinear state-dependent transformation, a continuous bounded scalar function, and lower and higher powers into adding a power integrator control design, full-state constraints are skillfully handled without imposing frequently used feasibility conditions in traditional barrier Lyapunov function-based methods, and an asymptotic tracking control design is provided. It is proved that all the closed-loop signals are bounded, full-state constraints are not transgressed, and the asymptotic tracking is achieved.

Finite-Time Neural Network Fault-Tolerant Control for Robotic Manipulators under Multiple Constraints

In this study, a backstepping-based fault-tolerant controller for a robotic manipulator system with input and output constraints was developed. First, a barrier Lyapunov function was adopted to ensure that the system output satisfied time-varying constraints. Subsequently, the actuator input saturation and asymmetric dead-zone characteristics were also considered, and the actuator characteristics were described using a continuous function. The impacts of actuator failures and unknown dynamical parameters of the system were eliminated by employing Gaussian radial basis function neural networks. The external disturbances were compensated for, using a disturbance observer. Meanwhile, a finite-time dynamic surface technique was adopted to accelerate the convergence of the system errors. Finally, simulation of a 2-degrees-of-freedom robotic manipulator system showed the effectiveness of the proposed controller.

Critic Learning-Based Control for Robotic Manipulators With Prescribed Constraints

In this article, the optimal control problem for robotic manipulators (RMs) with prescribed constraints is addressed. Considering the environmental conditions and requirements of practical applications, prescribed constraints are imposed on the system states to guarantee the control performance and normal operation of the robotic system. Accordingly, an error transformation function is adopted to cope with the prescribed constraints and generate an equivalent unconstrained error for the convenience of the intelligent control design. In order to improve the learning ability and optimize the control performance, critic learning (CL) is introduced to the control design of the constrained RM based on the transformed equivalent unconstrained system. In addition, the stability analysis is given to illustrate the feasibility of the proposed CL-based control. Finally, simulations are conducted on a two-degree-of-freedom (DOF)-constrained RM to further validate the effectiveness of the proposed controller.

Removing Feasibility Conditions on Adaptive Neural Tracking Control of Nonlinear Time-Delay Systems With Time-Varying Powers, Input, and Full-State Constraints

This article investigates the tracking control for input and full-state-constrained nonlinear time-delay systems with unknown time-varying powers, whose nonlinearities do not impose any growth assumption. By utilizing the auxiliary control signal and nonlinear state-dependent transformation (NSDT) to counteract the effect of input saturation and cope with full-state constraints, respectively, and then introducing lower and higher powers and Lyapunov-Krasovskii (L-K) functionals in control design together with the adaptive neural-networks (NNs) method, an adaptive neural tracking control design is provided without feasibility conditions. It is proved that NNs approximation is valid, all the closed-loop signals are semiglobally bounded, and input and full-state constraints are not violated.

UDE-based task space tracking control of uncertain robot manipulator with input saturation and output constraint

This paper investigates the trajectory tracking problem of uncertain robot manipulators with input saturation and output constraints. Uncertainty and disturbance estimator (UDE) is used to tackle the model uncertainties and external disturbances. Different from most existing methods, UDE only needs the bandwidth of the unknown plant model for design, which makes it easy to be implemented. Nonlinear state-dependent function is employed to cope with output constraints and a second order auxiliary system is constructed to solve the input saturation. Finally, an UDE-based tracking controller is proposed based on the backstepping method. With the proposed control scheme, the input saturation and the output constraints are not violated, and all signals in the closed-loop system are bounded. The comparative simulation results of a two-link robot manipulator are utilized to validate the effectiveness and superiority of the proposed control method.

Disturbance Observer-Based Fault-Tolerant Control for Robotic Systems With Guaranteed Prescribed Performance

The actuator failure compensation control problem of robotic systems possessing dynamic uncertainties has been investigated in this paper. Control design against partial loss of effectiveness (PLOE) and total loss of effectiveness (TLOE) of the actuator are considered and described, respectively, and a disturbance observer (DO) using neural networks is constructed to attenuate the influence of the unknown disturbance. Regarding the prescribed error bounds as time-varying constraints, the control design method based on barrier Lyapunov function (BLF) is used to strictly guarantee both the steady-state performance and the transient performance. A simulation study on a two-link planar manipulator verifies the effectiveness of the proposed controllers in dealing with the prescribed performance, the system uncertainties, and the unknown actuator failure simultaneously. Implementation on a Baxter robot gives an experimental verification of our controller.

