Robust distributed control for a class of continuum damage models

This paper derives robust control strategies based upon game theoretic principles for classes of continuum damage models encountered in active composite structures. In an earlier paper, it has been demonstrated that when a class of phenomenological power laws are employed to model damage evolution in composites, significant changes in microcrack density are predicted. The increase in microcrack density can have a profound effect on the dynamic response of the continuum, and in particular upon the constitutive parameters characterizing the continuum. This paper formulates a class of robust, distributed control laws in a Hilbert space setting. The work presented herein extends previous work by the authors in that the damage introduced by the power law model is represented as a structured perturbation that induces an unbounded disturbance influence operator. The convergence properties of the finite dimensional models representing the unbounded control influence operator are investigated. The theory presented in this paper is verified via numerical study of the performance of robust control designs for varying levels of distributed damage in beam and plate models