This paper presents trajectory generation and output-feedback control strategies for an underactuated Flying Inverted Pendulum (FIP) system operating under unknown time-varying disturbances. The proposed approach introduces a novel scheme that employs two Extended High Gain Observers (EHGOs) to efficiently estimate the inverted pendulum’s linear and angular velocities, as well as the unknown disturbances, independently. The control strategy integrates a nonlinear hierarchical Lyapunov-based framework with EHGOs to tackle complex trajectory-tracking missions. Leveraging the differential flatness property of the FIP system, a versatile trajectory generation method is developed for window-crossing maneuvers. This work marks a step toward achieving closed-loop integration of trajectory generation and nonlinear control for the aggressive maneuvering of an underactuated FIP. The robustness and effectiveness of the proposed algorithms are validated through numerical simulations and experimental tests, using an underactuated aerial vehicle as a benchmark.

This paper investigates the fixed-time prescribed performance tracking control problem for Euler-Lagrange systems with model uncertainties, external disturbances, and actuator faults. To the best of the authors’ knowledge, achieving prescribed transient and steady-state behaviors within a fixed time under unknown bounded initial conditions, while simultaneously ensuring effective compensation for system uncertainties and faults, still remains an open problem. To address these challenges concerning both performance-related and reliability-related constraints, we propose a novel adaptive neural fault-tolerant control with fixed-time prescribed performance (ANFTC-FPP). The performance-related constraints are handled through a unified framework that synergistically combines novel prescribed performance functions (PPFs) with barrier Lyapunov functions (BLFs). This integration relaxes initialization constraints and characterizes the relationship between initial conditions and transient performance, thereby considering overshoot for tracking errors within a fixed time while achieving specified steady-state accuracy, regardless of initial states. For reliability-related constraints, we establish a fixed-time compensation mechanism where model uncertainties are handled by extending radial basis function neural networks (RBFNNs) for uncertainty approximation, while actuator faults are addressed through adaptive fault-tolerant control (FTC). The semi-global practical fixed-time stability (SPFS) of all closed-loop signals is rigorously established through comprehensive Lyapunov stability analysis. The efficacy of the proposed control strategy is experimentally validated on a physical KINOVA robotic manipulator system through real-world implementation.

In this paper, we propose a novel event-triggered prescribed-time tracking (PTT) control method for an underactuated unmanned aerial vehicle (UAV). Unlike existing PTT control methods, where the transient behavior of the system depends solely on the controller gains, we design a novel reference error trajectory (RET) using a polynomial to guide the convergence of the tracking error, particularly during the transient phase. Based on this RET and within the backstepping framework, we design a thrust reference. Additionally, we introduce a novel event-triggered mechanism based on the tracking error to update the torque applied to the UAV. To streamline intricate mathematical expressions and improve robustness to external disturbances, a second-order linear system is used as a low-pass filter within the backstepping design. Finally, simulation results are provided to demonstrate the effectiveness of the proposed approach and validate the accuracy of the theoretical predictions.

In this paper, an adaptive fixed-time control approach is designed for a robot with dynamic uncertainty in the presence of input quantization by using the Broad learning system (BLS). The proposed BLS-based control algorithm is constructed by fusing the BLS with the radial basis function neural network, which is improved in terms of node selection rule with a self-adjusting Gaussian function center and enhancement layer. A hysteresis quantizer is applied to the requirement of a low transmission rate. For the nonlinearity occurring in the quantized input, a novel adaptive fixed-time method is developed such that 1) the adverse effect of quantization nonlinearity is removed in a finite interval; 2) the BLS-based approximation technique can improve the approximation accuracy, which enhances the robustness of the closed-loop system; and 3) via the Lyapunov stability method, the fixed-time convergence of the closed-loop system is proved. Finally, numerical simulations and experiments validate the effectiveness of the proposed control scheme.

This paper proposes a novel adaptive fast variational sparse Gaussian process (AFVSGP) framework to ensure real-time safety for high-order systems under model uncertainties and dynamic obstacle environments. The framework effectively addresses the challenge of maintaining real-time safety guarantees during unknown trajectory transitions in nonstationary environments. To achieve this, the proposed framework incorporates three key innovations. First, a specialized kernel function is embedded within the VSGP algorithm to decouple control inputs from uncertainties while preserving the convexity of posterior-based safety constraints. Second, an adaptive online incremental learning mechanism is introduced, integrating forgetting capabilities with dynamic reconstruction rules for training datasets and inducing sets, thereby accelerating inference convergence and enabling compact uncertainty prediction with reduced computational complexity. Third, a high-order control barrier function (HOCBF)-based safety filter is developed to synthesize safe control inputs by leveraging the proposed learning model, thereby establishing rigorous probabilistic bounds on the satisfaction of safety specifications. The effectiveness of the proposed framework is validated through both simulation and real-world obstacle avoidance experiments on a 7-DOF Franka robot. The video is available at: https://www.youtube.com/watch?v=2tCKYM_79S8.

An adaptive tracking control policy is investigated for uncertain nonlinear systems under the finite-time asymmetric output constraints (FTAOCs). Unlike common output constraints, FTAOCs are characterized as constraints that are initially imposed during system operation and are then removed after a certain time. To tackle this challenge, we have designed novel shift and barrier functions that transform FTAOCs into guarantees of boundedness for an auxiliary variable. Additionally, we have developed an adaptive estimation algorithm to estimate unknown parameters and proposed an adaptive control strategy. Simulation studies on the Resistance-inductance-capacitance (RLC) circuits have been conducted to demonstrate the feasibility of our proposal. In comparison with state-of-the-art methods, our algorithm offers the flexibility to simultaneously address both unconstrained and constrained requirements of nonlinear systems, without requiring revisions to the controller structure.

This paper presents an adaptive online learning framework for systems with uncertain parameters to ensure safety-critical control in non-stationary environments. Our approach consists of two phases. The initial phase is centered on a novel sparse Gaussian process (GP) framework. We first integrate a forgetting factor to refine a variational sparse GP algorithm, thus enhancing its adaptability. Subsequently, the hyperparameters of the Gaussian model are trained with a specially compound kernel, and the Gaussian model’s online inferential capability and computational efficiency are strengthened by updating a solitary inducing point derived from newly samples, in conjunction with the learned hyperparameters. In the second phase, we propose a safety filter based on high order control barrier functions (HOCBFs), synergized with the previously trained learning model. By leveraging the compound kernel from the first phase, we effectively address the inherent limitations of GPs in handling high-dimensional problems for real-time applications. The derived controller ensures a rigorous lower bound on the probability of satisfying the safety specification. Finally, the efficacy of our proposed algorithm is demonstrated through real-time obstacle avoidance experiments executed using both simulation platform and a real-world 7-DOF robot.

This article proposes an adaptive fault-tolerant control (AFTC) approach based on a fixed-time sliding mode for suppressing vibrations of an uncertain, stand-alone tall building-like structure (STABLS). The method incorporates adaptive improved radial basis function neural networks (RBFNNs) within the broad learning system (BLS) to estimate model uncertainty and uses an adaptive fixed-time sliding mode approach to mitigate the impact of actuator effectiveness failures. The key contribution of this article is its demonstration of theoretically and practically guaranteed fixed-time performance of the flexible structure against uncertainty and actuator effectiveness failures. Additionally, the method estimates the lower bound of actuator health when it is unknown. Simulation and experimental results confirm the efficacy of the proposed vibration suppression method.

We investigate the trajectory tracking problem of underactuated aerial vehicles with unknown mass in the presence of unknown non-vanishing disturbances using an event-triggered approach, while considering the constraint that the derivative of the reference trajectory is not available. In contrast to existing references where the derivative of the reference trajectory is needed, here we first introduce a high-gain observer to estimate the unknown derivative solely from the reference trajectory. A disturbance observer is designed to compensate for non-vanishing disturbances, such as wind, etc. Fuzzy logic systems are used to approximate the model uncertainty arising from the unknown mass of the vehicle, and then we derive a thrust command law that follows from a desired stabilizing force. Additionally, unlike traditional fixed and relative threshold strategies that rely solely on control signals, we develop a new time-varying eventtriggered mechanism linked to the performance of the controlled system, taking into account factors such as tracking errors, to develop angular velocity commands, enhancing tracking accuracy while efficiently conserving communication resources, especially in the absence of Zeno behavior. We present simulation results to demonstrate the efficacy of the proposed approach and validate the theoretical findings.

This article discusses a building-like structure composed of a flexible beam, a rigid beam, a support plate, and a motor fixture. The flexible beam causes significant vibration, which leads to user discomfort. This article proposes a solution to suppress the vibration by designing a performance constraint boundary to limit the vibration amplitude of the flexible beam in terms of transient and steady-state performance. The system model with uncertainties is approximated using radial basis function (RBF) neural networks. Fixed-time methods are employed to further reduce vibration and enhance convergence rate. To minimize communication load, an event-triggered mechanism is integrated into the controller design. The effectiveness of the controller is validated through simulation tests and real-world experiments conducted using the Quanser smart structure.

