Showing papers in "International Journal of Adaptive Control and Signal Processing in 1990"
TL;DR: It is shown that in both types of iterative learning algorithm a better performance is realized at every attempt of operation, provided a desired motion is given a priori and the actual motion can be measured at every operation.
Abstract: A new concept of learning control for the improvement of robot motions is proposed, which can be referred to a mathematical modelling of learning and generation of motor programmes in the central nervous system. It differs from conventional classical and modern control techniques. It stands for the repeatability of operating a given robotic system and the possibility of improving the command input on the basis of actual measurement data acquired at the previous operation. Hence adequate conditions on the repeatability and invariance of the system dynamics are assumed, but no precise description of the dynamics is required for construction of the learning algorithms. Two types of iterative learning algorithm are proposed: one uses a PD-type (proportional and differential) update of input commands and the other a PI-type (proportional and integral) update where velocity signals are regarded as outputs. It is shown that in both types a better performance is realized at every attempt of operation, provided a desired motion is given a priori and the actual motion (velocity signals) can be measured at every operation. Further, the robustness of such learning control algorithms with respect to the existence of perturbed errors of initialization of the robot, disturbances and measurement noise during operation is analysed in detail. It is shown that in PD-type learning laws such errors are neither amplified nor aggregated in later consecutive trials of operation. In the case of PI-type learning laws it is shown that such a robustness property is assured if a forgetting factor is adequately introduced into the repetitive learning law.
272 citations
TL;DR: Two indirect adaptive linearizing controllers are proposed, in continuous time, for the class of nonlinear systems which are linearly parametrized and which can be linearized by state feedback through a parametRIzed diffeomorphism.
Abstract: Two indirect adaptive linearizing controllers are proposed, in continuous time, for the class of nonlinear systems which are linearly parametrized and which can be linearized by state feedback through a parametrized diffeomorphism. In each case the stability of the closed loop is analysed in detail. It is also shown how these control laws can be extended to related situations, i.e. input-output feedback linearization and nonlinear parametrizations.
138 citations
TL;DR: A mathematical framework is established based on the functional spaces which have been heavily used in H∞ control theory and then applied to the study of the convergence problems associated with learning control.
Abstract: In this paper we study a control methodology now often referred to as learning control in the recent control literature. Our primary aim is to establish a mathematical framework which will allow systematic and continuing development of learning control theory. The framework is based on the functional spaces which have been heavily used in H∞ control theory. It is then applied to the study of the convergence problems associated with learning control. Three theorems on general convergence conditions are presented.
75 citations
TL;DR: In this article, a unified framework for the stability analysis of robot tracking control is presented by using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward.
Abstract: A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete non-linear dynamics, or linearized or non-linear dynamics with parameter adaptation. As a result, the dichotomous approaches to the robot control problem based on the open-loop linearization and non-linear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a priori model information are derived.
47 citations
TL;DR: In this article, a smooth non-linear observer with smooth or differentiable gains is proposed to estimate the speed of a rigid industrial robot manipulator from angular positions and the estimated velocities.
Abstract: High-precision measurements of joint displacements are available on robot manipulators. In contrast, the velocity measurements obtained through tachometers are in many cases contaminated by noise. It is therefore economically and technically interesting to investigate the possibility of accurately estimating the speed from direct available measurements such as the angular positions. This paper proposes a ‘smooth non-linear observer’ (i.e. an observer with ‘smooth’ or ‘differentiable’ gains) and a modified computed torque law which is a function of estimated velocities and measurement positions for rigid industrial robot manipulators. We derive local conditions for asymptotic stability of the closed-loop system.
46 citations
TL;DR: In this paper, the robust control of rigid and elastic joint robots is evaluated using upper bounds on non-linear quantities of the process for the robustness analysis, and the conservatism and usefulness of robustness criteria are determined by the accuracy of the upper bounds.
Abstract: Robust controller design approaches for non-linear control systems usually require the evaluation of upper bounds on non-linear quantities of the process for the robustness analysis. The conservatism and usefulness of robustness criteria are determined by the accuracy of the robustness bounds. This contribution deals with the robust control of robot manipulators and presents generally applicable evaluation techniques for bounds on robot manipulator non-linearities which may be remnants of an incomplete non-linear decoupling or feedback linearization. These bounds can be used to verify several robust stability criteria for the control of rigid and elastic joint robots. Apparently, these bounds give insight to the strength and significance of non-linear couplings and may be used to judge whether complicated model-based control laws should be preferred rather than simple linear controllers.
31 citations
TL;DR: It is proved here that under certain assumptions, it is possible to construct a reduced description of posterior densities (a reduced statistic) which is closed with respect to the Bayes rule.
