On the possible divergence of the projection algorithm

By means of an example, the authors show that the sequence of estimates generated by the projection algorithm does not always converge. The authors' construction shows that convergence is not automatically among the properties that can be derived without additional assumptions on the input sequenc

A design of a strongly stable generalized predictive control using coprime factorization approach

This paper proposes a new generalized predictive control (GPC) having new design parameters. In selecting the design parameters, the controller becomes a strongly stable GPC, that is, not only the closed-loop system is stable, but also the controller itself is stable. The parameters are introduced by applying the coprime factorization approach and comparing Youla parametrization of stabilizing compensators to the controller by the standard GPC</p

Adaptive poleplacement: the division by zero problem

We re-examine the division by zero problem which occurs in certainty equivalence based indirect adaptive control algorithms applied to linear systems. By exploiting a parametrization for linear systems induced by the continued fraction description of its transfer function, the division by zero problem obtains a very simple geometric representation that can be used to virtually eliminate the problem in the adaptive algorith

A new approach to state estimation in deterministic digital control systems

The paper presents a new approach to state estimation in deterministic digital control systems. The scheme is based on sampling the output of the plant at a high rate and prefiltering the discrete measurements in a multi-input/multi-output moving average (MA) process. The coefficient matrices in the MA prefilter are selected so the estimated state equals the true state. An example is presented which illustrates the procedure to follow to completely design the estimator

Prediction for control

5th IFAC Conference on System Structure and Control 1998 (SSC'98), Nantes, France, 8-10 JulyThis paper shows that "optimal" controllers based on "optimal" predictor structures are not "optimal" in their closed loop behaviour and that predictors should be designed taking into account closed-loop considerations. This is first illustrated with a first order plant with delay. The ISE index is computed for two typical optimal controllers (minimum variance controller and generalized predictive controller) when a stochastic disturbance is considered. The results are compared to those obtained by the use of a non optimal PI controller that uses a non optimal Smith predictor and performs better than the optimal controllers for the illustrative example. A general structure for predictors is proposed. In order to illustrate the results, some simulation examples are shown.Ce papier montre que des lois de commandes "optimales" basees sur des structures predictives "optimales" ne sont pas "optimales" dans leur comportement en boucle fermee et que la synthese de predicteurs devrait prendre en compte des considerations de boucle fermee. Cela est d'abord illustre avec un systeme du premier ordre a retard. l'index ISE est calcule pour deux lois de commandes optimales typiques (loi de commande a variance minim ale et loi de commande predictive generalisee), quand une perturbation stochastique est consideree. Les resultats sont compares a. ceux obtenus avec un regulateur PI non optimal base sur un predicteur de Smith non optimal et sont, pour l'exemple illustratif, meilleurs que ceux obtenus avec un regulateur optimal. Vne structure generale de predicteur est proposee. Pour illustrer les resultats, des exemples de simulations sont montres

Almost optimal adaptive LQ control: observed state case

In this paper we propose an almost optimal indirect adaptive controller for input/state dynamical systems. The control part of the adaptive scheme is based on a modified LQ control law: by adding a time varying gain to the certainty equivalent control law we avoid the conflict between identification and contro

Time-varying signal processing using multi-wavelet basis functions and a modified block least mean square algorithm

This paper introduces a novel parametric modeling and identification method for linear time-varying systems using a modified block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be used to track rapidly or even sharply varying processes and is more suitable for recursive estimation of process parameters by combining wavelet approximation theory with a modified block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstatinoary processes