In this article, neural network (NN)-based sliding mode control schemes are proposed for an n-link robotic manipulator with system uncertainties, input deadzone, and external perturbations. A novel error-shifting function is proposed to release initial conditions. NNs are employed to approximate the unknown parameters of both system uncertainties and input deadzone. To update the sliding mode scheme, two advanced sliding mode surfaces with error-shifting function and barrier function are proposed to reduce the dependency of prior information and to realize a finite time convergence result, collectively. It should be pointed out that the proposed methods do not require initial states to satisfy the prescribed constraint caused by the barrier function and can be applied under unknown initial conditions. Furthermore, finite-time convergence for both tracking errors and NN weights is guaranteed. The effectiveness of the proposed schemes is demonstrated by simulation and experiments on the KINOVA robot.

With the more extensive application of flexible robots, the expectation for flexible manipulators is also increasing rapidly. However, the fast convergence will cause the increase of vibration amplitude to some extent, and it is difficult to obtain vibration suppression and satisfactory transient performance at the same time. In order to deal with the problem, a fixed-time learning control method is proposed to realize the fast convergence. The constraint on system outputs, system uncertainty, and input saturation is addressed under the fixed-time convergence framework. A novel adaptive law for neural networks is integrated into the backstepping method, which enhances the learning rate of neural networks. The imposed constraint on the vibration amplitude is guaranteed by using the barrier Lyapunov function (BLF). Moreover, the chattering problem is addressed by approximating the sign function smoothly. In the end, some simulations have been carried out to show the effectiveness of the proposed method.

In this article, subject to time-varying delay and uncertainties in dynamics, we propose a novel adaptive fixed-time control strategy for a class of nonlinear bilateral teleoperation systems. First, an adaptive control scheme is applied to estimate the upper bound of delay, which can resolve the predicament that delay has significant impacts on the stability of bilateral teleoperation systems. Then, radial basis function neural networks (RBFNNs) are utilized for estimating uncertainties in bilateral teleoperation systems, including dynamics, operator, and environmental models. Novel adaptation laws are introduced to address systems' uncertainties in the fixed-time convergence settings. Next, a novel adaptive fixed-time neural network control scheme is proposed. Based on the Lyapunov stability theory, the bilateral teleoperation systems are proved to be stable in fixed time. Finally, simulations and experiments are presented to verify the validity of the control algorithm.

This article proposes an adaptive fuzzy control approach with an event-triggered mechanism and spatial motion constraint for a hybrid spacecraft system. The spacecraft system is composed of a rigid body and a slender flexible panel, with coupled dynamics captured by three ordinary differential equations and two partial differential equations. The overall control objective lies in utilizing an event-triggered control input to regulate the angular velocities of the rigid body and stabilize the vibrations of the flexible panel under unknown input disturbances and prescribed spatial motion performance. We collectively address the posture regulation and disturbance rejection purposes by introducing a barrier Lyapunov function and a fuzzy logic system. The event-triggered solution only updates the control signals at some discrete-time instants, and hence the communication burden is reduced significantly. The potential effectiveness and thrifty efficiency of the developed control strategy are theoretically demonstrated and numerically verified.

A neural learning-based finite-time control policy is presented for a robotic manipulator with unknown backlash-like hysteresis and system uncertainties. Adaptive neural networks are adopted to deal with unknown robotic dynamics. In order to eliminate the effect of unknown backlash-like hysteresis, a robust adaptive term is designed in the backstepping design process. A neural network-based finite-time controller is designed by introducing a fractional order term, which guarantees the finite-time convergence of both neural networks and adaptive terms, and this type of convergence improves control accuracy to a certain extent. With the Lyapunov stability theory, the proposed scheme can be proved to make the errors be semiglobally finite-time stable (SGFTS). The effectiveness of the proposed control is shown by simulation and experimental results.

A finite-time control method is presented for n -link robots with actuator saturation under time-varying constraints of work space. Barrier Lyapunov functions (BLFs) are designed for ensuring that the robot remains under time-varying constraints of the work space. In order to deal with asymmetric saturation nonlinearity, we transform asymmetric saturation into a symmetric one by using a hyperbolic tangent function, which is introduced to avoid the discontinuous problem existing in the auxiliary system-based saturation method. Combining fuzzy-logic systems (FLSs) with the backstepping technique, a finite-time control policy is designed for ensuring the stability of the closed-loop system. With the use of the Lyapunov stability theory, all the error signals are proved to be semiglobal finite-time stable (SGFS). Finally, the experiment is carried out to verify the effectiveness of the finite-time method.

