Non-linear output feedback tracking control for AUVs in shallow wave disturbance condition

This article presents a non-linear output feedback tracking controller deisgn for autonomous underwater vehicles (AUVs) operating in shallow water area. In a shallow water environment, significant disturbances due to shallow water waves affect the motion of marine vehicles greatly. Since it is not energy efficient to counteract the oscillatory disturbances due to waves, it is critical to obtain the wave information or wave induced disturbance information and design an energy efficient controller to reduce the action of actuators to counteract wave disturbances to avoid wear and tear on actuators. In this article, a non-linear observer is first designed to estimate the low frequency (LF) motion of AUVs and to filter out wave-frequency (WF) motion of AUVs due to shallow water wave by using position and attitude measurements. Based on the designed observer, a non-linear output feedback controller is subsequently derived by using the observer backstepping technique. By using this approach, the AUV achieves global exponential tracking without excessive energy consumption to counteract the wave disturbance and also avoids excessive wear and tear on thrusters. Global exponential stability (GES) of overall observer-controller system is proved through Lyapunov stability theory. A set of simulations is carried out by using the KAMBARA (Silpa-Anan 2001 Silpa-Anan, C. 2001. “Autonomous Underwater Robot: Vision and Control”. In Master's thesis, The Australian National University.  [Google Scholar]) AUV model to demonstrate the performance of the proposed observer and output feedback controller.     

基于神经网络的水下机器人三维航迹跟踪控制

本文研究了水下机器人三维航迹跟踪控制问题.在充分考虑了模型中不确定水动力系数和外界海流干扰的基础上,提出了基于神经网络的自适应输出反馈控制方法.控制器由3部分组成:基于动态补偿器的输出反馈控制项、神经网络自适应控制项和鲁棒控制项.神经网络所需的自适应学习信号由线性观测器提供.基于Lyapunov稳定性理论证明了控制系统的稳定性.最后针对某AUV进行了空间三维航迹跟踪控制仿真实验,结果表明设计的控制器可以较好地克服时变非线性水动力阻尼对系统的影响,并对外界海流干扰有较好的抑制作用,可以实现三维航迹的精确跟踪.     

Robust Nonlinear Observer And Observer‐Backstepping Control Design For Surface Ships

A robust passive non‐linear observer, utilizing the sliding mode concept and acceleration feedback (AFB) technique, is developed for ships. The main advantage of the proposed observer is that it is robust and that it takes the Coriolis‐centripetal matrix (C‐matrix) into account. The observer reconstructs velocities of ships and bias from slowly varying environmental disturbances. It also filters out the noise and wave frequency data from measurements to protect the actuators from wear and excessive fuel consumption. The sliding mode technique is introduced to improve robust performance against neglected disturbances, uncertainties, and unmodeled dynamics. The acceleration feedback technique and coordinate transformation are used for reshaping the inertia matrix and removing the C‐matrix from the mathematical model. Then, the observer design and stability analysis become simpler. An output feedback controller using observer backstepping and the Lyapunov redesign technique is derived, and the global stability of the observer and observer‐controller system is shown by Lyapunov stability theory. A set of simulations was carried out to verify the performance of the proposed observer and controller.     

Output Feedback Control of a Quadrotor UAV Using Neural Networks

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.      

垂直面欠驱动自治水下机器人定深问题的自适应输出反馈控制

针对垂直面欠驱动自治水下机器人(AUV)定深控制问题,本文仅使用可测量的深度和纵摇角信息,基于反步法设计自适应输出反馈控制器.为此首先设计观测器,实现不可测纵摇角速度反馈;再利用径向基神经网络对不确定水动力系数和纵荡、垂荡及纵摇角速度耦合产生的非线性结构进行补偿;采用自适应策略对纵荡和垂荡速度形成的有界干扰进行抑制.本文采用AUV一阶非完整模型,不以线性化为目的,放宽了纵摇角只能在小范围内变化的限制.最后通过理论证明和仿真实验表明该方法能够实现AUV深度和姿态控制,对未建模非线性动态和有界扰动具有很强的自适应性和鲁棒性.     

