Showing papers in "International Journal of Adaptive Control and Signal Processing in 1992"

Unifying the landmark developments in optimal bounding ellipsoid identification

Abstract: : A quite general class of Optimal Bounding Ellipsoid (OBE) algorithms including all methods published to date, can be unified into a single framework called the Unified OBE (UOBE) algorithm. UOBE is based on generalized weighted recursive least squares in which very broad classes of 'forgetting factors' and data weights may be employed. Different instances of UOBE are distinguished by their weighting policies and the criteria used to determine their optimal values. A study of existing OBE algorithms, with a particular interest in the tradeoff between algorithm performance interpretability and convergence properties, is presented. Results suggest that an interpretable, converging UOBE algorithm will be found. In this context, a new UOBE technique, the set membership stochastic approximation (SM-SA) algorithm is introduced. SM-SA possesses interpretable optimization measures and known conditions under which its estimator will converge.

The method of recursive aim inequalities in adaptive control theory

Abstract: The method of recursive aim inequalities has been used in the theory of adaptive control since the late 1960s by a group of Leningrad mathematicians. The problem is reduced to an infinite system of recursive inequalities on the vectors of unknown parameters. These inequalities can be solved by using specially developed, finitely convergent algorithms. The method is illustrated by the solution of adaptive control problems for linear discrete systems under different assumptions on the plant and disturbances.

Adaptive regulation: Lyapunov design with a growth condition

Abstract: We propose a new Lyapunov design of an adaptive regulator under some restriction on the dependence of a Lyapunov function on the parameters. This restriction has been introduced by Praly et al. Its interest is to involve only a Lyapunov function and not explicitly the system non-linearities. We show it is satisfied by strict pure feedback systems with polynomial growth non-linearities and some other non-feedback linearizable systems. Our new Lyapunov design leads to an adaptive regulator where the adapted parameter vector is transformed before being used in the control law; namely, the so-called certainty equivalence principle is not applied. Unfortunately, the implementation of this regulator needs the explicit solution of a fixed point problem, so in a second stage we propose a more practical solution obtained by replacing the fixed point static equation by a dynamical system with this fixed point as equilibrium.

Preliminary results about robust lagrange stability in adaptive non-linear regulation

Abstract: We are concerned with the problem of regulating the equilibrium point of a non-linear system in the presence of both parametric and dynamic uncertainties. For the parametric uncertainty we propose a new adaptive controller based on a Lyapunov design and guaranteeing the global boundedness of the solution if a growth condition is satisfied. For the dynamic uncertainty we propose a new way of characterizing the unmodelled effects which encompasses some singular and regular perturbations as illustrated by our worked example. Finally we show how, by modifying the above controller, the boundedness property can be made robust to these unmodelled effects.

Identification of a class of dynamic errors-in-variables models

Abstract: Dynamic errors-in-variables (EV) models are a new type of linear system models and have found extensive practical applications. One common and important concern with EV models is how to remove noise-induced bias in parameter estimators. In this paper some significant extensions to the newly established bias-eliminated least-squares (BELS) method are made, so that this BELS method can be applied to unbiased identification of a general class of dynamic EV models where input noise is white noise and output noise is correlated noise but the noise statistics are unknown a priori. Though still based on the bias correction principle, this method is very meaningful in that it presents a novel and efficient way of utilizing signal-processing techniques to draw much more useful information from sampled data in order to get desirable identification results. The performance of the proposed method is illustrated by numerical examples.

A comparative study of normalized and unnormalized tuning errors in parameter adaptive control

Abstract: In the past year several advances in the development of adaptive control for non-linear systems have made it clear that algorithms not using error normalization have several significant advantages over algorithms which do, in spite of their much greater complexity. In this paper simple examples are used to give a detailed account of the essential differences in structure between adaptive algorithms of the normalized and unnormalized types. It is explained why only the latter readily generalize to non-linear process models with non-global Lipschitz non-linearities. It is shown that one of these algorithms is capable of stabilizing linear process models with different relative degrees.

Hybrid adaptive-robust control for a robot manipulator

Abstract: In this paper we present a hybrid adaptive-robust controller to achieve trajectory following for a robot manipulator. The controller consists of two parts: a proportional-derivative (PD) feedback loop and an adaptive-robust law for the manipulator dynamics. An advantage of this method is that our controller takes advantage of the manipulator dynamic structure to allow the designer to select a controller that is a combination of an adaptive approach and a robust-adaptive approach.

Robustness of VS‐MRAC with respect to unmodelled dynamics and external disturbances

Abstract: A variable structure model reference adaptive controller (VS-MRAC) using only input and output measurements was recently proposed and shown to be globally asymptotically stable with superior transient behaviour and disturbance rejection properties. In this paper a singular perturbation approach is used in order to establish the robustness of the controller in the presence of unmodelled dynamics (parasitics) and disturbances. We develop a new Lyapunov-based technique to analyse the overall system and show that for sufficiently small parasitics the system remains stable and the output error is small in some sense.

