A generalization of the hyperstability conditions for model reference adaptive systems

A generalization of the hyperstability criterion given in the literature is discussed. The new hyperstability conditions were obtained by utilizing the properties of the positive definite kernels. The results presented here are directly applicable for the synthesis of hyperstable adaptation algorithms for various applications.     

超稳定性方法及其在机器人控制中的应用

本文用超稳定性方法研究了一类以工业机器人为背景的模型參考自适应控制问题,克服了过去用超稳定性方法设计不能保证渐近稳定的缺点,并把该方法应用到工业机器人控制中.     

Hyperstability and average hyperstability conditions for a broad class of gaussian stochastic systems

The author investigates the hyperstability problem for a broad class of single-control stochastic systems which may be considered as disturbed models of given deterministic systems. The stochasticity comes from the control, which is disturbed by an additive Gaussian noise with its own gain. Hyperstability conditions are given when the noise has a time-independent variance. When this variance depends explicitly upon the time, we define the time-average hyperstability, and conditions for average hyperstability are given. Similar problems are solved for multicontrol Gaussian systems. Illustrative examples show how one can derive from these results a broad class of absolute stability conditions.     

虚拟现实力觉临场感遥操作机器人系统的稳定性

具有良好的可操作性，又能确保系统稳定性是解决力觉临场感遥操作机器人系统时延问题的根本。本文阐述了采用Popov超稳定性理论分析并研究虚拟现实力觉临场感遥操作机器人系统的稳定性问题是行之有效的，并给出了其分析方法，指出Popov超稳定性与无源稳定性理论是条件一致的。实验显示本文所给出的方法的有效性。本文的论述对于系统的设计极具价值。     

On the hyperstability of a class of hybrid systems

Sufficient conditions of the hyperstability of a class of single-input single-output hybrid systems, composed of interconnected continuous and discrete subsystems, are given. Hyperstability is guaranteed by that of a discrete extended system which is built by incorporating samples of the continuous substrate. Asymptotic hyperstability is guaranteed by that of one discrete system, together with that of a continuous one. Both systems are related to an augmented state representation of the linear part of the overall system for all the nonlinear output-feedback time-varying actuators that satisfy generalized Popov-type inequalities.     

A result on the hyperstability of a class of hybrid dynamic systems

This paper presents a hyperstability theorem for a class of hybrid dynamic systems composed of coupled differential and difference equations subject to (possibly) time-varying nonlinearities satisfying a Popov-type inequality. The nonlinear controller generates the plant input at all times from its sampled values by defining an extended discrete system. The hyperstability results are obtained from this discrete system of special type whose state consists of the sampled continuous substate and the digital substate of the given hybrid system. Some corollaries and related physical interpretations are also given     

利用超稳定性理论证明随机自适应控制算法的稳定性

超稳定性理论是自适应控制稳定性证明的有力工具,但至今它只限于确定性系统.通过 对超稳定性理论进一步研究和算法结构变化,本文给出了利用超稳定性理论证明随机自适应 控制(特别是Goodwin的随机逼近法)的稳定性.结果表明,与目前的证明方法--Martingale 函数法和Ljurg的ODE法相比,超稳定性方法有相当的优越性.它不需要象Martingale 函数法那样去构造一个相当困难的随机Lyapunov函数,也可放松ODE法所必需的 系统噪声平稳的条件.     

Nonlinear adaptive control of robotic manipulators - hyperstability approach

A nonlinear model reference adaptive controller based on hyperstability approach, is presented for the control of robot manipulators. Use of hyperstability approach simplifies the stability proof of the adaptive system. The unknown parameters of the system, as well as its variable payload, are estimated on line and are adaptive to their actual values; tending to reduce the system error. In addition, any sudden change in the system parameters or payload is detected by the proposed intelligent controller. Robot path tracking, with unknown parameter values and variable payload, is simulated to show the effectiveness of the proposed adaptive control algorithm. Both system output error and parameter estimation error vanish under the proposed parameter adaptation algorithm.     

