Composite adaptation and learning for robot control: A survey

Composite adaptation and learning techniques were initially proposed for improving parameter convergence in adaptive control and have generated considerable research interest in the last three decades, inspiring numerous robot control applications. The key idea is that more sources of parametric information are applied to drive parameter estimates aside from trajectory tracking errors. Both composite adaptation and learning can ensure superior stability and performance. However, composite learning possesses a unique feature in that online data memory is fully exploited to extract parametric information such that parameter convergence can be achieved without a stringent condition termed persistent excitation. In this article, we provide the first systematic and comprehensive survey of prevalent composite adaptation and learning approaches for robot control, especially focusing on exponential parameter convergence. Composite adaptation is classified into regressor-filtering composite adaptation and error-filtering composite adaptation, and composite learning is classified into discrete-data regressor extension and continuous-data regressor extension. For the sake of clear presentation and better understanding, a general class of robotic systems is applied as a unifying framework to show the motivation, synthesis, and characteristics of each parameter estimation method for adaptive robot control. The strengths and deficiencies of all these methods are also discussed sufficiently. We have concluded by suggesting possible directions for future research in this area.     

An analytical comparison of a neural network and a model-basedadaptive controller

A neural network inverse dynamics controller with adjustable weights is compared with a computed-torque type adaptive controller. Lyapunov stability techniques, usually applied to adaptive systems, are used to derive a globally asymptotically stable adaptation law for a single-layer neural network controller that bears similarities to the well-known delta rule for neural networks. This alternative learning rule allows the learning rates of each connection weight to be individually adjusted to give faster convergence. The role of persistently exciting inputs in ensuring parameter convergence, often mentioned in the context of adaptive systems, is emphasized in relation to the convergence of neural network weights. A coupled, compound pendulum system is used to develop inverse dynamics controllers based on adaptive and neural network techniques. Adaptation performance is compared for a model-based adaptive controller and a simple neural network utilizing both delta-rule learning and the alternative adaptation law.     

Adaptive control with discontinuous σ-factor and saturation for improved robustness

An adaptive control law is proposed to improve the robustness of the adaptive system with respect to fast unmodelled dynamics represented by a singular perturbation. The new law is based on saturation of the regressor and control parameter vector with inclusion of a discontinuous σ-factor. The analysis of the resulting system is presented and the conclusions are illustrated by simulations. The introduction of a discontinuous σ-factor represents an extension of an earlier work. The advantages of this extension include global stability, with less restrictive assumptions, and better transient behaviour.     

A robust adaptive control method for Wiener nonlinear systems

This paper proposes a new robust adaptive control method for Wiener nonlinear systems with uncertain parameters. The considered Wiener systems are different from the previous ones in the sense that we consider nonlinear block approximation error, process noise, and measurement noise. The parameterization model is obtained based on the inverse of the nonlinear function block. The adaptive control method is derived from a modified criterion function that can overcome non‐minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. Theoretical analysis indicates that the closed‐loop system stability can be guaranteed under mild conditions. Numerical examples including an industrial problem are studied to validate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics

It has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties. However, not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution. This adaptive controller belongs to passivity-based control. Though passivity-based controllers have many attractive properties, in general, they are not able to guarantee the uniform performance of the robot over the entire workspace. Even in the ideal case of perfect knowledge of the manipulator parameters, the closed-loop system remains nonlinear and coupled. Thus the closed-loop tracking performance is difficult to quantify, while the inverse dynamics controllers can overcome these deficiencies. Therefore, in this work, we will develop a new adaptive Jacobian tracking controller based on the inverse manipulator dynamics. Using the Lyapunov approach, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the performance of the proposed controller.     

ODE analysis and redesign in blind adaptation

In blind adaptation the dynamics of an unknown channel (system) is recovered together with the transmitted symbol sequence (input signal). This paper generalizes the author's previous algorithm (1994, 1997), that is not derived by criterion minimization, to include adaptive regressor filtering. The resulting scheme, which adapts a finite-dimensional IIR channel model, is designed to converge only to a well-defined set of parameters when binary symbols are transmitted over the channel. This provides a partial solution to the recently discussed ill-convergence problem in blind adaptation. Some connections to adaptive control theory are noted     

An exponentially convergent adaptive sliding mode control of robot manipulators

A new robust adaptive algorithm for control of robot manipulators is proposed to account for a desired transient response with global exponential convergence of tracking errors without any persistent excitating assumption on the regressor. Its novelty lies in a new dynamic sliding surface that allows a systematic combination of adaptive control and variable structure control to yield a sliding mode inside an adaptive control loop. During sliding mode, parameter uncertainty appears in terms of known variables in such a manner that a new robust parameter estimator with enhanced stability properties is established. On the other hand, if the regressor meets the persistent exciting condition, the global uniform exponential stability of the equilibrium concerning the adaptive closed-loop error equation is easily established. The proposed controller from the VSS viewpoint relaxes the longstanding condition on a priori knowledge of the size of the parametric uncertainty to induce a sliding mode. On the other hand, from the adaptive control viewpoint it relaxes the standard assumption of the persistent excitation on the regressor to obtain the exponential convergence of tracking errors. Also, the stability against time-varying parameters is briefly discussed. Concluding remarks concerning its structural behaviour are given, and computer simulation data show a robust performance.     

