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Generalized risk sensitive building control: protecting civil structures with multiple cost cumulants

Risk-sensitive optimal stochastic control problems have an interpretation in terms of managing the value of a denumerable linear combination of the cumulants of a traditional performance index. Such an interpretation is particularly attractive in the context of physical control problems with a naturally occurring process which is well modelled in the stochastic sense. The extremely important case of civil structures assailed by earthquakes, wind, and seas is precisely such a problem. This paper considers a state-feedback solution to the LQG version of this problem class. The formulation is parametrized by the number k of cumulants chosen for design. A general solution of this k-cumulant problem, together with studies of its application to the SDOF system described by Chung et al. (1988), is the subject of this work.