T-S模糊系统输出反馈控制器的稳定性分析与设计

输出反馈控制是T-S模糊控制系统设计的一种重要方法．本文提出了一类由模糊状态观测器和模糊调节器构成的输出反馈控制器稳定性分析和解析设计的新方法．为了减小稳定性分析的保守性和难度,本文充分利用了模糊规则前件变量模糊隶属度函数的结构信息,对前件变量采用标准模糊分划的T-S模糊系统输出反馈控制器进行了研究,获得了一些新的稳定性条件．然后采用平行分布补偿法(PDC)和线性矩阵不等式方法(LMI),研究了该类输出反馈控制器的解析设计方法．通过一个非线性质量块-弹簧-阻尼器系统输出反馈控制器的设计和计算机仿真,验证了本文方法的有效性．     

带有海浪滤波器的船舶航向反步自适应输出反馈控制

针对复杂海况下船舶航向控制中的模型非线性、参数不确定和海浪扰动问题,提出了一种基于反步法的非线性自适应输出反馈控制算法.首先基于无源理论设计了一种状态观测器以实现海浪滤波和状态估计,这种观测器无需海浪扰动的方差信息从而减少了观测器参数数量.然后假定系统模型参数未知,基于反步法给出了非线性控制律和参数自适应律.利用Lyapunov理论证明了这种自适应输出反馈控制系统的稳定性.仿真结果表明本文所提控制器具有较好的控制性能,对不确定性模型参数具有良好的自适应性.     

Synchronization of multiple autonomous underwater vehicles without velocity measurements

In this paper,we investigate the synchronization control of multiple autonomous underwater vehicles (AUVs),considering both state feedback and output feedback cases.Treating multiple AUVs as a graph,we define the tracking error of each AUV with both its own tracking error and the relative position errors with respect to its neighbors taken into account.Lyapunov analysis is used to derive the control law for each AUV.For the output feedback case,a passive filter is used to compensate for the unknown relative velocity errors among AUVs,and an observer is employed to estimate the velocity of the AUV itself.Rigid mathematical proof is provided for the proposed algorithms for both state feedback and output feedback cases.Simulations are provided to demonstrate the effectiveness of the proposed approach.It is shown that,the synchronization error is smaller in the case of considering the relative errors between AUVs than in the case of considering the tracking error of the single AUV only.     

一类线性时变系统的输出反馈控制

基于线性时不变系统能控能观标准型变换及非线性系统高增益观测器方法,本文研究了一类线性时变系统 的输出反馈控制问题. 通过引入时变的状态变量坐标变换,分别设计了线性时变系统的状态反馈控制器、状态观测器以及基于 状态观测器的输出反馈控制器. 进一步地,本文分别证明了观测器动态误差是渐近收敛于零的,而状态反馈控制器以及输出反馈控制器可以 保证闭环系统的渐近稳定性.     

Robust State and Output Feedback Control of Launched MAVs with Unknown Varying External Loads

The operation of launched micro aerial vehicles (MAVs) with coaxial rotors is usually subject to unknown varying external disturbance. In this paper, a robust controller is designed to reject such uncertainties and track both position and orientation trajectories. A complete dynamic model of coaxial-rotor MAV is firstly established. When all system states are available, a nonlinear state-feedback control law is proposed based on feedback linearization and Lyapunov analysis. Further, to overcome the practical challenge that certain states are not measurable, a high gain observer is introduced to estimate unavailable states and an output feedback controller is developed. Rigid theoretical analysis verifies the stability of the entire closed-loop system. Additionally, extensive simulation studies have been conducted to validate the feasibility of the proposed scheme.     

Fuzzy neural network quadratic stabilization output feedback control for biped robots via H/sub /spl infin// approach

A novel fuzzy neural network (FNN) quadratic stabilization output feedback control scheme is proposed for the trajectory tracking problems of biped robots with an FNN nonlinear observer. First, a robust quadratic stabilization FNN nonlinear observer is presented to estimate the joint velocities of a biped robot, in which an H/sub /spl infin// approach and variable structure control (VSC) are embedded to attenuate the effect of external disturbances and parametric uncertainties. After the construction of the FNN nonlinear observer, a quadratic stabilization FNN controller is developed with a robust hybrid control scheme. As the employment of a quadratic stability approach, not only does it afford the possibility of trading off the design between FNN, H/sub /spl infin// optimal control, and VSC, but conservative estimation of the FNN reconstruction error bound is also avoided by considering the system matrix uncertainty separately. It is shown that all signals in the closed-loop control system are bounded.     

AUV近水面运动非线性观测器设计

针对AUV近水面低速运动中的波浪扰动问题,基于无源性原理设计了一种非线性状态观测器.观测器可以从包含高频运动信号、低频运动信号以及传感器噪声信号的AUV综合运动信号中估计出AUV的低频运动信号以及环境扰动作用力.该观测器克服了传统的线性化Kalman滤波器的缺陷,直接针对AUV的非线性模型进行观测器设计,用李亚普诺夫稳...     

