Neural network-based asymptotic tracking control of unknown nonlinear systems with continuous control command

ABSTRACT

This paper proposes a robust tracking controller for a class of nonlinear second-order systems with time-varying uncertainties. The controller is mainly based on the robust integral of the sign of the error (RISE) control approach to achieve an asymptotic stability result with a continuous control command in the presence of additive uncertainties. An adaptive feedforward neural network control term is blended with a new RISE controller to improve the system's transient performance. The proposed RISE controller is a modified version of the existing saturated RISE controller such that only sign of the derivative of the output is needed. The stability of the closed-loop system is well studied, where a local asymptotic stability is proven. The controller performance is validated through simulations on a two-degree-of-freedom lower limb robotic exoskeleton.     

Virtual-Point-Based asymptotic tracking control of 4WS vehicles

This paper studies the lateral and longitudinal path tracking control of four-wheel steering vehicles. By the introduction of virtual points, a robust and adaptive path tracking control strategy is proposed to simultaneously counteract modeling uncertainties, unexpected disturbances, and coupling effects. An adaptive model-based feedforward adaptive term and the robust integral of the sign of the error (RISE) feedback term can be used to yield an asymptotic tracking result, which improve the tracking performance and reduce the control effort. The stability of closed-loop system is analyzed using a Lyapunov-based method. Simulation results are provided to demonstrate the performance of the proposed controller under different driving conditions.     

Neural network robust control of a 3-DOF hydraulic manipulator with asymptotic tracking

Multiaxial hydraulic manipulators are complicated systems with highly nonlinear dynamics and various modeling uncertainties, which hinders the development of high-performance controller. In this paper, a neural network feedforward with a robust integral of the sign of the error (RISE) feedback is proposed for high precise tracking control of hydraulic manipulator systems. The established nonlinear model takes three-axis dynamic coupling, hydraulic actuator dynamics, and nonlinear friction effects into consideration. A radial basis function neural network (RBFNN) is synthesized to approximate the uncertain system dynamics and external disturbance, which can greatly reduce the dependence on accurate system model. In addition, a continuous RISE feedback law is judiciously integrated to deal with the residual unknown dynamics. Since the major unknown dynamics can be estimated by the RBFNN and then compensated in the feedforward design, the high-gain feedback issue in RISE feedback control will be avoided. The proposed RISE-based neural network robust controller theoretically guarantees an excellent semi-global asymptotic stability. Comparative simulation is performed on a 3-DOF hydraulic manipulator, and the obtained results verify the effectiveness of the proposed controller.     

Robust fuzzy 3D path following for autonomous underwater vehicle subject to uncertainties

This paper addresses a three-dimensional (3D) path following control problem for underactuated autonomous underwater vehicle (AUV) subject to both internal and external uncertainties. A two-layered framework synthesizing the 3D guidance law and heuristic fuzzy control is proposed to achieve robust adaptive following along a predefined path. In the first layer, a 3D guidance controller for underactuated AUV is presented to guarantee the stability of path following in the kinematics stage. In the second layer, a heuristic adaptive fuzzy algorithm based on the guidance command and feedback linearization Proportional-Integral-Derivative (PID) controller is developed in the dynamics stage to account for the nonlinear dynamics and system uncertainties, including inaccuracy modelling parameters and time-varying environmental disturbances. Furthermore, the sensitivity analysis of the heuristic fuzzy controller is presented. Against most existing methods for 3D path following, the proposed robust fuzzy control scheme reduces the design and implementation costs of complicated dynamics controller, and relaxes the knowledge of the accuracy dynamics modelling and environmental disturbances. Finally, numerical simulation results validate the effectiveness of the proposed control framework and illustrate the outperformance of the proposed controller as well.     

基于RISE反馈的串联弹性驱动器最优控制方法

串联弹性驱动器（Series elastic actuator,SEA）是机器人交互系统中的一种理想力源.本文针对非线性SEA的力矩控制问题提出一种基于RISE（Robust integral of the sign of the error）反馈的最优控制方法,能够克服模型参数不确定和有界扰动,实现SEA输出力矩在交互过程中快速平稳地收敛到期望值.具体来说,首先对SEA的模型进行分析和变换;然后假设模型参数和扰动均已知,并在此基础上基于二次型指标设计最优控制律;之后基于RISE反馈重新设计控制律抵消模型参数不确定性和有界扰动,基于Lyapunov理论分析控制器的收敛性和信号的有界性,实验结果表明这种基于RISE反馈的最优控制方法具有良好的控制性能和对有界扰动的鲁棒性.     

