Maximum Entropy Stochastic Approach to Control Design for Uncertain Structural Systems

This paper applies the minimum data/maximum entropy modelling approach to the mean-square optimal control of flexible mechanical systems having a priori uncertainties in the structural elastic operator. With appropriate choice of the state variables, these uncertainties may be modelled as random skew-hermitian perturbations of the system dynamics map. After formulating the maximum entropy stochastic model for such a system we consider the specific problem of mean-square optimal, full-state feedback regulation. Various properties of the resulting stochastic Riccati equation are investigated. In particular it is shown that for sufficiently large levels of modelled uncertainty, the mean-square optimal design under the maximum entropy model directly produces an inherently robust rate-feedback control. Moreover, the burden of design computations is shown to be dictated by the number of "well-known" or "coherent" modes, and the maximum entropy approach is seen to be particularly suited to the treatment of large order systems.