Inverse optimal adaptive backstepping control for spacecraft rendezvous on elliptical orbits

The spacecraft rendezvous problem with the target spacecraft on an arbitrary elliptical orbit is addressed using adaptive backstepping control. The relative motion of two spacecrafts is established based on the Lawden equations. In order to take the parametric uncertainties into consideration, an adaptive backstepping controller is proposed in this paper, which is optimal with respect to a family of cost functionals. With Lyapunov analysis, the proposed control laws can guarantee the globally asymptotic stability of the whole system and estimate the upper bounds of uncertain model parameters at the same time. Furthermore, a group of modified control laws is obtained, which stabilises the closed-loop system under input constraints. Finally, simulation results are presented to validate the effectiveness of the proposed approach.     

H∞ tracking-based sliding mode control foruncertain nonlinear systems via an adaptive fuzzy-neural approach

A novel adaptive fuzzy-neural sliding-mode controller with H(infinity) tracking performance for uncertain nonlinear systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbances and approximate errors. Because of the advantages of fuzzy-neural systems, which can uniformly approximate nonlinear continuous functions to arbitrary accuracy, adaptive fuzzy-neural control theory is then employed to derive the update laws for approximating the uncertain nonlinear functions of the dynamical system. Furthermore, the H(infinity) tracking design technique and the sliding-mode control method are incorporated into the adaptive fuzzy-neural control scheme so that the derived controller is robust with respect to unmodeled dynamics, disturbances and approximate errors. Compared with conventional methods, the proposed approach not only assures closed-loop stability, but also guarantees an H(infinity) tracking performance for the overall system based on a much relaxed assumption without prior knowledge on the upper bound of the lumped uncertainties. Simulation results have demonstrated that the effect of the lumped uncertainties on tracking error is efficiently attenuated, and chattering of the control input is significantly reduced by using the proposed approach.     

具有参数不确定性的轮式移动机器人自适应backstepping控制

针对参数不确定的轮式移动机器人的轨迹跟踪问题,设计自适应跟踪控制器.基于移动机器人的动力学模型,采用backstepping积分方法,通过逐步递推选择适当的Lyapunov函数,设计基于状态反馈的自适应控制器,并进行了相应的稳定性分析.与传统PID控制进行仿真对比,结果表明提出的自适应控制策略能较好地补偿系统参数摄动的影响,提高了移动机器人的轨迹跟踪性能和鲁棒性.     

大型空间飞行器的高阶滑模姿态控制律设计

针对大型空间飞行器的大角度姿态控制问题,考虑航天器惯量矩阵中的不确定性和外部扰动力矩,应用高阶滑模控制方法设计了姿态跟踪控制律.采用的二阶滑模控制方法改善了系统针对不确定性及外部扰动的鲁棒性,并减弱了振颤现象.针对所设计的控制器进行了仿真验证,并与一阶滑模控制进行了对比,仿真结果表明了所提出方法的有效性.     

Control design with arbitrary information structure constraints

In this paper, a new method is proposed for designing robust control laws that are subject to arbitrary information structure constraints. The computation of the gain matrix is formulated in terms of a static output feedback problem, which can be efficiently solved using linear matrix inequalities. The resulting control laws ensure stability with respect to a broad class of additive nonlinear uncertainties in the system.     

Robotic execution of everyday tasks by means of external vision/force control

In this article, we present an integrated manipulation framework for a service robot, that allows to interact with articulated objects at home environments through the coupling of vision and force modalities. We consider a robot which is observing simultaneously his hand and the object to manipulate, by using an external camera (i.e. robot head). Task-oriented grasping algorithms (Proc of IEEE Int Conf on robotics and automation, pp 1794–1799, 2007) are used in order to plan a suitable grasp on the object according to the task to perform. A new vision/force coupling approach (Int Conf on advanced robotics, 2007), based on external control, is used in order to, first, guide the robot hand towards the grasp position and, second, perform the task taking into account external forces. The coupling between these two complementary sensor modalities provides the robot with robustness against uncertainties in models and positioning. A position-based visual servoing control law has been designed in order to continuously align the robot hand with respect to the object that is being manipulated, independently of camera position. This allows to freely move the camera while the task is being executed and makes this approach amenable to be integrated in current humanoid robots without the need of hand-eye calibration. Experimental results on a real robot interacting with different kind of doors are presented.     

