Adaptive versus neural adaptive control: Application to robotics

A comparative study evaluates the problem of determining the control that must be exerted on manipulator joints. Two different techniques are studied: (i) direct and indirect adaptive controls and (ii) neural adaptive control. In the direct adaptive technique the Lyapunov stability-based approach is used with the objective of minimizing the tracking errors of the joints in the adaptation process. In the indirect adaptive technique the regulator parameters are updated via the estimation of the process model. This step, using a recursive least squares algorithm, is based on the error at the input and on the filtered dynamic model in order to avoid acceleration measurements. Neural adaptive control is based on learning from input-output measurements and not on parametricmodel-based dynamics. It is important to note that adaptive control requires a real-time estimation of the system parameters and a well-defined dynamic model, whereas neural adaptive control does not require any of these conditions. All the above-mentioned techniques are applied to the trajectory-tracking control of a two-degree-of-freedom (2DOF) manipulator. the experimental results show the effectiveness of the neural adaptive techniques for the trajectory-tracking errors.     

Chaotification of unknown linear and nonlinear systems with applications

A new chaotification method (chaos anti-control) of dynamical systems, which have unknown parameters, is proposed in this paper. The method is based on tracking reference models, through a control law that chaotifies a class of non-linear systems, linear in the control and fully state feedback linearizable. Besides, adaptive laws for control parameters are derived that guarantee the stability of the resulting adaptive system and the convergence of the tracking error to zero. The proposed method has two possible approaches: indirect and direct. Finally, the proposed scheme is applied to secure communications, by means of encrypted information transmission and reception of a message in a chaotic system.     

Linear and non-linear adaptive control of alcoholic fermentation process: Experimental results

This paper deals with the experimental implementation of several control algorithms on a continuous flow fermentation process. The regulation and tracking problems of the substrate concentration are considered. Our objective is to show the advantages and drawbacks of these algorithms in tracking and regulation behaviour, overshoot, knowledge contribution, number of tuning parameters, etc. The different controllers described in this paper are the PI controller, the non-linear adaptive L/A algorithm, the linear adaptive controller (predictive control with partial state reference model) and the adaptive controller based on the non-linear structure of the process model (pole placement control). These controllers are applied to a pilot-scale fermentation system with satisfactory results.     

Adaptive tracking control for electrically‐driven robots without overparametrization

This paper addresses the motion tracking control of robot systems actuated by brushed direct current motors in the presence of parametric uncertainties and external disturbances. By using the integrator backstepping technique, two kinds of adaptive control schemes are developed: one requires the measurements of link position, link velocity and armature current for feedback and the other requires only the measurements of link position and armature current for feedback. The developed adaptive controllers guarantee that the resulting closed‐loop system is locally stable, all the states and signals are bounded, and the tracking error can be made as small as possible. The attraction region can be not only arbitrarily preassigned but also explicitly constructed. The main novelty of the developed adaptive control laws is that the number of parameter estimates is exactly equal to the number of unknown parameters throughout the entire electromechanical system. Consequently, the phenomenon of overparametrization, a significant drawback of employing the integrator backstepping technique to treat the control of electrically driven robots in the previous literature, is eliminated in this study. Finally, simulation examples are given to illustrate the tracking performance of electrically driven robot manipulators with the developed adaptive control schemes. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

矩阵变换器驱动异步电机模糊自适应PI控制

在间接空间矢量调制的矩阵变换器和矢量控制原理的基础上,搭建了异步电机调速系统.为了进一步提高该系统的动态性能和抗干扰能力,在调速系统的矢量控制部分引入模糊自适应PI控制器,代替传统的PI控制器,对控制器参数进行实时校正.仿真结果表明,采用模糊PI控制器的矩阵变换器驱动的调速系统能够使能量回馈到电网,达到了节能目的,同时...     

