Reliability-Based Performance Objectives and Probabilistic Robustness in Structural Control Applications

A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the probability of structural failure. Failure is interpreted as the system's state trajectory exiting a safe region within a given time duration. This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters. For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to H_2 i.e., minimum variance controller synthesis is also examined.