17.1 Introduction

In order to analyze dynamical behavior of buildings, and to take into account soil-structure coupling, simple models have been introduced both for buildings (see [Filliatrault (1996)] for example) and soil-structure and foundation (see [Wolf (1994)] for example).

Translational cone and rotational cone models provide spring-dashpot mass models (see [Wolf (1994)]). Here we intend to introduce an extension of the model resulting from translational cone model for soil-foundation interaction: this extension includes elastoplastic terms. Such terms have been introduced in previous works ([Bastien (2000)], [Schatzman et. al. (1999)]) and have been described from experiments and identified via nonparametric models [Benedettini et. al. (1995)]. More general models are also considered. We are interested indeed in control procedure for such an extended model. Control procedures have already been extensively studied. In the literature, many papers are concerned with mechanical engineering or civil engineering applications of control. First results and applications involve linear modelling and different strategies of control based on minimization of quadratic energies (optimal, active, modal control etc. see [Filliatrault (1996)]). Recently, control strategies have been introduced for smooth non-linear systems [Zhu et. al. (2001)]. For further literature on the topic, see in [Housner et. al. (1997)] where a survey on structural control is given. In recent works, Yamada and Kobori [Yamada and Kobori (2001)] present a survey of strategies for a seismic structural control. In particular, they describe nonlinear velocity feedback laws. Many other recent references can be found in this paper. In [Wojtldewicz and...