Optimal Regulation of Structural Systems with Uncertain Parameters

摘要

Difficulties arising from inherent inaccuracies in structural modelling and from the high dimensionality of the dynamical system force a re-examination of the problem of optimal control of large flexible structures within the context of stochastic system theory. This work specifically addresses the mean-square optimal control of a linear mechanical system with random open-loop modal frequencies. Recognizing that a complete probabilistic description of modal parameters can never be provided, we first identify the minimum set of a-priori data needed to preserve any measure of modelling fidelity. Acknowledging this data as available, a complete probability assignment is then induced by a maximum entropy principle. The resulting mean-square optimization problem is consequently reduced to the solution of a modified Riccati equation. Various properties of this equation are explored. In particular, it is shown that the proposed approach guarantees stochastic stability, directly produces inherently robust controls for highly uncertain systems and significantly reduces the burden of design computation. (Author)