In this paper, a fixed-time adaptive deferred constrained control strategy is proposed for a flexible single-link manipulator system with input saturation. Fuzzy Neural Networks are utilized to estimate the unknown dynamics of the flexible manipulator system as well as the errors caused by input saturation. To address output constraints imposed within a prescribed time period, a time-shift function and an adjusted barrier function are introduced. The system’s stability is rigorously proven using the direct Lyapunov method. Finally, numerical simulations and experimental results are presented to validate the effectiveness and superiority of the proposed control approach.

This article focuses on the constrained optimization problem for second-order multiagent systems that experience heterogeneous communication delays. Specifically, the involved agents work together to find the optimal solution of a global payoff function, which is summed by multiple strongly convex local payoff functions, with each function being exclusively owned by an individual agent. However, the feasible solutions must satisfy a coupled equality constraint, formulated by individual parameters assigned to each agent. Initially, a basic anti-delay distributed protocol is developed, which leverages a scattering transformation to enhance the generation of received information. Using the Lyapunov framework, we demonstrate that the agents coordinated by this anti-delay distributed protocol can effectively reach a consensus on the expected optimal solution, despite the presence of communication delays. In addition, we present two results that extend the basic anti-delay distributed protocol. First, we consider the scenario of lacking velocity and develop a velocity-free anti-delay distributed protocol to achieve the concerned constrained optimization objective. Next, we augment the system order and develop an anti-delay distributed optimization protocol for integrator chain multiagent systems. Finally, we confirm the anti-delay performance of the developed distributed protocols through simulations.

A neuro adaptive control for deploying a partial differential equation-based multi-agent system in 3D space with a non-collocated observer is proposed in this study. Since the full states of the system are unavailable in practice, an observer-based control is developed to ensure stability of the underlying closed-loop system. In addition, the system uncertainty is addressed by introducing a neural network control. By choosing appropriate system parameters, the desired control objectives can be achieved. The proposed strategy is simple to implement and its implementation condition is easily satisfied. Finally, the effectiveness of the designed method is verified by the simulation results. Note to Practitioners— In this paper, we introduce a neuro-adaptive control strategy for a multi-agent system based on partial differential equations in 3D space, using a non-collocated observer. This approach is particularly relevant for practitioners dealing with dynamic and uncertain environments in control systems. Neural networks are employed to manage system uncertainties, adapting to changing conditions, which is crucial in environments with variable system parameters. The non-collocated observer allows for state estimation, beneficial in situations where direct measurement is impractical. Ensuring the observer’s accuracy is key for effective control. Our strategy focuses on simplicity and ease of implementation, making it accessible for integration into existing systems. The observer-based control ensures the stability of the closed-loop system, a critical factor for consistent performance.

This study proposes a neural-network (NN)-based adaptive fixed-time control method for a two-degree-of-freedom (2-DOF) nonlinear helicopter system with input quantization and output constraints. First, a hysteresis quantizer is employed to mitigate chattering during signal quantization, and adaptive variables are utilized to eliminate errors in the quantization process. Subsequently, the system uncertainties are approximated using a radial basis function NN. Simultaneously, a logarithmic barrier Lyapunov function (BLF) is constructed to prevent the system outputs from violating the constraint boundaries. Based on a rigorous Lyapunov stability analysis and the fixed-time stability criterion, the signals of the closed-loop system are proven to be bounded within a fixed time. Finally, numerical simulations and experiments verified the feasibility of the proposed method.

With the burgeoning growth of the maritime economy, marine risers have emerged as reliable and convenient conduits for the transport of oil and natural gas. However, these risers are vulnerable to vibrational disturbances, which can adversely impact system performance and induce fatigue damage. Therefore, effective vibration control strategies are required to address this issue. This study introduces an innovative adaptive quantized fault-tolerant control strategy designed to attenuate vibrations in a three-dimensional (3-D) riser-vessel system against the effects of actuator faults, unknown control direction, and external disturbances. Different from previous findings, the suggested controller can directly counteract the nonlinear component stemming from actuator faults and handle the nonlinear decomposition inherent to the quantizer, without the necessity for upper-limit estimation. Furthermore, to tackle the input saturation, control laws are formulated using the hyperbolic tangent operator. Finally, the proposed controller’s effectiveness and robustness are validated through thorough Lyapunov analysis and numerical simulations, affirming the system’s uniformly bounded stability.