Adaptive observers for a class of multi‐output non‐linear systems

Abstract: Sufficient differential geometric conditions are given for the existence of global adaptive observers for a class of multi-output non-linear systems which are linear with respect to a vector of unknown constant parameters. They extend to multi-output systems earlier results on adaptive observers for single-output systems; they also extend to systems with unknown parameters results obtained previously on the existence of non-adaptive observers with linear error dynamics.

Speed gradient adaptive control algorithms for mechanical systems

Abstract: A number of recent and some new adaptive control algorithms for robot manipulators are considered from the viewpoint of the speed gradient method. Various types of algorithms are considered in a unified framework that allows useful comparisons to be made.

Adaptively controlling non-linear systems, using trajectory approximations

Abstract: The structure underlying most adaptive algorithms is a linear parametrized set. This set either represents the universe of controllers the adaptive algorithm can choose from in order to achieve the control task or it may represent a class of models the adaptive algorithm may exploit to approximate the open-loop plant behaviour. In the latter approach the controller used to close the loop is selected via some non-linear map of the identified model parameters. The emphasis is on approximating the vector field that generates the trajectories of the system. Alternatively we propose to predict the trajectories over a short period of time directly, not indirectly involving a representation of the underlying vector fields. The feasibility of such an approach using a one-step-ahead-type algorithm for both prediction and control is analysed. The scheme is hybrid in that the plant is continuous-time, whilst the control action is implemented in discrete time. The control action is of the model reference type. The algorithm is applied to a class of (non)-linear time-varying systems of a given structure (known relative degree) and possessing a stable inverse. Given input/output measurements only, the algorithm can enforce a desired response within guaranteed error bounds. Robustness properties with respect to partial state measurement (e.g. neglecting parasitic dynamics) and violation of the stable inverse assumption are investigated.

Enhancing optimal controllers via techniques from robust and adaptive control

Abstract: Optimal control strategies for both non-linear and linear plants and indices are notoriously sensitive to modelling errors and external noise disturbances. In this paper a general framework to enhance robustness of an optimal control law is presented, with emphasis on the non-linear case. The framework allows a blending of off-line non-linear optimal control, on-line linear robust feedback control for regulation about the optimal trajectory and on-line adaptive techniques to enhance performance/robustness. The adaptive-Q techniques are those developed in previous work based on the Youla-Kucera parametrization for the class of all stabilizing two-degree-of-freedom controllers. Some general fundamental stability properties are developed which are new, at least for the non-linear plant and linear robust controller case. Also, performance enhancement results in the presence of unmodelled linear dynamics based on an averaging analysis are reviewed. A convergence analysis based on averaging theory appears possible in principle for any specific non-linear system but is beyond the scope of the present paper. Certain model reference adaptive control algorithms come out as special cases. A non-linear optimal control problem is studied to illustrate the efficacy of the techniques, and the possibility of further performance enhancement based on functional learning is noted.

Error‐based adaptive non‐linear control and regions of feasibility

Abstract: The nonlinear adaptive algorithm of Kanellakopoulos et al. (1991) was modified to produce an error-based algorithm. This permits global stabilizability for a large subset of pure-feedback nonlinear systems. The algorithm was demonstrated on the single-input stabilization problem, but extends easily to the multiple input tracking problems.

Frequency-filtering zoom

Abstract: Spectral component discrimination and the estimation of one or more signal frequencies are classical problems in signal processing. The purpose here is to study a new technique intended to increase the frequency resolution, called frequency-filtering zoom (FFZ). The advantage of the method is that it gives a faithful reproduction of the amplitude and phase spectra of signals, in contrast to existing methods which need a phase correction. Moreover, our zoom has been designed to enable software real-time analysis of low-frequency signals.

On adaptive control of fedbatch fermentation processes

Abstract: This paper presents an experimental evaluation of the partial state reference model adaptive control approach proposed by M'Saad et al. The plant to be controlled is a fedbatch fermentation process of alcohol production. Experimental results are presented to demonstrate the performances of the adaptive controller considered. Particular emphasis is placed on the choice of the predictor dynamics and the initialization of the parameter estimator

Adaptive control of siso plants with unmodelled dynamics

Abstract: In this paper we pursue a twofold aim. First we want to simplify the complexity of the classical Monopoli's scheme, the so-called ‘Augmented error signal control scheme’. Then we also wish to cope with the realistic situation in which the presence of unmodelled dynamics has to be taken into account. This latter problem has been faced in the literature by suitably modifying the adaptation mechanism in order to avoid undesired phenomena as well as to obtain an attractive stability region for the state trajectories starting from any point in a predefined initial condition set. In our case the necessity of introducing any sort of modification in the adaptation mechanism is completely avoided, but we still obtain asymptotic stability of the output error signal.