Robust observer design for nonlinear uncertain systems with LQ regulators

For a class of uncertain systems with linear nominal dynamics and nonlinear uncertainties, it has been shown (Katayama and Sasaki 1987) that linear quadratic (LQ) state feedback regulators can be used to provide robust asymptotic stability. In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered. For the full-order observer, we propose an algorithm to synthesize the robust observer gain matrix. It is shown that with the observer it is still possible to achieve robust asymptotic stability. For the reduced-order observer, some conditions are derived to guarantee the robust asymptotic stabilizability of the uncertain systems. The trade-off between the magnitudes of controller and observer gains is clear in our approach. An example is used to illustrate the design process of the robust controller with full-order as well as reduced-order observers.     

基于LS-SVM的非线性系统自适应输出反馈控制

针对状态不可测的单输入单输出非线性不确定系统,提出一种基于最小二乘支持向量机(LS-SVM)的直接自适应输出反馈控制方法.该方法首先设计一种误差观测器,间接地估计出系统的状态,然后采用最小二乘支持向量机构造自适应控制器,控制器参数的在线调整规律由李亚普诺夫稳定性理论导出.文中严格证明了闭环系统的渐近稳定性,仿真研究表明了此控制方法的可行性和有效性.     

一类非线性系统的控制器和观测器设计

研究一类非线性系统的全状态反馈控制问题、观测器设计问题及输出反馈控制设计问题.首先设计出非线性全状态反馈控制器,获得了系统指数镇定的充分条件.然后提出了非线性观测器,并证明了该观测器是指数稳定观测器.进一步,在控制器和观测器问题的充分条件满足的假设下,证明了提出的带估计状态的反馈控制能达到指数镇定.最后,仿真实例验证了所得结果的有效性.     

输出约束的有限时间自适应区间二型模糊输出反馈PMSM伺服控制

针对永磁同步电机驱动的伺服系统在不确定性摩擦和未知负载的影响下难以达到高精度的控制效果,提出一种基于区间二型模糊系统的带有输出约束的有限时间自适应输出反馈控制方案.首先,构建一个基于非线性扰动观测器的区间二型模糊状态观测器,分别完成对于未知扰动和速度的估计,区间二型模糊系统完成对于非线性摩擦的逼近;然后,在此基础上,结合滤波误差补偿机制和有限时间技术,引入障碍Lyapunov函数和反步控制技术设计输出约束的自适应区间二型模糊输出反馈控制器;最后,根据Lyapunov稳定性理论提出严格的稳定性分析,保证闭环系统的所有信号均是有限时间内有界的,并通过数值仿真和实验验证了所提出方法的有效性.     

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable.One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input–output, state variable feedback pole assignment, International Journal of Control 46 (1987) 1867–1881; C. Wang, P.C. Young, Direct digital control by input–output, state variable feedback: theoretical background, International Journal of Control 47 (1988) 97–109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states.     

严格反馈非线性系统的自适应神经网络输出反馈控制

基于非线性反馈函数,文章设计神经网络状态观测器,解决一类非线性系统的输出反馈控制问题.非线性反馈神经网络观测器在系统存在不确定性函数的情况下实时估计系统状态.利用所获得的状态信号,设计了自适应神经网络动态面控制器,同时保证了闭环系统的稳定性和所有信号的有界性.通过调节设计参数的取值能够达到期望的闭环跟踪性能.数值仿真表明,所设计的状态观测器不需要对原系统做状态变换,能够克服输出反馈滑模控制器带来的抖震问题.     

Results on the Robust Observer-based Position Controller for Parallel Kinematic Machines

The problem of state observation and position control by output feedback for a nonlinear three degrees-of-freedom (3-DOF) parallel kinematic machine (PKM) system is considered, based on the limited signal availability (only the moving platform displacement measurements are assumed available). Unknown velocity signals are estimated via a nonlinear robust observer that is designed for the nonlinear system with observable linear dynamics part and bounded nonlinearities and disturbances, and that guarantees global exponential stability of the observation error. A proportional-derivative (PD) controller is designed to solve the position control problem, utilizing the estimated velocity, as well as the gravitation compensation, dynamic friction and external disturbance compensation for the PKM. The closed-loop system is proven to have global asymptotical stability according to the Lyapunov analysis method and LaSalle’s invariance principle. Performance of the resulting observer and controller is illustrated in a simulation study of a 3-DOF PKM. Modifications to the nonlinear observer and control law are discussed, that assure convergence of the position error and state observation error to zero when the upper bounds on the model uncertainties/disturbances are not known a priori.     

Robust backstepping control for a class of time delayed systems

In this note, the problem of robust output feedback control for a class of nonlinear time delayed systems is considered. The systems considered are in strict-feedback form. State observer is first designed, then based on the observed states the controller is designed via backstepping method. Both the designed observer and controller are independent of the time delays. Based on Lyapunov stability theory, we prove that the constructed controller can render the closed-loop system asymptotically stable. Simulation results further verify the effectiveness of the proposed approach.