M. B. Zarrop

On a general concept of forgetting

Practice leads us to seek a simple method which would make parameter estimation (and subsequent control or signal processing) reliably adaptive. Unfortunately, in most applications we lack sufficient information to specify a complete model of parameter variations. In other words, the problem is ‘under-determined’ which prevents us from employing standard equations of probability calculus. In this paper we apply known principles of rational behaviour in such situations to propose a plausible and well justified solution. The result we get is close to classical exponential forgetting, but regularized by available prior information. We demonstrate the practical implications of this feature.

Input design for detection of abrupt changes in dynamical systems

The detection and diagnosis of changes in stationary dynamical systems via statistical methods and using input design to improve detection performance are discussed. A cumulative sum test to detect a change towards one of several hypotheses is obtained by exploiting connections with the sequential probability ratio test. For input design, the objectives are taken to be to decrease the detection time and, at the same time, to ensure a tolerable false alarm rate. Both off-line auxiliary inputs and on-line generation of the input signal by a linear output feedback are considered. The problem is first introduced for the two-hypotheses case and then the design techniques are extended to the general multiple-hypotheses case.

Generalized pole-placement self-tuning controller Part 1, Basic algorithm

Abstract A new type of self-tuning pole-placement controller is proposed based on multi-step cost function minimization and using single-input single-output models of the controlled autoregressive moving average form. The generalized pole-placement (GPP) algorithm has advantages over standard pole-placement self-tuners in having a set of tuning knobs for improving transient response and overall control performance. The GPP is particularly suitable for programmed control in which future set-point values are known.

On optimality and time consistency when expectations are rational

Abstract This paper explores the implications of time inconsistency for optimal economic policy-making. It is found that if policy-makers determine policy on the assumption that expectations are adaptive when in fact they are rational economic policy can be destabilising. This adds support to reservations which Kydland and Prescott (1977) have raised about the appropriateness of standard optimal control methods. A method is proposed which is a modification of standard optimal control techniques and which allows for the endogeneity of expectations. When this method is used to determine policy there is no indication that policy is destabilising.

A suboptimal dual controller for stochastic systems with unknown parameters

In this paper a simple suboptimal dual controller is proposed which brings together Clarke and Gawthrops (1975) self-tuning controller framework and a generalization of Militos (Milito el at. 1982) innovations dual controller for a class of linear single-input single-output stochastic systems with unknown parameters. A cost function which includes the variances of both an auxiliary output and its prediction error is used to optimize the system performance. The latter variance term forces the controller to gather information to enhance parameter estimation and thus to indirectly improve control performance. Consequently the dual property inherent in optimal stochastic control is embedded in the structure of the suboptimal controller. Various interpretations and properties of the new algorithm are discussed. Comparative performances of the generalized minimum variance self-tuning controller and the suboptimal dual controller when applied to various simulated stochastic systems are examined. The. improveme...

Reduced-variance pole-assignment self-tuning regulation

Abstract In this paper the standard explicit self-tuning pole-assignment regulator is generalized to allow the output and/or input variances to be reduced. This is achieved by a suitable overparametrization of the controller polynomials allowing scope for optimization. In the regular case, simulation results indicate that the self-tuning property remains valid, and this is proved in a particular case. A reduced-variance servo controller is briefly discussed. The algorithms can give significant reductions in variance for little extra computational effort.

Brief paper: Variable forgetting factors in parameter estimation

This paper is concerned with the influence of forgetting factors on the consistency of prediction error methods of identification. Based on Ljungs analysis of the off-line case, it is shown that the use of forgetting factors can give rise to identifiability problems, unless the behaviour of these factors over time satisfied certain conditions. The main theorem covers the cases when the factors are deterministic functions of time or calculated via an adaptive mechanism.

Globally convergent adaptive pole assignment for a class of non-minimum-phase stochastic systems

A key difficulty of the explicit approach to self-tuning control—both theoretically and computationally—is the need to solve a polynomial identity to generate the required controller coefficients. For systems with uncorrelated output noise, however, the identity has a simple solution, and in this paper the implications of this phenomenon are discussed in relation to self-tuning regulation. A suitable explicit algorithm is introduced, and it is shown that, under certain conditions, global stability and system identifiability can be established without recourse to sophisticated estimator management techniques.

Variance calculations for two-dimensional ARMA processes

This technical note describes a method for computing the exact numerical value of the variance of a two-dimensional (2–D) ARMA process. Such calculations are useful in connection with current work on 2–D smoothers and predictors. Comparison is made of various methods of variance calculation using both 1–D and 2–D models.

Control Exercises with a Small Linear Model of the UK Economy

The use of the methods of optimal control in the formulation of economic policies has been demonstrated in Bray (1975) and Wall and Westcott (1975), as well as in countless other papers. The results reported here are in the same vein as the Bray and Wall and Westcott papers with a linear model, a quadratic objective function and gaussian stochastic disturbances. Rather, however, than go over ground that has already been covered we will focus in this paper on some less central aspects of the control framework. This will provide a complementary study to some more recent work reported in Rustem et al. and Zarrop et al. (Chapters 6 and 10 of this volume).