Prescribed performance tracking control for a class of nonlinear system considering input and state constraints

This article develops a new anti-saturation tracking approach for effectively controlling a type of state-constrained systems under actuator failure. To construct a feedback control loop possessed the predetermined indexes, an auxiliary variable incorporated with a performance guider is first introduced into the design process. Then, a robust fault tolerant control law with the variable-gains is devised to guarantee that the tracking errors can be suppressed in the specified range after a predetermined time. In order to dispose of the input constraint problem, an anti-saturation algorithm is designed without compromising the prescribed capability indexes in control process, it is shown that the proposed feedback control loop can efficiently fulfill the fast and accurate requirement of the constraint tasks. Finally, computer simulation related with robot manipulator is taken to evaluate the validity of designed method.

Event-Triggered Adaptive Fuzzy Output-Feedback Control for Nonstrict-Feedback Nonlinear Systems With Asymmetric Output Constraint

This article addresses the event-triggered adaptive fuzzy output-feedback control problem for a class of nonstrict-feedback nonlinear systems with asymmetric and time-varying output constraints, as well as unknown nonlinear functions. By designing a linear observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy output-feedback control scheme is proposed. The barrier Lyapunov function (BLF) and the error transformation technique are used to handle the output constraint under a completely unknown initial tracking condition. It is shown that with the proposed control scheme, all the solutions of the closed-loop system are semiglobally bounded, and the tracking error converges to a small set near zero, while the output constraint is satisfied within a predetermined finite time, even when the constraint condition is violated initially. Moreover, with the proposed event-triggering mechanism (ETM), the Zeno behavior can be strictly ruled out. An example is finally provided to demonstrate the effectiveness of the proposed control method.

Adaptive Finite-Time Containment Control of Uncertain Multiple Manipulator Systems

This article is concerned with the containment control of multiple manipulators with uncertain parameters. A novel distributed adaptive backstepping strategy is given in the finite-time control framework. The finite-time command filters (FTCFs) used in the strategy can avoid the explosion of complexity problem for conventional backstepping. To further improve the control performance, the filtering errors caused by the used FTCFs are removed by using the error compensation mechanism (ECM). The proposed virtual control signal, the control torque, and the adaptive updating law can guarantee the set tracking errors converge to an adjustable neighborhood of the origin in finite time in the presence of uncertain parameters. Because the virtual control signal and ECM only use the local information, the established method is completely distributed. Two simulation examples are given to show the effectiveness of the proposed scheme.

Nonlinear time delay estimation based model reference adaptive impedance control for an upper-limb human-robot interaction

A nonlinear Time Delay Estimation (TDE) based model reference adaptive impedance controller was developed for Tarbiat Modares University Upper Limbs Rehabilitation Robot (TUERR). The proposed controller uses a stable reference impedance model, which produces desired dynamic relationship between applied force and position error for the robot End-effector to track the desired trajectory. TDE based model reference adaptive controller estimates unknown system dynamics and uncertainties, and the adaption law modifies the controller gains. Using a Lyapunov function was shown trajectory tracking errors in the overall system are bounded. In addition, a performance-based velocity profile proposed to modify the pace of trajectory planning considering the deviation from the desired path. Finally, the performance of the presented controller and rehabilitation process is experimentally investigated for TUERR.

HOSM controller design with an output constraint and its application

This work has developed an approach to a high-order sliding mode (HOSM) controller design for nonlinear systems subject to output constraints. To handle the output constraints, a barrier Lyapunov function (BLF) has been adopted. By inserting the BLF into the revamped adding a power integrator (API) technique, a HOSM controller, which can handle the closed-loop sliding mode dynamics synchronously with and without output constraints, is constructively framed. The strictly mathematical proof shows that the presented strategy can assure the finite-time stability of the closed-loop system and the achievement of a pre-set output constraint. The differences between the proposed HOSM controller and the traditional HOSM controller are discussed via a numerical example. Finally, the theoretical results obtained are successfully applied to a series elastic actuator system. The simulation results clearly confirm the merit of the presented HOSM algorithm.

Large-Angle Velocity-Free Attitude Tracking Control of Satellites: An Observer-Free Framework

The challenging problem on the design of a large-angle attitude tracking controller for rigid satellites without angular velocity measurements is investigated in this article. An efficient and practical angular velocity-free control strategy with a simple, yet efficient structure is proposed. The attitude tracking maneuver is accomplished with the desired attitude pointing accuracy ensured despite disturbances. Compared with the existing observer-based velocity-free schemes, no observer is embedded into the control scheme. The developed approach can be implemented online and in real time. It does not require expensive online computation, enabling its convenient application to practical large-angle attitude tracking maneuvers. The presented control solution is numerically and experimentally validated on a rigid satellite testbed.

