Robust attitude tracking control of flexible spacecraft for achieving globally asymptotic stability

The three‐axis attitude tracking control problem in the presence of parameter uncertainties and external disturbances for a spacecraft with flexible appendages is investigated in this paper. Novel simple robust Lyapunov‐based controllers that require only the attitude and angular velocity measurement are proposed. The first controller is a discontinuous one composed of a nonlinear PD part plus a sign function, whereas the second one is continuous or even smooth by modifying the discontinuous part of the first one. For a general desired trajectory, both controllers can achieve globally asymptotic stability of the attitude and angular velocity tracking errors instead of ultimate boundedness. By using a two‐step proof technique, the partial stability of the proposed controllers for the resulting closed‐loop systems in the face of model uncertainties and unexpected disturbances is proven theoretically. To further enhance the control performance, a continuous controller is presented that utilizes the tracking errors for estimating the external disturbances. In addition, stability analysis is done. For all the developed controllers, numerical simulation results are provided to demonstrate their performance. Copyright © 2008 John Wiley & Sons, Ltd.     

Supervised Multi‐Rejector of Periodic Disturbances for Nonlinear Systems Using Decoupled State Multimodel

In this paper, a multi‐rejector of periodic disturbances is proposed for discrete‐time nonlinear systems represented by a decoupled state multimodel. We report a decoupled state multimodel repetitive‐predictive control based on a supervised algorithm to ensure reference trajectory tracking and periodic disturbances rejection. Partial predictors associated to the local controllers make the best choice of the most valid partial controller that meets the desired closed loop performances. The effectiveness of the supervised multi‐rejector is shown via a simulation example. The obtained results are satisfactory and show a good rejection of periodic disturbances and reference trajectory tracking.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities

This paper studies synchronization to a desired trajectory for multi‐agent systems with second‐order integrator dynamics and unknown nonlinearities and disturbances. The agents can have different dynamics and the treatment is for directed graphs with fixed communication topologies. The command generator or leader node dynamics is also nonlinear and unknown. Cooperative tracking adaptive controllers are designed based on each node maintaining a neural network parametric approximator and suitably tuning it to guarantee stability and performance. A Lyapunov‐based proof shows the ultimate boundedness of the tracking error. A simulation example with nodes having second‐order Lagrangian dynamics verifies the performance of the cooperative tracking adaptive controller. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust attitude and vibration control of a nonlinear flexible spacecraft

In this paper, the problem of attitude control of a three dimension nonlinear flexible spacecraft is investigated. Two nonlinear controllers are presented. The first controller is based on dynamic inversion, while the second approach is composed of dynamic inversion and µ‐synthesis schemes. It is assumed that only three torques in three directions on the hub are used. Actuator saturation is also considered in the design of controllers. To evaluate the performance of the proposed controllers, an extensive number of simulations on a nonlinear model of the spacecraft are performed. The performances of the proposed controllers are compared in terms of nominal performance, robustness to uncertainties, vibration suppression of panel, sensitivity to measurement noise, environmental disturbance and nonlinearity in large maneuvers. Simulation results confirm the ability of the proposed controller in tracking the attitude trajectory while suppressing the panel vibration. It is also verified that the perturbations, environment disturbances and measurement errors have only slight effects on the tracking and suppression performances. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Optimal Output Feedback Controllers for Spacecraft Attitude Tracking

This paper investigates the problem of output feedback attitude tracking control of a rigid spacecraft in the presence of external disturbances. Two optimal control laws with a disturbance estimator are developed to deal with this problem. An adapted extended state observer is used to estimate the angular velocity tracking errors and to allow for compensation for the total disturbances. The proposed control can be expressed as the sum of a nonlinear optimal controller and an estimated disturbance. For the optimal controller, the state‐dependent Riccati equation and optimal Lyapunov techniques are employed to solve the infinite‐time nonlinear optimal control problem. The developed controllers can minimize a performance index and ensure the stability of the closed‐loop system and external disturbance attenuation. On the other hand, using the adapted extended state observer, the asymptotic convergence of estimation error dynamics is proven. An example of multiaxial attitude manoeuvres is given and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.     

Adaptive tracking control of manipulators: Theory and experiments

This paper considers the trajectory tracking problem for uncertain robot manipulators and proposes two adaptive controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. The adaptive schemes are very general and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies ensure uniform boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the tracking errors can be made arbitrarily small. Experimental results are presented for a PUMA 560 manipulator and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers.     