Output feedback adaptive RISE control for uncertain nonlinear systems

In this article, committed to extending the robust integral of the sign of the error (RISE) feedback control to the working condition of output feedback, a novel output feedback controller with a continuously bounded control input which combines the adaptive control and integral robust feedback will be proposed for trajectory tracking of a family of nonlinear systems subject to modeling uncertainties. A novel adaptive state observer (ASO) with disturbance rejection performance is creatively constructed to derive real-time estimation of the unmeasured state signals. Moreover, a projection-type adaption law is integrated to handle parameter uncertainties and an integral robust term is employed to deal with external disturbances. It is shown that asymptotic estimation performance and meanwhile asymptotic tracking result can eventually be derived. Simulation validations are implemented to demonstrate the high tracking performance of the presented controller. Notably, the synthesized control algorithm can be readily extended to the Euler–Lagrange systems. Typically, it can be extended to practical electromechanical equipment such as three-dimensional vector forming robots to improve the real-time forming accuracy.     

Path tracking control of Lagrange systems with obstacle avoidance

This paper addresses a path tracking problem with obstacle avoidance for Lagrange systems. The proposed method is based on field potential methods in combination with navigation functions for obstacle avoidance. First, it is shown that a simple combination of the navigation function with the conventional path tracking controller does not work. Therefore, in order to cope with this problem, a new feedback law is proposed for a path parameter which characterizes the reference path. It is proved that the proposed controller achieves both path following and collision avoidance. Moreover, since the method adopts bounded navigation functions, the proposed controllers generate bounded input signals even when target systems approach obstacles. Finally, an experimental evaluation is performed with a two-link manipulator to illustrate the effectiveness of the proposed method.     

CPG modulation for navigation and omnidirectional quadruped locomotion

Navigation in biological mechanisms represents a set of skills needed for the survival of individuals, including target acquisition and obstacle avoidance.In this article, we focus on the development of a quadruped locomotion controller able to generate omnidirectional locomotion and a path planning controller for heading direction. The heading direction controller is able to adapt to sensory-motor visual feedback, and online adapt its trajectory according to visual information that modifies the control parameters. This allows for integration of sensory-motor feedback and closed-loop control. This issue is crucial for autonomous and adaptive control, and has received little attention so far. This modeling is based on the concept of dynamical systems.We present experiments performed on a real AIBO platform. The obtained results demonstrate both the adequacy of the proposed locomotor controller to generate the required trajectories and to generate the desired movement in terms of the walking velocity, orientation and angular velocity. Further, the controller is demonstrated on a simulated quadruped robot which walks towards a visually acquired target while avoiding online-visually detected obstacles in its path.     

非线性迭代滑模的欠驱动AUV路径跟踪控制

为实现欠驱动自治水下机器人（AUV）在未知海流干扰作用下的路径跟踪控制,提出一种基于非线性迭代滑模增量反馈的路径跟踪控制器。选用一般曲线参数和Serret-Frenet坐标系描述路径跟踪误差,建立AUV水平面路径跟踪误差方程。采用迭代方法,设计滑模增量反馈控制器,无需对AUV模型参数不确定部分和海流干扰进行估计。仿真实验表明,设计的控制器参数易于调节,可用于实际欠驱动水下机器人来实现对水平面路径的精确跟踪。     

Discrete-Time Adaptive Command Following and Disturbance Rejection With Unknown Exogenous Dynamics

We present an adaptive controller that requires limited model information for stabilization, command following, and disturbance rejection for mult-input multi-output minimum-phase discrete-time systems. Specifically, the controller requires knowledge of the open-loop system's relative degree as well as a bound on the first nonzero Markov parameter. Notably, the controller does not require knowledge of the command or the disturbance spectrum as long as the command and disturbance signals are generated by a Lyapunov-stable linear system. Thus, the command and disturbance signals are combinations of discrete-time sinusoids and steps. In addition, the Markov-parameter-based adaptive controller uses feedback action only, and thus does not require a direct measurement of the command or disturbance signals. Using a logarithmic Lyapunov function, we prove global asymptotic convergence for command following and disturbance rejection as well as Lyapunov stability of the adaptive system when the open-loop system is asymptotically stable.      