This article presents a disturbance observer (DO)-based neural network (NN) control for a two-degree-of-freedom (2-DOF) helicopter system with input saturation, external disturbances, and output constraints. First, the uncertainties in the helicopter system are approximated using a radial basis function NN. Subsequently, a DO is used to approximate unknown compound disturbances, involving errors from NN estimation, input saturation, and external disturbances. To address the issue of output constraints imposed at a prescribed time period, a novel time-shift function and an adjusted barrier function are employed. Through the direct Lyapunov method, the boundedness of all control signals in the closed-loop system is verified. Finally, the effectiveness of the proposed control method is validated through numerical simulation results.

This study focuses on the novel reinforcement learning control strategy of a nonlinear two-degrees-of-freedom (2-DOF) helicopter system for tracking the desired trajectory while minimizing the tracking error. First, gradient descent algorithm is incorporated in the context of the reinforcement learning control scheme to obtain the adaptive laws. Subsequently, considering the uncertainties in the nonlinear system, radial basis function (RBF) neural networks (NNs) are exploited to approximate the unknown internal dynamics. In contrast to the previous studies, aiming at accelerating the convergence in reinforcement learning control, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Under the proposed control strategy, the states of the closed-loop system are proven to be semi-globally uniformly ultimately bounded through rigorous Lyapunov analyses, and the state constraints are satisfied. Furthermore, the simulations and experiments conducted on a Quanser laboratory platform reveal that the proposed control functions are suitable and effective. Note to Practitioners—This paper is motivated by designing a reinforcement learning control strategy to enhance online learning capability and control performance of the controller for a nonlinear 2-DOF helicopter system. The control framework is divided into the design of the critic and actor NNs, responsible primarily for evaluating the control performance and approximating uncertainties in the system separately. Unlike the adaptive NN control, the actor NN weights are updated by combining information of states and inputs from the critic NN. In addition, aiming at accelerating the convergence, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Finally, the proposed control strategy is validated in simulation and experiment on the Quanser laboratory platform.

This article proposes an adaptive inverse neural network (NN) control of an uncertain flexible single-link manipulator with input backlash and output constraint. First, an adaptive inverse function is applied to eliminate the input backlash of the actuator. Second, an NN is applied to approximate the system uncertainty. Third, a barrier Lyapunov function is used to guarantee that the system is maintained within the constraints. Subsequently, the system’s semi-globally uniformly ultimately bounded stability is proved by the Lyapunov direct method. Finally, the simulation and experimental results manifest the feasibility of the proposed controller.

Recently, with the development of the marine economy, marine risers have garnered increasing attention as they present facile and reliable methods for oil and gas transportation. However, these risers are susceptible to vibrations, which can lead to system performance degradation and fatigue damage. Therefore, effective vibration control strategies are required to address this issue. In this study, a novel adaptive fault-tolerant control (FTC) strategy is adopted to suppress the vibrations of a 3-D riser-vessel system against the effects of actuator failures, backlash-like hysteresis, and external disturbances. A barrier-based Lyapunov function is merged to eliminate the time-varying output constraints of the system. Adaptive FTC laws with projection mapping operators are designed to compensate for parameter uncertainties and consider input nonlinearities to improve system robustness. Finally, a rigorous Lyapunov analysis and numerical simulations are performed to verify the validity of the proposed controller and guarantee uniformly bounded stability of the system.

An adaptive neural network (NN) control is proposed for an unknown two-degree of freedom (2-DOF) helicopter system with unknown backlash-like hysteresis and output constraint in this study. A radial basis function NN is adopted to estimate the unknown dynamics model of the helicopter, adaptive variables are employed to eliminate the effect of unknown backlash-like hysteresis present in the system, and a barrier Lyapunov function is designed to deal with the output constraint. Through the Lyapunov stability analysis, the closed-loop system is proven to be semiglobally and uniformly bounded, and the asymptotic attitude adjustment and tracking of the desired set point and trajectory are achieved. Finally, numerical simulation and experiments on a Quanser's experimental platform verify that the control method is appropriate and effective.

This article proposes an adaptive control for a flexible manipulator (FM) under the influence of distributed disturbances, unknown dead zones, and input quantization. First, the hybrid effect of the unknown dead zone and input quantization is formulated and represented based on some essential transformations. Then, an adaptive robust quantized control with online updating laws is developed to address the uncertainty of the dead zone, ensure robustness and angle position, and dampen the vibration in the FM system. Subsequently, the Lyapunov theoretical analysis is employed to ensure the bounded stability of the system. Finally, numerical simulations and experiments with a Quanser platform are given to further verify the feasibility and superiority of the designed scheme.