Linear Model‐based Feedforward Control for Improving Tracking‐performance of Linear Motors

The main purpose of this article is to propose a linear model‐based approach for improving the tracking performance of linear motors. In particular, P‐ and PI‐controllers, augmented with a linear‐model‐based feedforward controller and disturbance observer (DOB), were utilized in this research. Experimental results show that the feedforward controller can substantially reduce the phase‐delay problem resulting from the limitation of closed‐loop bandwidth. In addition, the DOB can reject nonlinear behaviors to keep a motor‐system close to our nominal linear model. Compared with the results of using P‐ and PI‐controllers only, tracking errors were reduced from 4.44% to 0.67% of the desired trajectory. Therefore, the proposed method provides a solution for improving the tracking performance of linear motors.     

Active DIsturbance Rejection Control of Surface Vessels Using Composite Error Updated Extended State Observer

In this paper, a composite‐errors‐based active disturbance rejection control law is proposed for surface vessels with exogeneous disturbances. The low‐frequency disturbances from wind, wave and ocean currents are estimated by a novel composite‐errors‐based extended state observer (ESO). Since the composite errors are composed of trajectory tracking errors and estimation errors, the disturbance rejection control is feedforward‐feedback composite control. The advantages of feedforward control and feedback control are exploited to reject system disturbances. Compared with conventional ESO‐based active disturbance rejection control, smaller estimation errors and smaller tracking errors can be achieved by the proposed disturbance compensation control. The effectiveness and superiority of the designed control law are illustrated by theoretical analysis and simulation results.     

Dynamic modeling and nonlinear tracking control of a novel modified quadrotor

In this article, a nonlinear tracking controller is designed based on Lyapunov stability for a novel aerial robot. The proposed 6‐rotor configuration improves stability and payload lifting capacity of the robot compared with conventional quadrotors while avoiding further complexities in the robot dynamics and steering principles. The dynamical model of the robot is derived using Newton‐Euler method. The model represents a nonlinear, coupled, and underactuated system. The proposed control strategy includes 2 main parts: an attitude controller and a position controller. Both the attitude and position controls are Lyapunov‐based nonlinear tracking controllers that guarantee the asymptotic convergence of the states' tracking errors to zero. Simulation results are presented to illustrate appropriate performance of the closed‐loop system in terms of position/attitude tracking even in the presence of wind disturbance.     

A neural network based adaptive robot controller

Neural network based adaptive controllers have been shown to achieve much improved accuracy compared with traditional adaptive controllers when applied to trajectory tracking in robot manipulators. This paper describes a new Recursive Prediction Error technique for estimating network parameters which is more computationally efficient. Results show that this neural controller suppresses disturbances accurately and achieves very small errors between commanded and actual trajectories.     

基于干扰观测器的机械臂广义模型预测轨迹跟踪控制

为实现对多自由度机械臂关节运动精确轨迹跟踪,提出一种基于非线性干扰观测器的广义模型预测轨迹跟踪控制方法。针对机械臂轨迹跟踪运动学子系统,采用广义预测控制（Generalized Predictive Control,GPC）方法设计期望的虚拟关节角速度。对于机械臂轨迹跟踪动力学子系统,考虑机械臂的参数不确定性和未知外界扰动,利用GPC方法设计关节力矩控制输入,基于非线性干扰观测器方法实时估计和补偿系统模型中的不确定性。在李雅普诺夫稳定性理论框架下证明了机械臂关节角位置和角速度的跟踪误差最终收敛于零的小邻域。数值仿真验证了所提出控制方法的有效性和优越性。     

Perfomance-based adaptive tracking control of robot manipulators

This article presents two new adaptive schemes for the motion control of robot manipulators. The proposed controllers are very general and computationally efficient because they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies are globally stable in the presence of bounded disturbances, and that in the absence of disturbances the ultimate bound on the size of the tracking errors can be made arbitrarily small. Computer simulation results are given for a PUMA 560 manipulator, and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers. Experimental results are presented for an IMI Zebra Zero manipulator and confirm that the control schemes provide a simple and effective means of obtaining high-performance trajectory tracking. © 1995 John Wiley & Sons, Inc.     

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

In this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.     

A family of virtual contraction based controllers for tracking of flexible‐joints port‐Hamiltonian robots: Theory and experiments

In this work, we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible‐joint robots in the port‐Hamiltonian framework. The proposed design method, called virtual contraction based control, combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed‐loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed‐loop virtual system exhibits properties such as structure preservation, differential passivity, and the existence of (incrementally) passive maps. The method is later applied to a planar RR robot, and two nonlinear tracking control schemes in the developed controllers family are designed using different contraction analysis approaches. Experiments confirm the theoretical results for each controller.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive fault‐tolerant spacecraft attitude control using a novel integral terminal sliding mode

The attitude tracking of a rigid spacecraft is approached in the presence of uncertain inertias, unknown disturbances, and sudden actuator faults. First, a novel integral terminal sliding mode (ITSM) is designed such that the sliding motion realizes the action of a quaternion‐based nonlinear proportional‐derivative controller. More precisely, on the ITSM, the attitude dynamics behave equivalently to an uncertainty‐free system, and finite‐time convergence of the tracking error is achieved almost globally. A basic ITSM controller is then designed to ensure the ITSM from onset when an upper bound on the system uncertainties is known. Further, to remove this requirement, adaptive techniques are employed to compensate for the uncertainties, and the resultant adaptive ITSM controller stabilizes the system states to a small neighborhood around the sliding surface in finite time. The proposed schemes avoid the singularity intrinsic to terminal sliding mode‐based controllers and the unwinding phenomenon associated with some quaternion‐based controllers. Numerical examples demonstrate the advantageous features of the proposed algorithm. Copyright © 2017 John Wiley & Sons, Ltd.     