Filtered adaptive constrained sampled-data control for uncertain multivariable nonlinear systems

A filtered adaptive constrained sampled-data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed-loop system with the sampled-data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled-data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.     

Novel model reference adaptive control architecture using semi‐initial excitation‐based switched parameter estimator

This paper is a generalization of the recently developed techniques of initial excitation (IE)–based adaptive control with an introduction to the definition of semi‐initial excitation (semi‐IE), a still more relaxed notion than IE. Classical adaptive controllers typically ensure Lyapunov stability of the extended error dynamics (tracking error + parameter estimation error) and asymptotic tracking, while requiring a stringent condition of persistence of excitation (PE) for parameter convergence. Of late, the authors have proposed a new adaptive control architecture, which guarantees parameter convergence under the online‐verifiable IE condition leading to exponential stability of the extended error dynamics. In earlier works, it has been established that the IE condition is significantly milder than the classical PE condition. The current work further slackens the excitation condition by proposing the concept of semi‐IE. The proposed adaptive controller is proved to ensure convergence of the parameter estimation error to a lower‐dimensional manifold under the weaker semi‐IE condition, while the stronger condition of IE guarantees convergence of the parameter estimation error to zero. The designed algorithm is shown to improve transient response of tracking error sufficiently in contrast to conventional adaptive controllers.     

Modeling and Optimal Tracking Control for WMR Systems with Control Delay

Abstract

This article studies the issue of modeling and tracking control for wheeled mobile robot systems with control delay. The kinematics wheeled mobile robot (WMR) is modeled under the nonholonomic constraint. Further, the state-space representations of WMR and tracking error equations with control delays are modeled. Using functional transformation, the tracking error system with control delay is converted into a delay-free one. Then, the optimal control law including a control memory compensation term is obtained by using Maximum Value Principle. The effectiveness and utility of the designed controllers, the horizontal speed and the angular speed, are verified in simulation.     

Fast estimation of voltage and current phasors in power networksusing an adaptive neural network

A new algorithm for the estimation of parameters of voltage or current waveform of power networks contaminated by noise is proposed. The problem of estimation is formulated by using an adaptive neural network consisting of linear adaptive neurons called adaline. The learning parameters of the adaline are adjusted to force the error between the actual and desired outputs to satisfy a stable difference error equation, rather than to minimize an error function. Illustrative computer simulation results confirm the validity and accurate performance of the proposed method. Laboratory test results are also presented in this paper to support the effectiveness of the proposed approach in tracking the waveforms in real-time     

Anti-unwinding adaptive attitude tracking control for spacecraft with quantized torques

The adaptive attitude tracking control with limited communication to actuators is addressed in this paper. To avoid unwinding, a rotation matrix rather than a quaternion is used to describe the attitude, for which the stability is proved by Morse-Lyapunov function. To meet the need of restricted communication, two different quantizers, logarithmic quantizer and hysteres quantizer, are used to quantize the control torque signal. Two robust adaptive control techniques, indirect and direct, are proposed to deal with the impacts of quantization error and external disturbances. The proposed control schemes, in conjunction with quantizers, guarantee the global boundedness of all signals in the closed-loop system, allowing the attitude tracking error to converge toward an ultimately bounded region. Finally, numerical simulations are conducted to illustrate the performance of the proposed controllers.     

Decentralized stochastic adaptive control of interconnected systems

This paper considers the stochastic adaptive control problem for a class of large-scale systems formed by arbitrary interconnection of subsystems with unknown parameters and non-linearities. For the estimation of the unknown parameters of the local controllers, stochastic approximation algorithms are used. Conditions sufficient for global stability of the overall system are established. It is shown that the overall tracking error is bounded by a quantity depending on the size of interconnections.     

A probabilistic indirect adaptive control for systems with input‐dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system. Copyright © 2010 John Wiley & Sons, Ltd.     

