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In this paper, the attitude control of the quadrotor system under external disturbance is studied. A novel adaptive sliding mode control (ASMC) based on the linear extended state observer (LESO) is proposed, and the LESO is designed to estimate the lumped disturbance. An adaptive switching algorithm for changing the switching gain in real time is contained in the proposed ASMC. Then the disturbance estimation error can be compensated by the variable gain switching term in real time, therefore the robustness of the system can be further improved. The stability of the system is proved by Lyapunov theory. Finally, the simulation and experimental results verify the effectiveness of the control method.

This paper proposes a new extended state observer-based sliding-mode control strategy with prescribed-time convergence. Firstly, a novel prescribed-time extended state observer is designed, which estimates the disturbance accurately within a prescribed time and effectively solves peaking value problem. Secondly, a new type of second-order prescribed-time sliding-mode controller is designed to ensure system states converge within a prescribed time. Then, the proposed control strategy is applied to the design of partial integrated guidance and control with two-loop controller structure. Finally, the validity of the proposed methodology is verified through numerical simulation.

An adaptive resilient control is concerned for a class of cyber-physical systems (CPSs) in the presence of stealthy false data injection attacks in sensor networks and strict-feedback nonlinear dynamics. As the sensors are attacked by ill-disposed hackers, the exactly measured state information is unavailable for state feedback control. After theory ratiocinations, the initial issue of false data injection attacks is transformed into nonlinear uncertainty dynamics and unknown control directions at the last step. At each step in the recursive backstepping control, extended state observers (ESOs) in active disturbance rejection control (ADRC) are investigated to approximate the lumped system uncertainties. Specially, the Nussbaum functions are introduced at the last step in the adaptive control. All the closed-loop signals are proved to be semi-globally uniformly ultimately bounded by Lyapunov theory. Finally, numerical simulations verify that the proposed control can afford favorable stabilization performance and counter false data injection attack.

In this paper, the problem of adaptive optimized tracking control design is addressed for a class of nonlinear systems in strict-feedback form. The system under consideration contains input delay and has unmeasurable and restricted states within predefined compact sets. First, neural networks (NNs) are employed to approximate the unknown nonlinear dynamics, and an adaptive neural network (NN) state observer is constructed to compensate for the absence of state information. Additionally, by utilizing an auxiliary system compensation method alongside the backstepping technique, the impact of input delay is eliminated, and the generation of intermediate variables is prevented. Second, tan-type barrier optimal cost functions are established for each subsystem within the backstepping method to prevent the state variables from exceeding preselected sets. Moreover, by establishing both actor and critic NNs to execute a reinforcement learning algorithm, the optimal controller and optimal performance index function are evaluated, while relaxing the persistence of excitation condition. According to the Lyapunov stability theorem, it is demonstrated that all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the output signal accurately tracks a reference trajectory with the desired precision. Finally, a practical simulation example is provided to verify the effectiveness of the proposed control strategy, demonstrating its potential for real-world implementation.

An accurate dynamic model of a robot is fundamentally important for a control system, while uncertainties residing in the model are inevitable in a physical robot system. The uncertainties can be categorized as internal disturbances and external disturbances in general. The former may include dynamic model errors and joint frictions, while the latter may include external payloads or human-exerted force to the robot. Disturbance observer is an important technique to estimate and compensate for the uncertainties of the dynamic model. Different types of disturbance observers have been developed to estimate the lumped uncertainties so far. In this paper, we conducted a brief survey on five typical types of observers from a perspective of practical implementation in a robot control system, including generalized momentum observer (GMO), joint velocity observer (JVOB), nonlinear disturbance observer (NDOB), disturbance Kalman filter (DKF), and extended state observer (ESO). First, we introduced the basics of each observer including equations and derivations. Two common types of disturbances are considered as two scenarios, that is, constant external disturbance and time-varying external disturbance. Then, the observers are separately implemented in each of the two simulated scenarios, and the disturbance tracking performance of each observer is presented while their performance in the same scenario has also been compared in the same figure. Finally, the main features and possible behaviors of each type of observer are summarized and discussed. This survey is devoted to helping readers learn the basic expressions of five typical observers and implement them in a robot control system.