A new RISE-based adaptive control of PKMs: design,stability analysis and experiments

This paper deals with the development of a new adaptive control scheme for parallel kinematic manipulators (PKMs) based on Rrbust integral of the sign of the error (RISE) control theory. Original RISE control law is only based on state feedback and does not take advantage of the modelled dynamics of the manipulator. Consequently, the overall performance of the resulting closed-loop system may be poor compared to modern advanced model-based control strategies. We propose in this work to extend RISE by including the nonlinear dynamics of the PKM in the control loop to improve its overall performance. More precisely, we augment original RISE control scheme with a model-based adaptive control term to account for the inherent nonlinearities in the closed-loop system. To demonstrate the relevance of the proposed controller, real-time experiments are conducted on the Delta robot, a three-degree-of-freedom (3-DOF) PKM.     

Combined Vector Field Approach for 2D and 3D Arbitrary Twice Differentiable Curved Path Following with Constrained UAVs

Path following is an essential requirement for unmanned aerial vehicles (UAVs). Path following problems of 2-dimensional (2D) straight lines and planar circles have been studied and many approaches have been proposed during the past few years. In this paper the problem of following arbitrary twice differentiable curved paths in both 2D and 3D spaces is investigated. Based on the Helmholtz theorem, respective combined guidance vector fields for any given 2D and 3D arbitrary twice differentiable curved paths are constructed by trading off the respective conservative and solenoidal vector fields making use of the defined distance between the UAV and the desired path. Conditions for the two combined vector fields to be globally feasible are given. UAV input constraints and constant wind disturbance are assumed to be present. By tracking the constructed combined vector fields, a saturated course rate controller for 2D curved path following and a jointly saturated course rate and climb rate controller for 3D curved path following are designed. The Lyapunov stability of the saturated course rate controller for 2D curved path following is proved. Numerical simulations are given to assess the proposed approach.     

Teach‐and‐repeat path following for an autonomous underwater vehicle

This paper presents a teach‐and‐repeat path‐following method for an autonomous underwater vehicle (AUV) navigating long distances in environments where external navigation aides are denied. This method utilizes sonar images to construct a series of reference views along a path, stored as a topological map. The AUV can then renavigate along this path, either to return to the start location or to repeat the route. Utilizing unique assumptions about the sonar image‐generation process, this system exhibits robust image‐matching capabilities, providing observations to a discrete Bayesian filter that maintains an estimate of progress along the path. Image‐matching also provides an estimate of offset from the path, allowing the AUV to correct its heading and effectively close the gap. Over a series of field trials, this system demonstrated online control of an AUV in the ocean environment of Holyrood Arm, Newfoundland and Labrador, Canada. The system was implemented on an International Submarine Engineering Ltd. Explorer AUV and performed multiple path completions over both a 1 and 5 km track. These trials illustrated an AUV operating in a fully autonomous mode, in which navigation was driven solely by sensor feedback and adaptive control. Path‐following performance was as desired, with the AUV maintaining close offset to the path.     

Fuzzy PDFF-IIR controller for PMSM drive systems

Pseudo-derivative feedback with feed-forward gain (PDFF) combines the advantages of proportional-integral (PI) and pseudo-derivative feedback (PDF) controllers. However, PDFF responds more slowly to a command than does PI. To increase the speed of response of the PDFF controller, this work presents a PDFF with moving average errors control. A low-pass IIR filter path for errors compensation that accelerates the slow response is added to a PDFF control loop. A fuzzy inferencer is utilized to adjust the feed-forward gain and integral gain of the PDFF controller to allow closed-loop poles of the transfer function to be properly placed to improve load torque disturbance rejection capability. Simulated and experimental results reveal that the response and load disturbance rejection ability of the fuzzy PDFF-IIR controller are better than those of the traditional PDFF controller.     

Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels

The problem of path following for marine surface vessels using the rudder angle is addressed in this paper. A four-degree-of-freedom nonlinear surface vessel model, together with the Serret-Frenet equations, is introduced to describe the ship dynamics and path following error dynamics. While similar models have been used and reported in the literature for path following control algorithm development, the novelty of the approach presented in this work lies in the following aspects. (a) The back-stepping nonlinear controller design is based on feedback dominance, instead of feedback linearization and nonlinearity cancelation; (b) additional design parameters are employed in the Lyapunov function that lead to simplification of the controller in the design procedure and normalization of different variables in the Lyapunov function to improve the controller performance; (c) relying on feedback dominance and the introduction of the additional parameters in the Lyapunov function, the resulting controller is almost linear, with very benign nonlinearities allowing for analysis and evaluation; and (d) the performance of the nonlinear controller, in terms of path following, is analyzed for robustness in the presence of model uncertainties. The simulation results are presented to verify and illustrate the analytic development and the effectiveness of the resulting control against rudder saturation and rate limits, and delays in the control execution, as well as measurement noises. Furthermore, the control design is validated by experimental results conducted in a tank using a model ship.     

Direct parametric attitude tracking control for generic hypersonic vehicle

This paper considers the attitude tracking problem for the generic hypersonic vehicle (GHV). First, the second-order nonlinear GHV attitude model is introduced. Second, by utilising the direct parametric approach, a modified parametric controller composed of the parametric state proportional plus derivative feedback controller and the feedforward controller is proposed. With application of the first part, the closed-loop system is a constant linear system with desired eigenstructures, and the second part is used to ensure the asymptotic tracking property of the outputs of the GHV attitude system. Since the control input of the established GHV attitude model is moment command, an algorithm that transforms the moment commands into the fins deflection command is proposed. Finally, the effectiveness of the proposed parametric controller and transform algorithm is illustrated by the numerical simulation results.     

欠驱动飞艇平面路径跟踪控制

针对欠驱动飞艇模型,提出一种基于制导向量场的平面路径跟踪控制方法.首先,基于牛顿-欧拉方程建立欠驱动飞艇动力学模型;然后,基于向量场理论构造制导向量场以获得期望偏航角,结合反步法设计路径跟踪控制律,并通过稳定性分析证明所设计的控制律能够使路径跟踪误差收敛到零而且闭环系统状态有界;最后,通过仿真对比了所提出方法与已有方法的控制效果,仿真结果验证了所提出方法的有效性和优越性.     

基于迭代滑模增量反馈的欠驱动AUV地形跟踪控制

为实现欠驱动自治水下机器人(AUV)在未知海流干扰作用下的地形跟踪控制,提出一种基于非线性迭代滑模增量反馈的航迹跟踪控制器.基于虚拟向导的方法,建立AUV垂直面航迹跟踪误差方程.采用迭代方法,设计滑模增量反馈控制器,无需对AUV模型参数不确定部分和海流干扰进行估计,这样避免了AUV俯仰舵的抖振现象,并且减小了输出反馈控制的稳态误差与超调问题.仿真实验表明,所设计的控制器对AUV系统的模型参数摄动及海流干扰变化不敏感,所设计的参数易于调节.     

Command filtered path tracking control of saturated ASVs based on time‐varying disturbance observer

This paper investigates the path‐tracking control problem for an autonomous surface vessel (ASV) with unknown time‐varying disturbances and input saturation. A robust nonlinear control law is proposed based on a disturbance observer and an auxiliary system in the context of command filtered control. The disturbance observer is constructed to estimate the unknown time‐varying disturbances, the auxiliary dynamic system is employed to handle input saturation, and the compensator based command filtered control technique makes the designed path‐tracking control law simple and easy to implement in practice. It is proved that the nonlinear control law can track the desired vessel's position and heading, while guaranteeing the uniform ultimate boundedness of all signals in the path‐tracking control system. Simulation results further demonstrate the effectiveness of the method.     

Application of type-2 fuzzy logic system for load frequency control using feedback error learning approaches

In this paper, the type-2 fuzzy logic system (T2FLS) controller using the feedback error learning (FEL) strategy has been proposed for load frequency control (LFC) in the restructure power system. The original FEL strategy consists of an intelligent feedforward controller (INFC) (i.e. artificial neural network (ANN)) and the conventional feedback controller (CFC). The CFC acting as a general feedback controller to guarantee the stability of the system plays a crucial role in the transient state. The INFC is adopted in forward path to take over the control problem in the steady state. In this work, to improve the performance of the FEL strategy, the T2FLS is adopted instead of ANN in the INFC part due to its ability to model uncertainties, which may exist in the rules and measured data of sensors more effectively. The proposed FEL controller has been compared with a type-1 fuzzy logic system (T1FLS) – based FEL controller and the proportional, integral and derivative (PID) controller to highlight the effectiveness of the proposed method.