State‐Feedback, Finite‐Horizon, Cost Density‐Shaping Control for the Linear Quadratic Gaussian Framework

A Multiple‐Cumulant Cost Density‐Shaping (MCCDS) control is proposed for the case when the system is linear and the cost is quadratic. This linear optimal control results from the minimization of an analytic, convex, non‐negative function of cost cumulants and target cost cumulants. The MCCDS control allows the designer to shape the initial cost density with respect to a target density approximated by target cost cumulants. A numerical experiment shows that MCCDS control compares favorably with competing control paradigms in terms of official performance measures for inter‐story drifts and per‐story accelerations used in the first‐generation structure benchmark for seismically excited buildings.