Transverse function control with prescribed performance guarantees for underactuated marine surface vehicles

This paper studies the problem of stabilizing reference trajectories (also called as the trajectory tracking problem) for underactuated marine vehicles under predefined tracking error constraints. The boundary functions of the predefined constraints are asymmetric and time‐varying. The time‐varying boundary functions allow us to quantify prescribed performance of tracking errors on both transient and steady‐state stages. To overcome difficulties raised by underactuation and nonzero off‐diagonal terms in the system matrices, we develop a novel transverse function control approach to introduce an additional control input in backstepping procedure. This approach provides practical stabilization of any smooth reference trajectory, whether this trajectory is feasible or not. By practical stabilization, we mean that the tracking errors of vehicle position and orientation converge to a small neighborhood of zero. With the introduction of an error transformation function, we construct an inverse‐hyperbolic‐tangent‐like barrier Lyapunov function to show practical stability of the closed‐loop systems with prescribed transient and steady‐state performances. To deal with unmodeled dynamic uncertainties and external disturbances, we employ neural network (NN) approximators to estimate uncertain dynamics and present disturbance observers to estimate unknown disturbances. Subsequently, we develop adaptive control, based on NN approximators and disturbance estimates, that guarantees the prescribed performance of tracking errors during the transient stage of on‐line NN weight adaptations and disturbance estimates. Simulation results show the performance of the proposed tracking control.     

Intelligent trajectory tracking of an aircraft in the presence of internal and external disturbances

This research deals with developing an intelligent trajectory tracking control approach for an aircraft in the presence of internal and external disturbances. Internal disturbances including actuators faults, unmodeled dynamics, and model uncertainties as well as the external disturbances such as wind turbulence significantly affect the performance of the common trajectory tracking control approaches. There are several fault‐tolerant control approaches in the literature to overcome the effects of specific actuator or sensor faults during the flight. However, trajectory tracking control of an air vehicle in the presence of unexpected faults and simultaneous presence of wind turbulence is still a challenging problem. In this paper, an intelligent neural network‐based model predictive control structure is proposed, where the prediction model is updated in each iteration based on a novel proposed online sequential multimodel structure. A hybrid offline‐online learning algorithm is adopted in the introduced online sequential multimodel structure to identify the time‐varying dynamics of the system. The proposed control structure can satisfactorily deal with unexpected actuator faults and structural damages as well as unmodeled dynamics and wind turbulence. The stability of the closed‐loop system is proved under some realistic assumptions. The simulation results demonstrate the high capability of the proposed approach for trajectory tracking control of a conventional aircraft in the simultaneous presence of system faults and external disturbances.     

From Nonlinear to Fuzzy Approaches in Trajectory Tracking Control of Wheeled Mobile Robots

In this paper, two knowledge based controllers are proposed to overcome the difficulties of a computed torque nonlinear controller (NC) in perfect trajectory tracking of nonholonomic wheeled mobile robots (WMRs). First, the effects of different dynamic models developed in angular and Cartesian coordinate systems are fully examined on the persistent excitation condition and consequently on the trajectory tracking performance of WMRs. Using the dynamic model coordinated in the Cartesian frame as the base of the NC results in perfect compensation of large position off‐tracks and unbiased estimation of the plant's unknown parameters. However, using the WMR's dynamic model with rotation angles of driving wheels as the base of nonlinear and fuzzy controllers leads to accurate orientation tracking. Through replacing the proportional and differential terms of the NC by fuzzy functions, a fuzzy nonlinear controller (FNC) is generated. Due to the complicated dynamics of the WMR in which the center of mass does not coincide with the center of rotation, the expert knowledge of fuzzy controllers is extracted considering the rotation angles and rates of driving wheels as input variables. Fuzzy tuning of the NC results in a superior tracking performance against measurement noises, though the control torques are decreased and smoothed significantly. Second, a complete fuzzy controller (FC) is generated to make perfect tracking of the WMR's position and orientation. The local stability analysis of fuzzy controllers is examined considering the corresponding analytical structures as nonlinear controllers. The superior performances of the proposed fuzzy controllers compared to those of the NCs are evaluated through simulations.