Regeneratively-constrained LQG control of vibration networks with polytopic model uncertainty

This paper considers the use of a regenerative controller to achieve vibration suppression in an externally-excited vibratory network, characterized by a model with polytopic parameter uncertainty. A regenerative controller must satisfy the constraint that, on average, more energy is extracted from the network than injected. We consider the multi-objective LQG optimization of such a regenerative control law, which exhibits performance robustness over the polytopic uncertainty domain. It is shown that, although the presence of uncertainty makes the optimal control problem nonconvex, an efficient numerical algorithm can be used to arrive at an optimal controller. The algorithm makes use of convex over-bounding Linear Matrix Inequality (LMI) techniques. The concepts are demonstrated by an example pertaining to structural vibration suppression.