摘要:

In this paper we develop an algebraic approach to the multiple time scale analysis of perturbed linear systems based on the examination of the Smith form of the system matrix viewed as a matrix over a ring of functions in the perturbation parameter. This perspective allows us to obtain a strengthened version of the results of Coderchet al. (1983) and to provide a bridge between these complex but general results and previous explicit, conceptually simple, but somewhat restrictive results such as those described by Kokotovic (1981) and Chow (1982). In addition, our algebraic framework allows us to investigate a variety of other problems. In this paper we study the problem of developing valid time scale decompositions in cases in which weak damping terms discarded in the approaches of Kokotovic (1981), Chow (1982) and Coderchet al. (1983) must be retained. Also, our approach exposes the role of the invariant factors of the system matrix in determining its time scales. This leads naturally to the problem of time scale modification (i.e. invariant factor placement) via state feedback. We present a result along these lines.

ISSN:0020-7179    

DOI:10.1080/00207178808906011

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A prediction-error estimation algorithm is developed for non-linear discrete-time systems which can be represented by the output-affine difference equation model. The theory of hypothesis testing is employed to select a model with the correct structure. Problems relating to the use of output-affine models in the identification of non-linear systems are discussed, and a comparison with the NARMAX (nonlinear ARMAX) model is given.

ISSN:0020-7179    

DOI:10.1080/00207178808906012

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Luenberger observer theory is extended to distributed parameter systems. This extension is based on the consideration of sensors. For systems with infinite dimensional state spaces, it is possible to construct the state vector asymptotically (or a part of the state vector) by a ‘good’ choice of sensors. We show that the link between detectability and sensor structure may be of some interest in the construction of observers.

ISSN:0020-7179    

DOI:10.1080/00207178808906013

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The paper presents a discussion on the problem of the robust real-time identification of linear multivariable time-varying dynamic systems working in a noisy environment. Two methodologically different approaches to the design of such algorithms are presented. The first is based on the one-step estimation, optimal in the sense of the minimal conditional mean-square error, combined with convenient approximations of the underlying error covariance matrix. The second is based on the general formulation of robustified stochastic approximation algorithms, characterized by a suitable non-linear transformation of normalized residuals. Particular algorithms are derived on the basis of step-by-step optimization with respect to the weighting matrix of the algorithm. Monte Carlo simulation results illustrate the discussion, and show the efficiency of the proposed robust algorithms in the presence of large disturbance realizations, the so-called outliers.

ISSN:0020-7179    

DOI:10.1080/00207178808906014

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Linear quadratic state feedback regulators make the resulting closed-loop systems stable enough, i.e. they realize robust stabilization. Many attempts at robust stabilization using linear quadratic regulators have been reported. One of the major trends of formulating uncertainty in systems is to express perturbed parameters as the sum of two terms, i.e. nominal values and the deviation from them. In this paper, it is assumed that the upper and lower bounds for each uncertain parameter can somehow be estimated. This enables us to dispense with nominal values. The main aim is to contrive a robust feedback stabilization law for systems with parameters falling into certain ranges via a linear quadratic regulator based only upon information on their bounds. The systems under consideration are therefore those having interval system matrices (in which each element has the above-mentioned two-sided bounds). A certain feedback law is a stabilizing law for a system with an interval system matrix if and only if the same feedback law remains so for systems with system matrices whose entries are all possible combinations of the endpoints of their variation range.

ISSN:0020-7179    

DOI:10.1080/00207178808906015

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

This paper is mainly concerned with the derivation of the necessary conditions, called the ‘generalized maximum principle’, for the optimal control of generalized state-space systems with a more general form. By making use of a method of the modern calculus of variations which has been used for the proof of Pontryagin's maximum principle, the generalized maximum principle is derived, and some problems related to this principle are discussed in detail. In addition, an illustrative example is given in the light of this principle.

ISSN:0020-7179    

DOI:10.1080/00207178808906016

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A result of the ‘law of large numbers’ type is obtained for the cost of tracking a discrete almost-periodic signal when the deterministic optimal feedback law is used in the presence of independent random perturbations.

ISSN:0020-7179    

DOI:10.1080/00207178808906017

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A very general control problem is solved in the context of the geometric approach to linear multivariable control theory. The problem to be considered is general in the sense that it contains as a special case not only the well-known disturbance decoupling problem by measurement feedback (Schumacher 1981) and the problem of stabilizing the output with respect to disturbances by means of state feedback (Hautus 1970), but also, for instance, the extension of the latter problem to the situation in which only the use of measurement feedback is allowed. Furthermore, connections with and extensions of recent work by Trentelman ( 1986) are given and fruitful use is made of a synthesis of concepts arising from the geometric and the frequency domain approaches to control theory.

ISSN:0020-7179    

DOI:10.1080/00207178808906018

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor