The third generation wind structural benchmark: a Nash cumulant robust approach

The use of cost-cumulant-based controllers to mitigate vibrations, caused in civil engineering structures by winds and seismic events, has led to performances [Pham, K. D., et al., June 30, 2004], [Pham, K. D., et al., April 2004], [Pham, K. D., et al., Dec. 2004], [Pham, K. D., et al., Sept. 2004], [Pham, K. D., et al., May 2002], [Pham, K. D., et al., May 2004], [Sain, M. K., et al., 2000], [Won, C. H., et al., July 1994] which compare well with other control paradigms, when applied to civil engineering benchmarks. In this paper, we extend the cost-cumulant control concept to include a provision for explicit consideration of robustness considerations. Structured uncertainty is associated with one player, while control is associated with another player. Each of the players has a distinct cost, which has cumulants generated by a wind or earthquake process. Design is carried out by a Nash-type algorithm. The method is applied to the third generation wind structural benchmark, and it seems to be a natural fit for the civil engineering applications which entail both environmental disturbances and modelling errors.