Adaptive Fixed-Time Neural Network Tracking Control of Nonlinear Interconnected Systems

In this article, a novel adaptive fixed-time neural network tracking control scheme for nonlinear interconnected systems is proposed. An adaptive backstepping technique is used to address unknown system uncertainties in the fixed-time settings. Neural networks are used to identify the unknown uncertainties. The study shows that, under the proposed control scheme, each state in the system can converge into small regions near zero with fixed-time convergence time via Lyapunov stability analysis. Finally, the simulation example is presented to demonstrate the effectiveness of the proposed approach. A step-by-step procedure for engineers in industry process applications is proposed.

Performance-Guaranteed Fault-Tolerant Control for Uncertain Nonlinear Systems via Learning-Based Switching Scheme

This article is concerned with the challenge of guaranteeing output constraints for fault-tolerant control (FTC) of a class of unknown multi-input single-output (MISO) nonlinear systems in the presence of actuator faults. Most industrial systems are equipped with redundant actuators and a fault detection-isolation mechanism for accommodating unexpected actuator faults. To simplify the system design and reduce the risk of false alarm or missed detection brought by the detection unit, a learning-based switching function scheme is proposed to automatically activate different sets of actuators in a rotational manner without human intervention. By this means, no explicit fault detection mechanism is needed. An additional step has been made to guarantee that the system output remains in user-defined time-varying asymmetric output constraints all the time during the occurrence of failures by utilizing error transformation techniques. The stability of the transformed system can equivalently deliver the result that the original system output stays in the required bounds. Hence, system crash or further catastrophic outcomes can be avoided. A neural network is integrated to embody the adaptive FTC design for dealing with unknown system dynamics. The dynamic surface control (DSC) technique is also invoked to decrease complexity. Furthermore, the stability analysis is carried out by the standard Lyapunov approach to guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the proposed scheme.

A General Position Control Method for Planar Underactuated Manipulators With Second-Order Nonholonomic Constraints

The study on the stabilization of planar underactuated manipulators without gravity is well recognized as a major challenge since the system includes a second-order nonholonomic constraint when the passive link is not located at the first link. It is important to solve this difficulty for applications such as systems working in aerospace or underwater. This article presents a position control method based on bidirectional motion planning and intelligent optimization for this kind of system. The control objective is to move the end effector of the manipulator from its initial position to a given target position. The differential evolution algorithm is applied to solve the target angles of all links corresponding to the target position of the end effector. Then, bidirectional motion planning is performed, which consists of forward and backward motions. Each motion is planned by designing a trajectory for every active link based on their initial and target angles. During the forward motion, all active links except the first one are moved to their target angles, and the first active link and the passive link to the intermediate angles. For the backward motion, the first active link is moved to its target angle, the other active links remain at their target angles, and the passive link will be moved to its target angle at the same time. The planned trajectories are chosen based on the time-scaling method and differential evolution algorithm to make sure that the forward and backward planned motions can be connected smoothly. Finally, the trajectory tracking controllers for all active links are designed based on the sliding-mode control method. The proposed control method is verified on planar four-link underactuated manipulators with different passive joints. This strategy has the advantage that it works for planar underactuated manipulators with a second-order nonholonomic constraint whose passive link can be at different positions. Meanwhile, by combining intelligent optimization with bidirectional motion planning, the control process becomes simpler and more effective.

TSM-Based Adaptive Fuzzy Control of Robotic Manipulators with Output Constraints

This paper proposes an adaptive control scheme based on terminal sliding mode (TSM) for robotic manipulators with output constraints and unknown disturbances. The fuzzy logic system (FLS) is developed to approximate unknown dynamics of robotic manipulators. An error transformation technique is used in the process of controller design to ensure that the output constraints are not violated. The advantage of the error transformation compared to traditional barrier Lyapunov functions (BLFs) is that there is no need to design a virtual controller. Thus, the design complexity of the controller is reduced. Through Lyapunov stability analysis, the system state can be proved to converge to the neighborhood near the balanced point in finite time. Extensive simulation results illustrated the validity of the proposed controller.

Adaptive Neural Network Fixed-Time Leader-Follower Consensus for Multiagent Systems With Constraints and Disturbances

This article is concerned with fixed-time leader-follower consensus problem for multiagent systems (MASs) with output constraints, unknown control direction, unknown system dynamics, unknown external disturbance, and dead-zone control input. First, a fixed-time distributed observer is presented for each follower to estimate the leader's states. Next, using a modified nonlinear mapping, an output-constrained system is transformed into an unconstrained system. Then, by adopting adding a power integrator technique, radial basis function neural network (RBFNN) approximation, and adaptive method, the ideal fixed-time stable virtual control protocol is derived and the issues of unknown control direction, unknown system dynamics, and unknown external disturbance are addressed. Finally, the actual control protocol is developed using the bound of dead-zone parameters. It is shown that the proposed control scheme achieves fixed-time leader-follower consensus of the studied MAS. The presented control protocol is applied to the leader-follower consensus of inverted pendulums and simulation results verify its effectiveness.