Passivity‐based adaptive output tracking control for switched nonlinear systems with uncertain parameters

This paper addresses the issue of the adaptive output tracking control for switched nonlinear systems with uncertain parameters. The solvability of the tracking control problem for each subsystem is not necessary to hold. Individual update laws corresponding to different unknown parameters are adopted to reduce the conservativeness produced from the adoption of a common undated law. By means of the dual design of the adaptive controllers and a state‐dependent switching law using multiple storage functions technique, several conditions are obtained under which the adaptive output tracking control problem for switched nonlinear systems is solvable. Finally, an example shows the effectiveness of the proposed method.     

Iterative learning control for robotic manipulators: A bounded‐error algorithm

This paper presents a model‐based nonlinear iterative learning control (NILC) for nonlinear multiple‐input and multiple‐output mechanical systems of robotic manipulators. An algorithm of a new strategy for the NILC implementation is proposed. This algorithm ensures that trajectory‐tracking errors of the proposed NILC, when implemented, are bounded by a given error norm bound. Both standard and bounded‐error learning control laws with feedback controllers attached are considered. The NILC synthesis is based on a dynamic model of a six degrees of freedom robotic manipulator. The dynamic model includes viscous and Coulomb friction and input generalized torques are bounded. With respect to the bounded‐error and standard learning processes applied to a virtual PUMA 560 robot (Unimation, Inc. Danburry, CT, USA), simulation results are presented in order to verify maximal tracking errors, convergence and applicability of the proposed learning control. Copyright © 2013 John Wiley & Sons, Ltd.     

无速度传感器的感应电机神经网络鲁棒自适应控制

针对感应电机定子电阻和负载转矩参数的不确定性,提出了无速度传感器的感应电机神经网络鲁棒自适应控制方案。用反步法设计了一种可以将各状态变量跟踪误差和神经网络各权值限制在规定范围内的神经网络鲁棒自适应控制器,提出了相应的算法,用Lyapunov定理对其稳定性进行了证明。提出了一种可以估算转子磁链和转速的观测器及相应的算法。仿真研究表明,所提出的感应电机无速度传感器控制方案对电机定子电阻、负载转矩的鲁棒性强,动态性能好,速度估算较精确。     

输入受限下非完整轮式移动机器人迭代学习跟踪控制

为了解决输入受限下非完整轮式移动机器人的跟踪控制问题,考虑迭代学习控制方法,设计了一种迭代学习控制律,这里所设计的迭代学习控制律结合了系统的跟踪误差和约束下的上一代控制律.通过应用范数分析理论,对跟踪误差的收敛性进行了理论分析,验证了设计的控制律的有效性.最后,给出了一个仿真实例以证明理论分析结果的正确性,仿真结果表明,在设计的迭代学习控制律作用下,具有输入受限的非完整轮式移动机器人能够获得很好的跟踪控制性能,跟踪误差最终收敛于零的很小邻域内.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Adaptive trajectory/force control scheme for constrained robot manipulators

An adaptive control scheme for the trajectory/force tracking of robot manipulators is presented. Asymptotic stability of state variables and convergence of constraint forces to any prespecified set are proven. The design procedure avoids the restrictive solvability condition of the constraint equation in the whole space of robot co-ordinates. A fairly accurate bound of the tracking error is derived by means of a Lyapunov analysis.     

Adaptive recurrent Chebyshev neural network control for PM synchronous motor servo‐drive electric scooter with V‐belt continuously variable transmission

Because of unknown nonlinearity and time‐varying characteristics of electric scooter with V‐belt continuously variable transmission (CVT) driven by permanent magnet synchronous motor (PMSM), its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network (NN) control system is proposed to control for PMSM servo‐drive electric scooter with V‐belt CVT under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev NN control system consists of a recurrent Chebyshev NN control and a compensated control with estimation law. In addition, the online parameters tuning methodology of the recurrent Chebyshev NN and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev NN based on a discrete‐type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme. Copyright © 2014 John Wiley & Sons, Ltd.