Robust stabilization of MIMO systems in finite/fixed time

The control design problem for finite‐time and fixed‐time stabilizations of linear multi‐input system with nonlinear uncertainties and disturbances is considered. The control design algorithm based on block decomposition and implicit Lyapunov function technique is developed. The robustness properties of the obtained control laws with respect to matched and unmatched uncertainties and disturbances are studied. Procedures for tuning of control parameters are presented in the form of linear matrix inequalities. Aspects of practical implementation of developed algorithms are discussed. Theoretical results are supported by numerical simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Hierarchical Design of Sigmoidal Generalized Moments of Manipulator under Uncertainty

For the orientation control system of the manipulator’s end effector with electrical actuators, we develop a decomposition pr ocedure of feedback law design to track given trajectories in the end effector’s coordinate system. Owing to the S-shaped smooth sigma-functions used as the local feedback laws and corrections of the state observer, the tracking system is invariant with a given accuracy with respect to existing uncertainties under constraints imposed on the variables of the mechanical subsystem. The suggested approach does not involve the solution of the inverse kinematics and dynamics problems and also relaxes the requirements to the volume of a priori information about the plant and external perturbations.     

Dynamical adaptive integral backstepping variable structure controller design for uncertain systems and experimental application

In this study, a dynamical adaptive integral backstepping variable structure control (DAIBVSC) system based on the Lyapunov stability theorem is proposed for the trajectory tracking control of a nonlinear uncertain mechatronic system with disturbances. In this control scheme, no prior knowledge is required on the uncertain parameters and disturbances because it is estimated by two types of dynamical adaptive laws. These adaptive laws are integrated into the dynamical adaptive integral backstepping control and variable structure control (VSC) parts of the DAIBVSC. The dynamical adaptive law in the dynamical adaptive integral backstepping control part updates parametric uncertainties, while the other in the VSC part adapts upper bounds of non‐parametric uncertainties and disturbances. In order to achieve a more robust output tracking and better parameter adaptation, the control system is extended by one integrator and sliding surface is augmented by an integral action. Experimental evaluation of the DAIBVSC is conducted with respect to performance and robustness to parametric uncertainties. Experimental results of the DAIBVSC are compared with those of a traditional VSC. The proposed DAIBVSC exhibits satisfactory output tracking performance, good estimation of the uncertain parameters and can reject disturbances with a chattering free control law. Copyright © 2017 John Wiley & Sons, Ltd.     

Attitude Control of Multiple Rigid Bodies with Uncertainties and Disturbances

Decentralized attitude synchronization and tracking control for multiple rigid bodies are investigated in this paper. In the presence of inertia uncertainties and environmental disturbances, we propose a class of decentralized adaptive sliding mode control laws. An adaptive control strategy is adopted to reject the uncertainties and disturbances. Using the Lyapunov approach and graph theory, it is shown that the control laws can guarantee a group of rigid bodies to track the desired time-varying attitude and angular velocity while maintaining attitude synchronization with other rigid bodies in the formation. Simulation examples are provided to illustrate the feasibility and advantage of the control algorithm.      

Robust adaptive output feedback control of a class of discrete‐time nonlinear systems with nonlinear uncertainties and unknown control directions

In this paper, robust adaptive output feedback control is studied for a class of discrete‐time nonlinear systems with functional nonlinear uncertainties of the Lipschitz type and unknown control directions. In order to construct an output feedback control, the system is transformed into the form of a nonlinear autoregressive moving average with eXogenous inputs (NARMAX) model. In order to avoid the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead‐zone technique are constructed on the basis of the NARMAX model. With the employment of the predicted future outputs, a constructive output feedback adaptive control is proposed, where the discrete Nussbaum gain technique and the dead‐zone technique are used in parameter update laws. The effect of the functional nonlinear uncertainties is compensated for, such that an asymptotic tracking performance is achieved, whereas other signals in the closed‐loop systems are guaranteed to be bounded. Simulation studies are performed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

不确定性R¨ossler 系统的自适应鲁棒跟踪控制

研究具有外部不确定性R¨ossler 混沌系统的鲁棒跟踪控制问题. 基于动态面控制原理设计自适应鲁棒控制器, 给出了系统参数的自适应更新律, 使得被控闭环系统的各误差变量一致有界. 系统输出曲线渐近跟踪任意期望轨道, 且跟踪误差能被控制在任意小的范围内, 而无须知道系统的参数及外部不确定性的界限. 基于稳定理论给出了具体的稳定性分析, 并通过数值仿真验证了该方法的有效性及鲁棒性.

     

Estimating the region of attraction for large-scale systems with uncertainties

In this paper, a new approach is proposed for estimating regions of attraction for large-scale dynamic systems. In designing control laws for such systems, it is essential to incorporate the underlying information structure constraints while keeping the number of optimization variables at a minimum. The proposed method successfully accomplishes both of these objectives. It is computationally efficient, and can produce decentralized control laws without imposing structural constraints on the Lyapunov function (a feature that can considerably improve the quality of the estimate). The design algorithm is based on linear matrix inequalities and can easily accommodate various types of uncertainties in the system model. An example with 300 states is provided to demonstrate the suitability of this approach for large, sparse systems.     