Abstract: To implement the Bayes estimation in a recursive manner means to cope with the need for storing a too large data statistic. We prove here that under certain assumptions, it is possible to construct a reduced description of posterior densities (a reduced statistic) which is closed with respect to the Bayes rule. Thus the optimal Bayes inference can be realized in terms of transitions between equivalence classes of densities matching the respective values of the description. Next we attempt to design a specific approximation of the recursive Bayes estimation by projecting the true posterior density orthogonally, along the appropriate equivalence class, onto a prespecified approximation family. We find that to ensure orthogonal projection globally, the approximation family must be of a mixture type and the description vector determined by the values of the Kullback-Leibler distance between the ‘base’ densities of the mixture approximation family and the true density. A simple simulation example compares the Bayes-closed approximation with some competitive methods.
30 citations
TL;DR: This evaluation involves suitable benchmark examples that have been proposed in Reference 3 to illustrate the essence of today's adaptive control design techniques and puts particular emphasis on the ability of the considered adaptive controller to accommodate state disturbances, sensor noise and unmodelled dynamics.
Abstract: This paper is a follow up to Reference 1. It presents further evaluation of the partial state model reference adaptive control approach proposed in Reference 2. This evaluation involves suitable benchmark examples that have been proposed in Reference 3 to illustrate the essence of today's adaptive control design techniques. Particular emphasis is put on the ability of the considered adaptive controller to accommodate state disturbances, sensor noise and unmodelled dynamics.
26 citations
TL;DR: In this article, the authors present adaptive autopilots for remotely operated underwater vehicles (ROVs) based on a simplified model of the open-loop dynamics and off-and on-line identification.
Abstract: Conventional autopilots for remotely operated underwater vehicles (ROVs) are difficult to design because the vessels' dynamics are strongly coupled, significantly non-linear and vary according to the operating configuration. In addition, the derivation of the open-loop dynamics requires the use of expensive, specialized testing equipment and is prone to error. A solution is to implement adaptive controllers. Three such schemes are presented here: the first two use a robust control law based on a simplified model of the open-loop dynamics and off- and on-line identification, while the third is an implicit linear quadratic on-line adaptive controller. These controllers are evaluated by examining their performance when controlling a comprehensive non-linear ROV simulation. The navigational hardware needed to realize an adaptive ROV auotopilot is also discussed.
21 citations
21 citations
TL;DR: In this paper, the authors define a set of standard problems which are then solved by several distinct adaptive control approaches and define the "ideal" closed-loop responses for each standard problem from which the results of the subsequent papers can be judged.
Abstract: The adaptive control literature contains numerous theories for deriving adaptive controllers. However, practising engineers who are not specialists in adaptive theory often have difficulty selecting which approach to use in a given application. The papers in this special issue address this situation by defining a set of standard problems which are then solved by several distinct adaptive control approaches. This introductory paper provides the motivation for the issue (why it is important, who is the target audience, what is the goal of the process), defines the standard problems to be considered and explains the rationale for their formulation, and describes the guidelines which were established for the participants. In addition, this paper defines the ‘ideal’ closed-loop responses for each standard problem, from which the results of the subsequent papers can be judged.
TL;DR: In this article, a model-based observer for elastic joint robots is proposed, which requires only the knowledge of the link positions and the asymptotic stability of the related error dynamics along with an estimate of the region of attraction are also given.
Abstract: The design of observers for elastic joint robots is investigated. Using some structural properties of the robot dynamics, a model-based observer is proposed which requires only the knowledge of the link positions. The asymptotic stability of the related error dynamics along with an estimate of the region of attraction are also given. The observer performances are analysed by means of simulation tests.
TL;DR: Direct control, indirect control and variable structure methods are combined with high-gain feedback in this paper for the robust adaptive control of first-, second- and third-order plants with increasing levels of uncertainty.
Abstract: Direct control, indirect control and variable structure methods are combined with high-gain feedback in this paper for the robust adaptive control of first-, second- and third-order plants with increasing levels of uncertainty. The latter include external disturbance, unmodelled dynamics, time delay and sensor noise. A judicious combination of the methods is found to result in satisfactory response in most cases.
TL;DR: In this paper, the essential driving force behind bursting is attributed to the correlation between the signal the near-end is to transmit and the signal it receives from the far-end, and a new test signal which approximately measures this correlation is proposed for use in the double-talk detector scheme that is commonly used to halt adaptation before a mishap such as bursting occurs.
Abstract: Echo cancellation in telephone communications can often be accomplished by using adaptive network echo cancellers. However, under certain circumstances, these generally effective echo cancellers can cause an undesirable bursting phenomenon. In this paper the essential driving force behind bursting is attributed to the correlation between the signal the near-end is to transmit and the signal the near-end receives from the far-end. This correlation and the subsequent potential for temporary destabilization arise as a result of the feedback loop structure of the four-wire telephone circuit. A new test signal which approximately measures this correlation is proposed for use in the double-talk detector scheme that is commonly used to halt adaptation before a mishap such as bursting occurs.