In this article, we propose a new adaptive fuzzy fault-tolerant control (FTC) for a three-dimensional riser-vessel system with unknown backlash nonlinearity. A model for the smooth inverse dynamics of the backlash is introduced; then, the control input is divided into an expected input and a compensation error. Considering the imprecision of system modeling and unknown external disturbances, we employ a fuzzy adaptive technology to achieve compensation. By incorporating the actuator fault term and backlash error, the adaptive FTC is developed to resolve loss faults in the actuator and compensate for the unknown backlash to some extent. The direct Lyapunov method is used to demonstrate the system’s bounded stability. Finally, simulation results demonstrate the effectiveness of the derived scheme.

Transcranial direct current stimulation (tDCS) has been shown to create neuroplasticity in healthy and diseased populations. The control of stimulation duration by providing real-time brain state feedback using neuroimaging is a topic of great interest. This study presents the feasibility of a closed-loop modulation for the targeted functional network in the prefrontal cortex. We hypothesize that we cannot improve the brain state further after reaching a specific state during a stimulation therapy session. A high-definition tDCS of 1[Formula: see text]mA arranged in a ring configuration was applied at the targeted right prefrontal cortex of 15 healthy male subjects for 10[Formula: see text]min. Functional near-infrared spectroscopy was used to monitor hemoglobin chromophores during the stimulation period continuously. The correlation matrices obtained from filtered oxyhemoglobin were binarized to form subnetworks of short- and long-range connections. The connectivity in all subnetworks was analyzed individually using a new quantification measure of connectivity percentage based on the correlation matrix. The short-range network in the stimulated hemisphere showed increased connectivity in the initial stimulation phase. However, the increase in connection density reduced significantly after 6[Formula: see text]min of stimulation. The short-range network of the left hemisphere and the long-range network gradually increased throughout the stimulation period. The connectivity percentage measure showed a similar response with network theory parameters. The connectivity percentage and network theory metrics represent the brain state during the stimulation therapy. The results from the network theory metrics, including degree centrality, efficiency, and connection density, support our hypothesis and provide a guideline for feedback on the brain state. The proposed neuro-feedback scheme is feasible to control the stimulation duration to avoid overdosage.

We propose an adaptive neural-network-based fault-tolerant control scheme for a flexible string considering the input constraint, actuator gain fault, and external disturbances. First, we utilize a radial basis function neural network to compensate for the actuator gain fault. In addition, an observer is used to handle composite disturbances, including unknown approximation errors and boundary disturbances. Then, an auxiliary system eliminates the effect of the input constraint. By integrating the composite disturbance observer and auxiliary system, adaptive fault-tolerant boundary control is achieved for an uncertain flexible string. Under rigorous Lyapunov stability analysis, the vibration scope of the flexible string is guaranteed to remain within a small compact set. Numerical simulations verify the high control performance of the proposed control scheme.

Transcranial direct and alternating current stimulation (tDCS and tACS, respectively) can modulate human brain dynamics and cognition. However, these modalities have not been compared using multiple imaging techniques concurrently. In this study, 15 participants participated in an experiment involving two sessions with a gap of 10 days. In the first and second sessions, tACS and tDCS were administered to the participants. The anode for tDCS was positioned at point FpZ, and four cathodes were positioned over the left and right prefrontal cortices (PFCs) to target the frontal regions simultaneously. tDCS was administered with 1 mA current. tACS was supplied with a current of 1 mA (zero-to-peak value) at 10 Hz frequency. Stimulation was applied concomitantly with functional near-infrared spectroscopy and electroencephalography acquisitions in the resting-state. The statistical test showed significant alteration (p < 0.001) in the mean hemodynamic responses during and after tDCS and tACS periods. Between-group comparison revealed a significantly less (p < 0.001) change in the mean hemodynamic response caused by tACS compared with tDCS. As hypothesized, we successfully increased the hemodynamics in both left and right PFCs using tDCS and tACS. Moreover, a significant increase in alpha-band power (p < 0.01) and low beta band power (p < 0.05) due to tACS was observed after the stimulation period. Although tDCS is not frequency-specific, it increased but not significantly (p > 0.05) the powers of most bands including delta, theta, alpha, low beta, high beta, and gamma. These findings suggest that both hemispheres can be targeted and that both tACS and tDCS are equally effective in high-definition configurations, which may be of clinical relevance.

