Reliability-based Performance Objectives and Probabilistic Model Uncertainty in Optimal Structural Control Applications

Abstract

A reliability-based structural control design approach is presented, which optimizes a control system explicitly to minimize the probability of structural failure. Here, failure is interpreted as the probability that the system state trajectory will exit a safe region, inside a given time duration. This safe region is bounded by hyperplanes in the system state space, each of which corresponds to an important dynamic response variable. The failure threshold for each of these response variables is designated as a bound on acceptable performance. Thus defined, an accurate analytical approximation for the probability of failure, and for its optimization through feedback control, are discussed. Versions of the approach are described for the case with no model uncertainty as well as for the case with uncertain model parameters. For the case with uncertain parameters it is reasonable to assume that, in most engineering applications, there will be a considerable knowledge about the relative likelihood of the different possible values of these parameters. This information is quantified through the use of probability distributions on the uncertain parameter space. The standard tools for design of feedback controllers which are robust to model uncertainty, such as Hoo and miou-synthesis, do not account for such probabilistic information.Examples are presented which apply the above ideas to a simple active structural control system. The influence of model uncertainty in the optimization process and the advantages of adopting a probabilistic uncertainty approach are discussed.