Some comments on the use of normalization in robust adaptive control

This paper discusses the role of normalization with respect to robust parameter estimation for discrete-time adaptive control in the presence of unmodeled dynamics. It is pointed out that the normalizing signal may be brought into the adaptive law in two distinct ways; (i) via normalization of the regressor and the error signal in the standard parameter update law, and (ii) by replacement of the error signal with a function of the normalizing signal and the error. The convergence properties for both approaches are derived and shown to be similar.     

基于扩展自适应Backstepping设计的TCSC非线性控制的新方法

首先针对一般的参数反馈型非线性系统提出一种扩展自适应Backstepp ing方法.该方法不仅保留系统的非线性特性和对未知参数的实时在线估计,而且突破经典的确定性等价性原理来设计参数估计器和动态反馈控制器.该方法可用于带有TCSC(thyristor controlled series compensation)的单机无穷大系统.仿真结果表明,该方法在系统响应和自适应速度方面优于传统的Backstepp ing方法.     

Adaptive inverse compensation for actuator backlash with piecewise time-varying parameters

Existing adaptive inverse compensation methods for cancelling actuator backlash nonlinearity are all restricted to handle constant backlash parameters. In other words, when discontinuity and time variation as both ubiquitous phenomena in practical actuators exist, such inverse compensation methods are no longer applicable theoretically. So far, no result has been reported in addressing such an issue, regardless of its importance in practice. In this paper, we solve this problem by developing a new piecewise Lyapunov function analysis and using parameter projection adaptation mechanism. Based on such approaches, an adaptive inverse compensation control scheme is designed to compensate for piecewise time-varying actuator backlash nonlinearity. It is proved that all signals of closed-loop system are ensured bounded. Moreover, the steady-state error is bounded by an adjustable scalar approaching to zero arbitrarily. Simulation also illustrates the obtained theoretical results.     

Composite Adaptive Control of Uncertain Euler‐Lagrange Systems with Parameter Convergence without PE Condition

This work proposes a novel composite adaptive controller for uncertain Euler‐Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.     

Adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters

In this article, we address the problem of adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters. Our new developments extend the results reported in our recently works. The case with known parameters has been studied by many researchers. However in this article we show that the generalized parameter estimation-based observer design provides a very simple solution for the unknown parameter case. Moreover, when this observer design technique is combined with the dynamic regressor extension and mixing estimation procedure the estimated state and parameters converge in fixed-time imposing extremely weak excitation assumptions.     

Adaptive fuzzy robust control of PMSM with smooth inverse based dead-zone compensation

It is a challenging work to design high precision/high performance motion controller for permanent magnet synchronous motor (PMSM) due to some difficulties, such as varying operating conditions, parametric uncertainties and external disturbances. In order to improve tracking control performance of PMSM, this paper proposes an adaptive fuzzy robust control (AFRC) algorithm with smooth inverse based dead-zone compensation. Instead of nonsmooth dead-zone inverse which would cause the possible control signal chattering phenomenon, a new smooth dead-zone inverse is proposed for non-symmetric dead-zone compensation in PMSM system. AFRC controller is synthesized by combining backstepping technique and small gain theorem. Discontinuous projectionbased parameter adaptive law is used to estimate unknown system parameters. The Takagi-Sugeno fuzzy logic systems are employed to approximate the unstructured dynamics. Robust control law ensures the robustness of closed loop control system. The proposed AFRC algorithm with smooth inverse based dead-zone compensation is verified on a practical PMSM control system. The comparative experimental results indicate that the smooth inverse for non-symmetric dead-zone nonlinearity can effectively avoid the chattering phenomenon which would be caused by nonsmooth dead-zone inverse, and the proposed control strategy can improve the PMSM output tracking performance.     