Adaptive Neural-Network Control of MIMO Nonaffine Nonlinear Systems With Asymmetric Time-Varying State Constraints

In this paper, a novel robust adaptive barrier Lyapunov function (BLF)-based backstepping controller has been proposed for a class of interconnected, multi-input-multi-output (MIMO) unknown nonaffine nonlinear systems with asymmetric time-varying (ATV) state constraints. The design involves a neural-network-based online approximator to cope with uncertain dynamics of the system. To tune its weights, a novel adaptive law is proposed based on the Hadamard product. A theorem has also been proposed to have the bounds on virtual control signals beforehand. This theorem eliminates the need for tedious offline computation for the feasibility condition on the virtual controller in BLF-based controller design. To overcome the problem of unknown control gain in the nonaffine system, Nussbaum gain has been used during the design. A simulation study on the robot manipulator in task space has been performed to illustrate the effectiveness of the proposed methodology.

Event-Triggered Reinforcement Learning-Based Adaptive Tracking Control for Completely Unknown Continuous-Time Nonlinear Systems

In this paper, event-triggered reinforcement learning-based adaptive tracking control is developed for the continuous-time nonlinear system with unknown dynamics and external disturbances. The critic and action neural networks are designed to approximate an unknown long-term performance index and controller, respectively. The dead-zone event-triggered condition is developed to reduce communication and computational costs. Rigorous theoretical analysis is provided to show that the closed-loop system can be stabilized. The weight errors and the filtered tracking error are all uniformly ultimately bounded. Finally, to demonstrate the developed controller, the simulation results are provided using an autonomous underwater vehicle model.

Guidance-Error-Based Robust Fuzzy Adaptive Control for Bottom Following of a Flight-Style AUV With Saturated Actuator Dynamics

This paper addresses the problem of robust bottom following control for a flight-style autonomous underwater vehicle (AUV) subject to system uncertainties, actuator dynamics, and input saturation. First, the actuator dynamics that is approximated by a first-order differential equation is inserted into the AUV dynamics model, which renders a high-order nonlinear dynamics analysis and design in the model-based backstepping controller by utilizing guidance errors. Second, to overcome the shaking control behavior resulted by the model-based high-order derivative calculation, a fuzzy approximator-based model-free controller is proposed, in order to online approximate the unknown part of the ideal backstepping architecture. In addition, the adaptive error estimation technology is resorted to compensate the system approximation error, ensuring that all the position and orientation errors of robust bottom following control tend to zero. Third, to further tackle the potential unstable control behavior from inherent saturation of control surfaces driven by rudders, an additional adaptive fuzzy compensator is introduced, in order to compensate control truncation between the unsaturated and saturation inputs. Subsequently, Lyapunov theory and Barbalat lemma are adopted to synthesize asymptotic stability of the entire bottom following control system. Finally, comparative numerical simulations with different controllers, environmental disturbances and initial states are provided to illustrate adaptability and robustness of the proposed bottom following controller for a flight-style AUV with saturated actuator dynamics.

Distributed tracking control for multiple Euler-Lagrange systems with communication delays and input saturation

This study mainly investigates the problem of distributed tracking control for time-varying delay existing multiple Euler-Lagrange systems considering full-state constraints and input saturation under the directed graph. Specifically, the system under consideration consists of system uncertainties and external disturbances. In the control law design, a distributed observer is first designed that the followers can obtain the leader's time-varying information. Then the barrier Lyapunov function technique is used to make sure the system errors can converge to a certain range while the anti-windup method is utilized to overcome the influence of control input saturation. Further, in order to prevent chattering, an adaptive law is given. Numerical simulations are given to verify the proposed algorithms.

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

This paper presents an adaptive neural network (NN) control of a two-degree-of-freedom manipulator driven by an electrohydraulic actuator. To restrict the system output in a prescribed performance constraint, a weighted performance function is designed to guarantee the dynamic and steady tracking errors of joint angle in a required accuracy. Then, a radial-basis-function NN is constructed to train the unknown model dynamics of a manipulator by traditional backstepping control (TBC) and obtain the preliminary estimated model, which can replace the preknown dynamics in the backstepping iteration. Furthermore, an adaptive estimation law is adopted to self-tune every trained-node weight, and the estimated model is online optimized to enhance the robustness of the NN controller. The effectiveness of the proposed control is verified by comparative simulation and experimental results with Proportional-integral-derivative and TBC methods.