In this paper, an extended state observer-based adaptive prescribed performance control technique is proposed for a class of nonlinear systems with full-state constraints and uncertainties. An extraordinary feature is that not only the control problem of prescribed performance tracking and full-state constraints are solved simultaneously, but also the parametric uncertainties and disturbances are considered, which will make it difficult to design a stable controller. For this purpose, the extended state observer and adaptive technique are integrated to obtain estimations of disturbances and parameters. Then, based on the combination of prescribed performance and barrier Lyapunov function, a novel backstepping control scheme is developed with feedforward compensation of parameters and disturbances to ensure that the tracking error is kept within a specified prescribed performance bound without violation of full states at all times. Moreover, the boundedness of all signals in the closed-loop system is proved and asymptotic tracking can be realized if the disturbances are time-invariant. Finally, two simulation examples are performed to highlight the efficiency of the proposed approach.

This paper proposes an active disturbance rejection adaptive controller for tracking control of a class of uncertain nonlinear systems with consideration of both parametric uncertainties and uncertain nonlinearities by effectively integrating adaptive control with extended state observer via backstepping method. Parametric uncertainties are handled by the synthesized adaptive law and the remaining uncertainties are estimated by extended state observer and then compensated in a feedforward way. Moreover, both matched uncertainties and unmatched uncertainties can be estimated by constructing an extended state observer for each channel of the considered nonlinear plant. Since parametric uncertainties can be reduced by parameter adaptation, the learning burden of extended state observer is much reduced. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically guarantees a prescribed transient tracking performance and final tracking accuracy in general while achieving asymptotic tracking when the uncertain nonlinearities are not time-variant. The motion control of a motor-driven robot manipulator is investigated as an application example with some suitable modifications and improvements, and comparative simulation results are obtained to verify the high tracking performance nature of the proposed control strategy.

A sliding mode control (SMC) method is designed to attenuate the disturbances in the DC–DC buck converter system based on the estimated values of extended state observer (ESO). A conventional ESO is unable to accurately estimate system states and disturbances in finite time limited by its linear nature. This weakness cannot ensure that the system reaches the nominal sliding mode surface within finite time, thus the sliding mode trajectory will be affected. Therefore, a novel finite-time extended state observer (FTESO) is presented, utilizing a homogeneous theorem for finite-time convergence. Subsequently, a FTESO-based nonsingular terminal sliding mode control (NTSMC) method is devised for achieving globally finite-time stable of the closed-loop system. The Lyapunov stability theorem and homogeneous theorem are used to prove the finite-time stability, and the upper bound of settling time is estimated explicitly. Finally, both numerical simulations and experiments demonstrate the superiority of the designed control scheme with modeling errors and load disturbances.

The attitude control problem is addressed for a quadrotor system subject to the modeling uncertainties and unknown disturbances. A novel attitude control scheme is proposed based on nonsingular fast terminal sliding mode (NFTSM) technique. First, the tracking differentiator (TD) is designed to obtain the smooth tracking signal and its derivative. Then, the extended state observer (ESO) is constructed to provide the estimate of the modeling uncertainties and unknown disturbances. With the designed TD and ESO, a novel NFTSM controller is developed such that tracking error converges to zero in finite time. The transient-state and the steady-state performances are both achieved with the new controller. Finally, the simulation and real experiment results verify the effectiveness and superiority of the proposed control method.

This paper presents an advanced robust active disturbance rejection control (ADRC) for flexible link manipulator (FLM) to track desired trajectories in the joint space and minimize the link’s vibrations. It has been shown that the ADRC technique has a very good disturbance rejection capability. Both the internal dynamics and the external disturbances can be estimated and compensated in real time. The proposed robust ADRC control law is developed to solve the problems existing in the original version of the ADRC related to the disturbance estimation errors and the variation of the parameters. Indeed, these parameters cannot be included in the existing disturbances and then be estimated by the extended state observer. The proposed control law is based on the sliding mode technique, which considers the uncertainties in the control gains and disturbance estimation errors. Lyapunov theory is used to prove the closed-loop stability of the system. The proposed control strategy is simulated and tested experimentally on one FLM. The effect of the observer bandwidth on the system performance is simulated and studied to select the best values of the bandwidth frequency. The simulation and experimental results show that the proposed robust ADRC has better performance than the traditional ADRC.