TL;DR: In this article, a new BIBO-type stability criterion is proven for linear systems described by partial differential operators with constant coefficients, and a frequency domain synthesis procedure is developed leading to an economic feedback loop (i.e. significant noise reduction achieved).
Abstract: A new BIBO-type stability criterion is proven for linear systems described by partial differential operators with constant coefficients. The class of inputs contains functions which are step-like in time and which decay appropriately in the space variables. On the basis of this result, a frequency domain synthesis procedure was developed leading to an ‘economic’ feedback loop (i.e. significant noise reduction achieved). The procedure is illustrated by means of an example.
TL;DR: In this paper, the stochastic adaptive control problem for a class of large-scale systems formed by arbitrary interconnection of subsystems with unknown parameters and non-linearities is considered.
Abstract: 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.
TL;DR: Extended least squares ELS algorithms are proposed for ARMAX model identification with the objective of avoiding the positive real condition associated with standard equation error and output error algorithms by an overparametrization at the cost of additional richness requirements on excitation signals.
Abstract: Extended least squares (ELS) algorithms are proposed for ARMAX model identification with the objective of avoiding the positive real condition associated with standard equation error and output error algorithms. This is achieved by an overparametrization at the cost of additional richness requirements on excitation signals, but without introducing ill-conditioning or infinite dimensional calculations as in earlier methods. Results for the case of D-step-ahead prediction ELS algorithms for ARMAX models also explored in the paper.
TL;DR: The almost sure convergence of the algorithm is proved under the assumption of non-stationary and correlated signals, to improve the efficiency by utilizing a number of processors updating the same array element.
Abstract: A new approach for algorithms of linearly constrained adaptive array processing is developed in this paper. The new algorithm is the product of an effort to provide a more efficient procedure for real-time implementation of adaptive array processing. The essence of our approach is to improve the efficiency by utilizing a number of processors updating the same array element. A delay is introduced in the computation for each processor. The structure (delay and multiprocessors) of our algorithm requires all processors to operate asynchronously and in a pipeline manner so that the recursively computed data flow in a rhythmic fashion, passing through each processor periodically. The almost sure convergence of the algorithm is proved under the assumption of non-stationary and correlated signals.
TL;DR: In this article, conditions for the stability of a decentralized adaptive control scheme are derived using an extended I/O sector stability theorem of Safonov, where the stability is obtained if the blocks verify certain sector conditions.
Abstract: In this paper some results of direct decentralized adaptive control based on input/output methods are presented. The plant is assumed to have several local adaptive controllers, each of which can observe only local system outputs and control only local inputs. Conditions for the stability of the decentralized control scheme are derived using an extended I/O sector stability theorem of Safonov.20 The associated error model of the adaptive scheme can be represented in the form of an equivalent feedback configuration comprising a non-linear time-varying feedforward block describing the adaptation law and a linear time-invariant feedback block which depends on the interactions of the different control loops. Stability is obtained if the blocks verify certain sector conditions. It will be demonstrated that conventional adaptation algorithms have to be modified. The proposed RLS parameter adaptation law differs from standard algorithms by the introduction of signal normalization, interlaced parameter adaptation and a variable forgetting factor.
The allowable class of interactions is restricted by the sector condition for the linear feedback block. It will be shown that less conservative conditions can be found when a parallel filter, the so-called correction network, is introduced. Such filters make direct adaptive control possible even for non-minimum phase systems. In addition, the correction network makes the adaptive controller robust to uncertainties in the structure of the plant.
TL;DR: In this paper, it is shown that the directional forgetting algorithm is not exponentially convergent and that it implies poor tracking performance in the case of time-varying parameters, which is a major drawback.
Abstract: In this paper it is shown that the so-called directional forgetting algorithm is not exponentially convergent. This is a major drawback since it implies poor tracking performance in the case of time-varying parameters.
TL;DR: In this paper, the authors compare conditions for instability with conditions for global asymptotic stability of a discretetime output error adaptive estimation algorithm, which leads to a boundedness conjecture which states that all signals within this adaptive system as well as the output error and parameter estimates remain globally bounded for all time despite any unstable behaviour.
Abstract: This paper compares conditions for instability with conditions for global asymptotic stability of a discretetime output error adaptive estimation algorithm. This comparison leads to a boundedness conjecture which states that all signals within this adaptive system as well as the output error and parameter estimates remain globally bounded for all time despite any unstable behaviour. The investigation into the stability properties of this algorithm begins with a global stability criterion applied to a transfer function which is not strictly positive real. This criterion states that for large enough adaptation gain and/or input signal magnitude the system will be asymptotically stable. Then a local result is applied which states that for small enough adaptation gain and/or input signal magnitude the same system is unstable. The result is a bifurcation due to the decrease of the adaptation gain and/or input signal magnitude as the system goes from asymptotic stability to instability which remains bounded. The results suggested by the computer simulations are verified by an exact analysis of a linearized periodic version of the adaptive system.