This study is concerned with the dynamical analysis and vibration attenuation for a three-dimensional (3-D) suspension cable system of a helicopter preceded by output constraints and input backlash. First, the dynamic model of a 3-D suspension cable is constructed in accordance with Hamilton’s principle. Then, a backlash inverse compensator is established to tackle the input backlash nonlinearities. Subsequently, three boundary controllers together with output signal barrier functions are proposed to dampen the oscillations while not violating the cable swing constraints. The uniform boundedness of the closed-loop system is guaranteed with recourse to the direct Lyapunov’s method. Finally, the validity and efficiency of the derived control laws are testified through simulation results.

In this study, an adaptive robust control technique for an uncertain riser-vessel system in a three-dimensional space is developed. A projection mapping technique and a hyperbolic tangent function are exploited to construct novel adaptive robust controllers based on adaptive laws dynamically updated online to restrain the vibration, tackle parametric uncertainties, compensate for the unknown upper bound of disturbances, and ensure robustness of the coupled system. Lyapunov’s method is adopted to analyze and demonstrate the bounded stability of the closed-loop system. Simulation results are provided to validate the feasibility and effectiveness of the proposed approach.

This article develops an adaptive neural-network (NN) boundary control scheme for a flexible manipulator subject to input constraints, model uncertainties, and external disturbances. First, a radial basis function NN method is utilized to tackle the unknown input saturations, dead zones, and model uncertainties. Then, based on the backstepping approach, two adaptive NN boundary controllers with update laws are employed to stabilize the like-position loop subsystem and like-posture loop subsystem, respectively. With the introduced control laws, the uniform ultimate boundedness of the deflection and angle tracking errors for the flexible manipulator are guaranteed. Finally, the control performance of the developed control technique is examined by a numerical example.

In this paper, a new vector phase diagram differentiating the initial decreasing phase (i.e. initial dip) and the delayed hemodynamic response (HR) phase of oxy-hemoglobin changes ([Formula: see text]HbO) of functional near-infrared spectroscopy (fNIRS) is developed. The vector phase diagram displays the trajectories of [Formula: see text]HbO and deoxy-hemoglobin changes ([Formula: see text]HbR), as orthogonal components, in the [Formula: see text]HbO–[Formula: see text]HbR polar coordinates. To determine the occurrence of an initial dip, dual threshold circles (an inner circle from the resting state, an outer circle from the peak values of the initial dip and the main HR) are incorporated into the phase diagram for making decisions. The proposed scheme is then applied to a brain–computer interface scheme, and its performance is evaluated in classifying two finger tapping tasks (right-hand thumb and little finger) from the left motor cortex. Three gamma functions are used to model the initial dip, the main HR, and the undershoot in generating the designed HR function. In classifying two tapping tasks, the signal mean and signal minimum values during 0–2.5[Formula: see text]s, as features of initial dip, are used. The linear discriminant analysis was utilized as a classifier. The experimental results show that the active brain locations of the two tasks were quite distinctive ([Formula: see text]), and moreover, spatially specific if using the initial dip map at 4[Formula: see text]s in comparison to the map of HRs at 14[Formula: see text]s. Also, the average classification accuracy was improved from 59% to 74.9% when using the phase diagram of dual threshold circles.

In this paper, we investigate active brain regions for motor execution and motor imagination tasks after training with a rehabilitation robot. Functional near-infrared spectroscopy (fNIRS) is used to measure the hemodynamic responses in the motor cortices of five subjects. An assistive robot (IMT 2.0, connected to the right hand) is used during the training session to make the subject to reach a target point displayed on a computer screen. During the training, the subjects have to reach the target point in two directions (left and right) using right arm movement. Our intention is to investigate the differences between brain signals generated from left and right movements of the right hand. It was found that the same brain region was activated for both left- and right-directional motions. During the testing, we asked the subjects to imagine the executed movement. We found that although the imagined movement activity is weak but it appears in the same region as that of motor execution during the reach task. The results show that executed and imagined movements can be discriminated using fNIRS. However, for brain-computer interface it is difficult to generate two commands using only one arm movement signals.

In this paper, we present a systematic method to reduce the time lag in detecting initial dips using a vector-based phase diagram and an autoregressive moving average with exogenous signals (ARMAX) model-based q-step-ahead prediction algorithm. With functional near-infrared spectroscopy (fNIRS), signals related to mental arithmetic and right-hand clenching are acquired from the prefrontal and left primary motor cortices, respectively. The interrelationship between oxygenated hemoglobin, deoxygenated hemoglobin, total hemoglobin and cerebral oxygen exchange are related to initial dips. Specifically, a threshold value from the resting state hemodynamics is incorporated, as a decision criterion, into the vector-based phase diagram to determine the occurrence of initial dips. To further reduce the time lag, a [Formula: see text]-step-ahead prediction method is applied to predict the occurrence of the dips. A combination of the threshold criterion and the prediction method resulted in the delay time of about 0.9[Formula: see text]s. The results demonstrate that rapid detection of initial dip is possible and therefore can be used for real-time brain-computer interfacing.