A hyperstability criterion for model reference adaptive control systems

This paper considers the stability problem of the model reference adaptive control systems by means of the properties of hyperstable systems. A theorem concerning the hyperstability of model reference adaptive control systems is presented. This theorem directly gives a structure of the adaption mechanism. The results presented here include all the results obtained by Butchart, Shackcloth, Parks, Winsor, Roy, and Dressler. The hyperstability approach presented in this paper also allows for other solutions to the adaption mechanism and represents a general method for studying this type of adaptive systems. The results are directly applicable to the design of model reference adaptive control systems and they were verified for some particular cases by analogical simulation.     

A review of: “Design of Modern Control Systems” Edited by D. J. BELL,P. A. COOK and N. MUNRO. (I.E. 13. Control Engineering Series 20) Peter Peregrinus Ltd, 1982, pp. 330. Price £19·50.

A nonlinear state-space model representing the robot dynamics and containing a disturbance term due to gravitational loading is presented. An adaptive model-following control problem satisfying the matching conditions is formulated using a suitable linear time-invariant reference model. The control input is designed to have two components: a non-adaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further added and then the overall asymptotic hyperstability is established. Simulation experiments on the first three joints of a PUMA 560 robot manipulator have indicated the potential of our design approach.     

Synthesis of discrete model reference adaptive systems

The synthesis of discrete model reference adaptive systems is discussed from the hyperstability point of view. The results included here are an extension of previous results obtained by the author for the continuous case [1].     

Hyperstability of control evolution processes in Hilbert spaces

In this paper the hyperstability of infinite-dimensional systems defined by integral equations given in terms of evolution operators in Hilbert spaces is studied. The results obtained are generalizations, for the infinite-dimensional case, of the well-known results of Popov.     

A design approach to adaptive model-following control of robotic manipulators

In this paper, the robot dynamics are represented by a nonlinear state-space model containing a disturbance term due to gravitational loading. Using a suitable linear time-invariant reference model, an adaptive model-following control problem is formulated which satisfies the matching conditions. The control input is designed to have two components: a nonadaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further superimposed and then the overall asymptotic hyperstability is established. The simulation results on the first three joints of PUMA 560 robot manipulator indicate the potential of our design approach.Based on research supported by Kuwait University Research Administration under Grant No. EE 049.     

Sufficient conditions for hyperstability of a class of nonlinear systems

The concept of hyperstability is applied to obtain a new stability criterion for a class of nonlinear systems. The physical system considered is the chemical reactor which gives rise to a very interesting aspect of stability study.     

关于Popov积分不等式解的注记

本文给出了用渐近超稳定定理综合自适应系统所出现的Popov积分不等式的严格解,揭示了用李亚普诺夫和超稳定两种方法所得自适应律之间的差别。     

On a multidimensional systems identification method

This correspondence concerns the application of the "state variable filters" technique for the hyperstable real-time identification system with adjustable model, synthetized by Landau via hyperstability of model reference adaptive control systems, in order to avoid implementation difficulties due to a derivative compensator introduced in the adaptation mechanism.     

A new form of stable adaptive observer

A new form of adaptive observer which is guaranteed to be globally stable via hyperstability theories is presented. Its main advantage over existing designs is that asymptotic unbiased estimates are obtained in the presence of output noise. Experimental results are given to demonstrate the performance of this observer.     

Recursive parameter identification algorithm stability analysis via pi-sharing

Pi-sharing is introduced as an extension of the application of passivity and hyperstability concepts for discrete-time systems, providing connections between input-output and state-space stability notions. Using tools developed within the pi-sharing framework, new stability results for the output error class identification algorithm are derived. This approach offers a clear interpretation of the role of the SPR condition in the work of Landau and Silveira and its absence in the work of Tomizuka and Altay.     

On state variables filters for adaptive system design

An alternative way of using the state variable filters, coupled with the Kalman-Yacubovich lemma or Popov's hyperstability theorem, in the design of model reference adaptive systems is proposed. The improvement over previous designs is the increased flexibility in the selection of the filter parameters to reduce the effects of noise or initial conditions.