On using least-squares updates without regressor filtering in identification and adaptive control of nonlinear systems

In continuous-time system identification and adaptive control the least-squares parameter estimation algorithm has always been used with regressor filtering, which adds to the dynamic order of the identifier and affects its performance. We present an approach for designing a least-squares estimator that uses an unfiltered regressor. We also consider a problem of adaptive nonlinear control and present the first least-squares-based adaptive nonlinear control design that yields a complete Lyapunov function. The design is presented for linearly parametrized nonlinear control systems in ‘normal form’. A scalar linear example is included which adds insight into the key ideas of our approach and allows showing that, for linear systems, our Lyapunov-LS design with unfiltered regressor, presented in the note for unnormalized least-squares, can also be extended to normalized least-squares.     

一种基于正则化参数自适应选择的快速近似求逆的图像恢复新算法

本文根据正则化恢复中正则化参数应具有的性质,提出了一种基于正则化参数自适选择方案的新的空域迭代恢复算法。     

Is normalization necessary for stable model reference adaptive control?

One of the longest standing open questions in adaptive control concerns the correctness of the stability claim of the un-normalized model reference scheme proposed by Monopoli in 1974. Although provably correct solutions to the problem now abound, in particular, it is well known that adding a normalization to Monopoli's original scheme ensures global convergence, it is interesting to know whether this technique-driven modification is really necessary or only required to complete the stability proof in the absence of more elaborate arguments. In this note, we construct a counterexample that provides a definite-unfortunately, negative-answer to the claim. Instrumental for the establishment of this result is a technical lemma that shows that, under some conditions on the regressor that may appear in Monopoli's scheme, the parameter error freezes as the adaptation gain goes to infinity. On the lighter side, we also prove that Monopoli's scheme is semiglobally stable, underscoring the relevance of this important contribution.     

Adaptive Neural Network Control For Smart Materials Robots Using Singular Perturbation Technique

In this paper, an adaptive neural network controller is presented for smart materials robots using Singular Perturbation techniques by modeling the flexible modes and their derivatives as the fast variables and link variables as slow variables. The neural network (NN) controller is to control the slow dynamics in order to eliminate the need tor the tedious dynamic modeling and the error prone process in obtaining the regressor matrix. In addition, inverse dynamic model evaluation is not required and the time‐consuming training process is avoided except for initializing the NNs based on the approximate function values at the initial posture at time t=0. The smart materials bonded along the links are used to active suppress the residue vibration. Simulation results have shown that the controller can control the system successfully and effectively.     

Universal stabilization using control Lyapunov functions, adaptivederivative feedback, and neural network approximators

In this paper, the problem of stabilization of unknown nonlinear dynamical systems is considered. An adaptive feedback law is constructed that is based on the switching adaptive strategy proposed by the author and uses linear-in-the-weights neural networks accompanied with appropriate robust adaptive laws in order to estimate the time-derivative of the control Lyapunov function (CLF) of the system. The closed-loop system is shown to be stable; moreover, the state vector of the controlled system converges to a ball centered at the origin and having a radius that can be made arbitrarily small by increasing the high gain K and the number of neural network regressor terms. No growth conditions on the nonlinearities of the system are imposed with the exception that such nonlinearities are sufficiently smooth. Finally, we mention that neither the system dynamics or the CLF of the system need to be known in order to apply the proposed methodology.     

Sign‐Regressor Adaptive Filtering Algorithms for Markovian Parameters

This work is devoted to analyzing adaptive filtering algorithms with the use of sign‐regressor for randomly time‐varying parameters (a discrete‐time Markov chain). In accordance with different adaption and transition rates, we analyze the corresponding asymptotic properties of the algorithms. When the adaptation rate is in line with the transition rate, we obtain a limit of a Markov switched differential equation. When the Markov chain is slowly changing the parameter process is almost a constant, and we derive a limit differential equation. When the Markov chain is fast varying, the limit system is again a differential equation that is an average with respect to the stationary distribution of the Markov chain. In addition to the limit dynamic systems, we obtain asymptotic properties of centered and scaled tracking errors. We obtain mean square errors to illustrate the dependence on the stepsize as well as on the transition rate. The limit distributions in terms of scaled errors are studied by examining certain centered and scaled error sequences.     

Direct adaptive control of manipulators in cartesian space

A new adaptive-control scheme for direct control of manipulator end effector to achieve trajectory tracking in Cartesian space is developed in this article. The control structure is obtained from linear multivariable theory and is composed of simple feedforward and feedback controllers and an auxiliary input. The direct adaptation laws are derived from model reference adaptive control theory and are not based on parameter estimation of the robot model. The utilization of adaptive feedforward control and the inclusion of auxiliary input are novel features of the present scheme and result in improved dynamic performance over existing adaptive control schemes. The adaptive controller does not require the complex mathematical model of the robot dynamics or any knowledge of the robot parameters or the payload, and is computationally fast for on-line implementation with high sampling rates. The control scheme is applied to a two-link manipulator for illustration.