A path-planning algorithm for a complex workspace split into triangular regions is investigated. The algorithm, which is formulated to achieve a goal configuration subject to the desired goal-point orientation, generates a collision-free region-to-region-compliant path. To that end, a set of vector potential functions is used. These functions are calculated using information on the triangular regions' vertices, the obstacles' positions, and the goal configuration. Path-planning procedures based on these constraint-satisfying functions are constructed. The proposed path-planning method, entailing velocity-and-orientation tracking control and configuration control, is applied to a unicycle vehicle, and its performance is compared with that of an existing path-planning scheme.

This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. To overcome the design difficulty from non-affine structure of pure-feedback system, mean value theorem is exploited to deduce affine appearance of state variables x(i) as virtual controls α(i), and of the actual control u. The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. The novel Lyapunov-Krasovskii functionals are employed to compensate for the unknown functions of current delayed state, which is effectively free from any restriction on unknown time-delay functions and overcomes the circular construction of controller caused by the neural approximation of a function of u and [Formula: see text] . Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter. To achieve uniformly ultimate boundedness of all the signals in the closed-loop system and tracking performance, control gains are effectively modified as a dynamic form with a class of even function, which makes stability analysis be carried out at the present of multiple time-varying delays. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.

In this paper, a robust time delay control for a reclaimer is investigated. Supplying the same amount of raw material throughout the reclaimation process, from the raw yard to a sinter plant, it is important to keep the quality of the molten steel in a blast furnace uniform. Since the parameter values of the reclaimer are not available, the boom rotational dynamics is modeled as a second order differential equation with unknown coefficients. The unknown parameters in the nominal model are estimated using recursive estimation method. Another important factor in the control problem of a reclaimer is the large time delay in output measurement. A robust Smith predictor is designed, and a robust stability criterion for the multiplicative uncertainty is derived. Following the work of Goodwin et al. (1992), a quantifying procedure of the multiplicative uncertainty bound, through experiments, is described. Experimental and simulation results are provided.

Large excavation reclaimers are used to dig ore and transfer it to the blast furnaces that refine the ore into pure metal form. The reclaiming job consists of two operations: (1) landing a reclaimer bucket on the surface of a pile and (2) slewing its boom with rotating buckets to scoop the ore. An automatic landing method for choosing where to dig in a pile of raw ore is proposed to achieve autonomous reclaiming. The method comprises detecting the shape of a pile, extracting contour lines of the pile, obtaining the joint angles of the reclaimer and determining an optimal landing point. A 3D range finder was developed with laser radar concepts to detect the shape and height of the ore pile. A series of image processing techniques for extracting the contour line from the 3D range data of a pile is suggested. A height map is obtained from the acquired range data for a pile and a contour map is obtained through image processing steps, including interpolation and edge following. The optimal landing point of the bucket on the contour line is determined so that an overload problem does not occur in the slewing operation and the reclaiming efficiency can be maximized. The algorithm for finding the landing point requires an inverse kinematics solution for the reclaimer. The forward kinematics of the reclaimer is first obtained. A constraint equation based on the geometrical relationship is suggested to solve the inverse kinematics of the reclaimer with redundancy. The proposed method was successfully applied to a working reclaimer. An autonomous reclaimer is now being operated in the yards of Kwangyang Steelworks in Korea.

The inverse kinematics problem of a reclaimer which excavates and transports raw materials in a raw yard is investigated Because of the geometric feature of the equipment of which scooping buckets are attached around a rotating disk, kinematic redundancy occurs in determining joint variables. Link coordinates are introduced following the Denavit-Hatenberg representation. For a given excavation point the forward kinematics yields 3 equations however the number of involved joint variables in the equations is four. It is shown that the rotating disk at the end of the boom provides an extra passive degree of freedom. Two approaches are investigated in obtaining inverse kinematics solution. The first method pre-assigns the height of excavation point which can be determined through path planning. A closed form solution is obtained for the first approach. The second method exploits the orthogonality between the normal vector at an excavation point and the z axis of the end-effector coordinate system. The geometry near the reclaiming point has been approximated as a plane, and the plane equation has been obtained by the least square method considering 8 adjacent points near the point. A closed form solution is not found for the second approach, however a linear approximate solution is provided.