Mario E. Salgado

Modified least squares algorithm incorporating exponential resetting and forgetting

In this paper we present the general analysis of a class of least squares algorithms with emphasis on their dynamic performance particularly in the presence of poor excitation. The analysis is carried out in a deterministic framework and stresses geometrical interpretations. The core of this paper is the proposal and analysis of a new algorithm which incorporates exponential forgetting and resetting to an unprejudiced treatment of data when excitation is poor. The algorithm is particularly suitable for tracking time-varying parameters and is similar in computational complexity to the standard recursive least squares algorithm. The superior performance of the algorithm is verified via simulation studies.

Potential benefits of hybrid control for linear time invariant plants

A question which has bothered control researchers for some time is whether hybrid control offers any advantage over linear control for linear plants. We show in this paper, via several examples, that hybrid control can indeed overcome certain types of limitation which are unavoidable if linear feedback control is used.

Performance limitations for linear feedback systems in the presence of plant uncertainty

The goal of this paper is to contribute to the understanding of fundamental performance limits for feedback control systems. In the literature to date on this topic, all available results assume that the designer has an exact model of the plant. Heuristically, however, one would expect that plant uncertainty should play a significant role in determining the best achievable performance. The goal of this paper is to investigate performance limitations for linear feedback control systems in the presence of plant uncertainty. We formulate the problem by utilizing stochastic embedding of the uncertainty. The results allow one to evaluate the best average performance in the presence of uncertainty. They also allow one to judge whether uncertainty or other properties, e.g., nonminimum phase behavior, are dominant limiting factors.

Quantification of Uncertainty in Estimation using an Embedding Principle

In this paper a new method to quantify uncertainty due to undermodelling is presented. The unmodelled dynamics are embedded in a general class of systems which is defined using realistic a priori information. This embedding principle can be formalized in several different ways; the one presented in this paper involves the setting of a stochastic framework, where the unmodelled dynamics are taken to be a particular realization of a Stochastic Embedding Process (S.E.P.) A priori knowledge is used to choose suitable statistics for this process. This approach allows one to quantify the effect of the modelling errors on the estimated transfer function in the frequency domain. The principal advantage of this approach is that it allows one to consider robust and adaptive control within the same conceptual framework.

UNCERTAINTY, INFORMATION AND ESTIMATION

Abstract This paper aims to explore the role played by uncertainty in control system design with particular emphasis on estimation and adaptation. It is argued that a key issue in design is the fidelity of the model. If the model is known to be a perfect description of the system, then optimal performance can be achieved. However, model uncertainty, disturbances and noise place fundamental limits on the achievable performance. Estimation can be viewed as a mechanism for reducing model uncertainty and thus as a way of improving performance. However, a crucial factor in this context is that the estimator should not only yield a nominal model, but also give a measure of confidence in that model. In this paper, we show how such a measure might be obtained and how this allows adaptation and robust design to be integrated into a unified design philosophy. This enables us to define more clearly the role of adaptation and provides a framework for developing future adaptive control systems for practical use.

Issues in Time Delay Modelling

Abstract This paper addresses the problem of time delay modelling using rational approximations. Two classes of models are discussed based on all-pole and all-pass transfer functions. A detailed analysis is carried out comparing the respective merits of these approximate models. The estimation of the parameters in these models is investigated and the associated control design problem using rational models for the delay is studied. Simulation results are presented which support the theoretical analysis