Dynamic integral sliding mode for MIMO uncertain nonlinear systems

In this paper the authors propose a novel sliding mode control methodology for Multi-Input and Multi-Output (MIMO) uncertain nonlinear systems. The proposed approach synthesizes dynamic sliding mode and integral sliding mode control strategies into dynamic integral sliding mode. The new control laws establish sliding mode without reaching phase with the use of an integral sliding manifold. Consequently, robustness against uncertainties increases from the very beginning of the process. Furthermore, the control laws considerably alleviate chattering along the switching manifold. In addition, the performance of the controller boost up in the presence of uncertainties. A comprehensive comparative analysis carried out with dynamic sliding mode control and integral sliding mode control demonstrates superiority of the newly designed control law. A chatter free regulation control of two uncertain nonlinear systems with improved performance in the presence of uncertainties ensures the robustness of the proposed dynamic integral sliding mode controller.     

一类不确定非线性纯反馈系统的自适应鲁棒模糊控制

针对一类带有不确定性的非线性MIMO纯反馈系统,提出一种自适应鲁棒模糊控制方法,该方法放宽了已有文献对系统模型的限制条件,基于李雅普诺夫分析方法获得了控制输入和自适应律．在控制输入设计中,鲁棒控制项用于补偿逼近误差向量．通过选择适当的设计参数。提出的控制方法使得闭环系统的所有信号是一致有界的和跟踪误差向量的范数收敛到小的零邻域内．仿真结果表明了所提出方法的有效性．     

Robust Position Stabilization of Underactuated Surface Vessels With Unknown Modeling Parameters Via Simple P/D‐Like Feedback: The Center Manifold Approach

In this work, two smooth time‐invariant control laws are proposed to achieve asymptotic position stabilization of underactuated surface vessels despite modeling parameter uncertainties. The proposed control laws take a strikingly simple linear proportional derivative (PD)‐like feedback form or just a simplest proportional (P)‐like one, where the former relies on measuring the relative position error and surge/yaw velocity and the latter relies on measuring only the relative position error, decreasing or minimizing the sensing cost. The stabilities of the closed‐loop systems for the both control laws are strictly proved via the center manifold approach despite the unknown model parameters. The effectiveness of the proposed control laws is verified by simulation examples.     

漂浮基空间机器人的径向基神经网络鲁棒自适应控制

针对一类同时具有参数及非参数不确定性的自由漂浮空间机器人系统的轨迹跟踪问题,采用了一种RBF神经网络的自适应鲁棒补偿控制策略.对于系统的参数不确定性,通过对径向基神经网络来自适应学习并补偿,逼近误差通过滑模控制器消除,神经网络权重的自适应修正规则基于Lyapunov函数方法得到;而非参数不确定通过鲁棒控制器来实时自适应...     

Global asymptotic tracking of asymmetrical underactuated surface vessels with parameter uncertainties

In this work, we investigate the tracking control problem of asymmetrical underactuated surface vessels with parameter uncertainties. The tracking error model is first derived via appropriate coordinate transformations, and is considered as a cascade structure composed of two subsystems. The Lyapunov redesign approach is employed to construct the control laws separately to stabilize the two subsystems with unknown model parameters. The cascade system theory is applied to prove the global uniform asymptotic convergence of the state trajectory to the reference one provided the desired yaw velocity is not vanishing. The effectiveness of the proposed control laws is verified by simulation examples.     

Observer-based robust optimal control for helicopter with uncertainties and disturbances

Unknown model uncertainties and external disturbances widely exist in helicopter dynamics and bring adverse effects on control performance. Optimal control techniques have been extensively studied for helicopters, but these methods cannot effectively handle flight control problems since they are sensitive to uncertainties and disturbances. This paper proposes an observer-based robust optimal control scheme that enables a helicopter to fly optimally and reduce the influence of unknown model uncertainties and external disturbances. A control Lyapunov function (CLF) is firstly constructed using the backstepping method, then Sontag's formula is utilized to design an inverse optimal controller to stabilize the nominal system. Furthermore, it is stressed that the radial basis function (RBF) neural network is introduced to establish an observer with adaptive laws, approximating and compensating for the unknown model uncertainties and external disturbances to enhance the robustness of the closed-loop system. The uniform ultimate boundedness of the closed-loop system is ensured using the presented control approach via Lyapunov stability analysis. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control strategy.     

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.