We aim at the optimization of the tracking control of a robot to improve the robustness, under the effect of unknown nonlinear perturbations. First, an auxiliary system is introduced, and optimal control of the auxiliary system can be seen as an approximate optimal control of the robot. Then, neural networks (NNs) are employed to approximate the solution of the Hamilton-Jacobi-Isaacs equation under the frame of adaptive dynamic programming. Next, based on the standard gradient attenuation algorithm and adaptive critic design, NNs are trained depending on the designed updating law with relaxing the requirement of initial stabilizing control. In light of the Lyapunov stability theory, all the error signals can be proved to be uniformly ultimately bounded. A series of simulation studies are carried out to show the effectiveness of the proposed control.

The impedance control for coordinated robots interacting with the unknown environment is investigated in this article, subject to unknown system dynamics and the environment with which coordinated robots come into contact. For the whole system, impedance control is developed for coordinated robots. The notable feature is that the robot-environment interaction performance is improved without any information about the environment, so that the robotic system follows the commanded position trajectory in noncontact phase, while the desired destination is obtained according to the force exerted on the environment during contact phase. Moreover, based on assumption that some system signals are unmeasurable, output feedback control is designed for coordinated robot systems, where a state observer based on neural network technique is designed, that can force the state estimate error converge to a small neighborhood of zero. Simulation results are provided to demonstrate the effectiveness of the proposed control algorithm.

In this paper, an adaptive neural bounded control scheme is proposed for an ${n}$ -link rigid robotic manipulator with unknown dynamics. With the combination of the neural approximation and backstepping technique, an adaptive neural network control policy is developed to guarantee the tracking performance of the robot. Different from the existing results, the bounds of the designed controller are known a priori, and they are determined by controller gains, making them applicable within actuator limitations. Furthermore, the designed controller is also able to compensate the effect of unknown robotic dynamics. Via the Lyapunov stability theory, it can be proved that all the signals are uniformly ultimately bounded. Simulations are carried out to verify the effectiveness of the proposed scheme.

This article develops a robust fault tolerant (FT) control scheme for an n-link uncertain robotic system with actuator failures. In order to eliminate the influence of both the uncertainties and actuator failures on the system performance, the Gaussian radial basis function neural networks are used to compensate for the actuator failures and uncertain dynamics. An adaptive observer is designed to compensate for external disturbance. In addition, in order to accelerate the recovery of system stability after failure, a nonsingular fast terminal sliding mode is given. Finally, the simulation results on a two-link manipulator confirms the superior performance of the proposed neural networks-based FT controller, and the experiment results on the Baxter robot further verify the effectiveness of the control method.

In this paper, we investigate fuzzy neural network (FNN) control using impedance learning for coordinated multiple constrained robots carrying a common object in the presence of the unknown robotic dynamics and the unknown environment with which the robot comes into contact. First, an FNN learning algorithm is developed to identify the unknown plant model. Second, impedance learning is introduced to regulate the control input in order to improve the environment-robot interaction, and the robot can track the desired trajectory generated by impedance learning. Third, in light of the condition requiring the robot to move in a finite space or to move at a limited velocity in a finite space, the algorithm based on the position constraint and the velocity constraint are proposed, respectively. To guarantee the position constraint and the velocity constraint, an integral barrier Lyapunov function is introduced to avoid the violation of the constraint. According to Lyapunov's stability theory, it can be proved that the tracking errors are uniformly bounded ultimately. At last, some simulation examples are carried out to verify the effectiveness of the designed control.

In this paper, an adaptive fuzzy neural network (FNN) control scheme is developed for a class of multipleinput and multiple-output (MIMO) nonlinear systems subject to unknown dynamics and state constraints. FNNs are used to approximate the unknown dynamics that comprises the effects of uncertain parameters and functions. Also, integral Lyapunov functions are introduced to address state constraints. A neuralnetwork-based observer is designed to estimate the unmeasurable states. With state-feedback and output feedback tracking control, the stability of closed-loop system is guaranteed via Lyapunov's stability theory. Two cases of simulations for MIMO systems with state constraints are conducted to verify the effectiveness of the proposed control.