Adaptive control of non-completely controlled mechanical systems using dynamic feedback linearization and estimation design

Abstract: We propose here an indirect adaptive scheme for a class of non-completely controlled mechanical systems comprising a classical manipulator terminated by a simple pendulum. In the case of known parameters a dynamic state feedback produces full linearization. An adaptive version is obtained by a simple estimation method together with a certainty equivalence law. Global stability is proved without growth conditions. Simulation results for an overhead crane are given.

Adaptive non-linear control of fed-batch stirred tank reactors

Abstract: Chemical and biological fed-batch stirred tank reactors (FSTRs) are often good candidates for the application of adaptive non-linear control techniques because in many cases their dynamical models include highly uncertain kinetic parameters. A general unified methodology for the design of adaptive on-linear controllers for FSTRs is presented. The conditions under which this control approach helps to solve process optimization problems are emphasized.

Effective identification algorithms for adaptive control

Abstract: Minimum variance adaptive control schemes are considered. By means of the concept of excitation subspace, the notion of effective identification algorithm is introduced. It is shown that, if the system to be controlled is noise-free and minimum phase, the tracking error tends to zero provided that the identification is effective. Finally, the effectiveness of the most popular recursive identification techniques (recursive least squares, stochastic gradient, projection algorithm) is discussed.

Model reference adaptive control applied to electrical machines

Abstract: This contribution reports about a discrete-time robust adaptive control strategy for single-input/single-output systems with arbitrary zeros. The adaptive algorithm is mainly based on a direct model reference method. The basic idea presented here is to divide the feedback law into a direct adaptive and a fixed part. By a certain choice of the non-adaptive controller parameters the robustness of the adaptive control loop with respect to unmodelled dynamics of the plant may be increased. The non-adaptive part of the controller can be reformulated as a bypass to the plant and will be denoted as the ‘correction network’ owing to its action on the open-loop zeros of the augmented plant. The new adaptive control strategy removes the major drawbacks of model reference control and is investigated for speed control of a DC motor and voltage control of a synchronous generator.

Adaptive control of a biped robot walking across a horizontal plane

Abstract: The problem of biped robot walk control is considered. Intertial robot parameters are assumed unknown and control actions are applied only twice during one step. For adaptation the recurrent aim inequalities method is used. The control algorithm is designed and theoretically justified. Computer simulation results are presented.

A discussion of model accuracy in system identification

Abstract: Model quality and model accuracy are of prime interest in system identification. In this contribution we will review and discuss these concepts. In particular we will split model errors into contributions from a ‘random error’ and a ‘bias error’ and describe and discuss how to assess these two concepts.

Adaptive non-linear control with incomplete state information

Abstract: Motivated by several recent adaptive non-linear control results which use either full-state or single-output feedback, we present two new adaptive design tools and show how they can be used to construct systematic design procedures for non-linear systems with incomplete state information. The main features of these procedures are illustrated on a simple third-order system. We also provide the geometric conditions which give a co-ordinate-free characterization of one of the partial-state-feedback forms to which these procedures are applicable.

Functional learning in signal processing via least squares

Abstract: This paper addresses certain functional learning tasks in signal processing using familiar algorithms and analytical tools of least squares for autoregressive moving average exogenous input (ARMAX) models, the models can be viewed as conventional ARMAX models but with parameters dependent on variables such as inputs or states, termed function input variables. The functional dependence of the parameters on these variables is represented in terms of basis function expansions or, more generally, interpolation function representations. The interpolation functions in a least-squares identification of coefficients also turn out to be in essence spread functions that spread learning throughout the space of function input variables. Thus for a set of training sequences or trajectories in function input space, system parameters and thereby system functionals can be updated. The idea is that these will have relevance for similar sequences or neighbouring trajectories. The concept of persistence of excitation to achieve complete function learning or, equivalently, signal model learning is studied using least-squares convergence results. Application of the proposed algorithms and theory within the signal-processing context is addressed by means of simple illustrative examples.

A new robust model reference control with improved performance for a class of multivariable unknown plants

Abstract: Motivated by recent works on parametrization of multivariable plants for model reference adaptive control (MRAC), a new robust model reference control (MRC) scheme for a class of multivariable unknown plants is presented. The salient feature of this control scheme is the improved performance of the output-tracking property, which is hardly attainable by the traditional MRAC schemes. The controller here is devised using the concept of variable structure design which prevails in the robust control context. It is shown by a Lyapunov approach that without any persistent excitation the global stability of the overall system is achieved and the tracking errors will converge to a residual set. The size of that set can be directly related to the size of unmodelled dynamics and output disturbances explicitly as long as a set of control parameters is chosen properly (large).

Evolution of intelligent control in adaptive systems

Abstract: The evolution of adaptive control systems is considered from the viewpoint of the use of informatics and artificial intelligence (AI) tools. Some general principles of intellectronics (AI tools) are discussed taking into consideration adaptive control systems with non-linear dynamics operating under conditions of uncertainty. The principles are illustrated by an analytical review of adaptive-intelligent robot control and logical-probabilistic decision rules as applied to expert systems of adaptive control. Example of the use of intellectronics in adaptive systems are given.