Probabilistic Approach for Integrated Structural Control Design

Introduction D URING the development phase of a new engineering project, the design requirements and the project variables are usually deŽ ned in a deterministic sense, and, for robustnessconsiderations, the uncertaintyof the parameters is consideredto occur around their design value by means of simpliŽ ed models. SufŽ cient conditions must then be satisŽ ed to achieve conŽ dence in the quality of the Ž nal design.To meet the requirementconstraints, a control strategy can be integrated within the structural design process so that the design of the structure and that of the control system are developed in parallel. The use of a classical robust control system design may be properly employed in the case where the problem at hand is convex and sufŽ cient conditions can be met. In this case, however, the real distribution of the random variables involved in the design is not considered. As an alternative,we suggestconsideringthe problemof integrating thecontroland structuredesignwithin an appropriateprobabilistic framework in order to take into account, with a high degree of accuracy, the project constraints and the system uncertainties.This approach implies the possibilityof modeling the design parameters as randomvariables in order to guarantee that a given probabilityof satisfying the design requirementsmay be obtained. In many cases, the design through probabilistic constraints is performed with the hypothesis of normal distribution of the involved variables, even if this hypothesismay be too strong an assumption.A better model is possible using some theoretical results that were Ž rst obtained in the Ž eld of structural reliability in civil and offshore engineering. These results led to the deŽ nition of the so-calledclassicalstructural reliabilitymethodologies.These methodologies allow one to properly take into account the correct probability distribution function of the design variables and, due to an asymptotic approximation,to perform a set of highly informative evaluationswith a low computational cost. In this way, it is possible to avoid failures in the design strategy in the case of nonconvex problems and to apply an appropriate