TL;DR: This paper illustrates the application of an integrated approach to adaptive control by reference to the case study problem proposed by Mike Masten and Herb Cohen and includes the integration of robust and adaptive control and the unification of continuous and discrete systems theory.
Abstract: This paper illustrates the application of an integrated approach to adaptive control by reference to the case study problem proposed by Masten and Cohen The underlying philosophy of our approach includes the integration of robust and adaptive control and the unification of continuous and discrete systems theory A feature of the examples presented below is that they have been run in real time using a general-purpose adaptive control toolbox
TL;DR: The fully two-dimensional self-tuning smoother and predictor derived in this paper represent an important generalization of the previous work which concerned prediction and filtering with arbitrary lead/lag on the current line.
Abstract: The paper describes new self-tuning algorithms for two-dimensional signal processing. Specifically, extended algorithms are developed for filtering, smoothing and prediction of two-dimensional data fields. These algorithms provide a transfer function approach to the problems of smoothing and prediction in two-dimensional space with arbitrary lag and lead. As such, the fully two-dimensional self-tuning smoother and predictor derived in this paper represent an important generalization of the previous work which concerned prediction and filtering with arbitrary lead/lag on the current line. The generalization is in two parts. The first concerns the formal extension of the theory. The second concerns the development of efficient algorithms for calculation of the extended predictors and filters, with special attention being paid to the approximations required in order to realize the algorithms.
TL;DR: In this article, the damping and stiffness properties of some flexible elements are parametrized linearly in μ−1 and μ−2 respectively, where μ > 0 and these components become more rigid as μ approaches zero.
Abstract: We consider a class of uncertain mechanical systems containing flexible elements and subject to memoryless output-feedback controllers. The damping and stiffness properties of some of the flexible elements are parametrized linearly in μ−1 and μ−2 respectively, where μ > 0 and these components become more rigid as μ approaches zero. We propose a class of ‘stabilizing’ controllers for a system model in which the above components are rigid. Subject to a ‘linear growth condition’, the controllers also stabilize the model in which the components are flexible provided μ > 0 is sufficiently small.
TL;DR: In this article, an adaptive controller based on this concept is developed and applied to the problem with good results, including selection of model structure, design parameters, and excitation features.
Abstract: The previous investigation showed the usefulness of a two-degree-of-freedom configuration. Such a controller can also be designed using pole placement. An adaptive controller based on this concept is developed and applied to the problem with good results. Particular features, such as selection of model structure, design parameters and excitation, are also discussed.
TL;DR: In this article, extended least squares (ELS) for ARMAX model identification of continuous-time and certain discrete-time systems were proposed, which have a relaxed strictly positive real (SPR) conditi...
Abstract: This paper proposes extended least-squares (ELS) for ARMAX model identification of continuous-time and certain discrete-time systems. The schemes have a relaxed strictly positive real (SPR) conditi ...
TL;DR: A new structure algorithm is given which makes possible the computation of the aforementioned distributions as well as the differential output rank of the considered system, which the authors must know for solving the DBDP.
Abstract: In this paper our aim is twofold. Firstly, we briefly recall the solution to the dynamic block-decoupling problem (DBDP) we presented at ‘NOLCOS 89’. This solution generalizes the approach taken for solving Morgan's problem, i.e. the row-by-row decoupling problem, by Descusse and Moog. The results we develop here are strongly connected with the structure algorithm of Hirschorn. Using the latter it is possible to exhibit particular (degenerate) controlled invariant distributions which appear to be crucial in the solution of the considered problem. The solution goes through an algorithmic procedure. Secondly, we give a new structure algorithm which makes possible the computation of the aforementioned distributions as well as the differential output rank of the considered system, which we must know for solving the DBDP. It is well known that the differential output rank, and more generally the structure at infinity, can be computed from the structure algorithm of Singh but not from the structure algorithm of Hirschorn. The former provides algebraic quantities (the structure at infinity) while the latter is mainly of interest for knowing geometric quantities (controlled invariant distributions). Our structure algorithm provides both features simultaneously.
TL;DR: In this paper, a non-linear adaptive filter is introduced and applied to the classical problem of estimating time-varying-parameter linear regression models with unknown error variances and a time varying transition matrix.
Abstract: A non-linear adaptive filter is introduced and applied to the classical problem of estimating time-varying-parameter linear regression models with unknown error variances and a time-varying transition matrix. The filter is basically a new result in what is known as Sridhar filtering theory. In deriving the filter, which we call the ‘Pontryagin filter’, the Pontryagin minimum principle and the method of invariant imbedding were used. The properties (bias and consistency) of the estimates of the time-varying parameters are then established.