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State-feedback, finite-horizon, cost density-shaping control for the linear quadratic Gaussian framework. (English) Zbl 1223.93123
Summary: A Multiple-Cumulant Cost Density-Shaping (MCCDS) control is proposed for the case when the system is linear and the cost is quadratic. This 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.

93E20Optimal stochastic control (systems)
49L20Dynamic programming method (infinite-dimensional problems)
86A17Global dynamics, earthquake problems
49N10Linear-quadratic optimal control problems
Full Text: DOI
[1] Zyskowski, M.J., Sain, M.K., Diersing, R.W.: Maximum Bhattacharyya coefficient, cost density-shaping: a new cumulant-based control paradigm with applications to seismic protection. In: 5th World Conference on Structural Control and Monitoring, 5WCSCM-10402 (2010)
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[9] Zyskowski, M.J.: Cost density-shaping for stochastic optimal control. Ph.D. thesis, University of Notre Dame (2010)
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