First generation seismic-AMD benchmark: robust structural protection by the cost cumulant control paradigm

The topic of Risk Sensitive (RS) control is receiving substantial and continued research from the theoretical community oriented toward stochastic control theory. As yet, however, RS control design has not made a substantial entry into control applications. Moreover, its properties have not yet been compared in any detail with those of other paradigms for control thinking. If one regards the RS optimization criterion as a denumerable linear combination of cumulants, then it is seen as a very interesting case of control design based upon linear combinations of cumulants. In this guise, the problem class goes back to the mid-1960s, when linear combinations of the first two cost cumulants, mean cost and cost variance, were first studied. The present paper reports the application of cost-cumulant control, based upon the first three cumulants, to control of the Benchmark Structural Control Problem (http://www.nd.edu/~quake/) recently studied by numerous authors using a variety of control algorithms. Although it is definitely the novice in the competition, cost-cumulant control performs quite respectably, as the reader may judge from the tabular results included herein. Moreover, the present results involving the first three cost cumulants appear to be the first of their type to appear in the literature.