zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.
MSC:
93E20Optimal stochastic control (systems)
49L20Dynamic programming method (infinite-dimensional problems)
86A17Global dynamics, earthquake problems
49N10Linear-quadratic optimal control problems
References:
[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)
[2]Mou, L., Liberty, S.R., Pham, K.D., Sain, M.K.: Linear cumulant control and its relationship to risk-sensitive control. In: Proceedings of the 38th Annual Allerton Conference on Communication, Control, and Computing, pp. 422–430 (2000)
[3]Pham, K.D., Sain, M.K., Liberty, S.R.: Cost cumulant control: state-feedback, finite-horizon paradigm with application to seismic protection. J. Optim. Theory Appl. 115(3), 685–710 (2002) · Zbl 1033.49037 · doi:10.1023/A:1021263416188
[4]Lin, J.J., Saito, N., Levine, R.A.: On approximation of the Kullback–Leibler information by Edgeworth expansion. Technical report, Dept. of Statistics, University of California-Davis (2001)
[5]Sain, M.K., Liberty, S.R.: Performance-measure densities for a class of LQG control systems. IEEE Trans. Autom. Control AC-16(5), 431–439 (1971) · doi:10.1109/TAC.1971.1099784
[6]Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, Berlin (1975)
[7]Liberty, S.R., Hartwig, R.C.: Design-performance-measure statistics for stochastic linear control systems. IEEE Trans. Autom. Control AC-23(6), 1085–1090 (1978) · Zbl 0389.93056 · doi:10.1109/TAC.1978.1101915
[8]Liberty, S.R., Hartwig, R.C.: On the essential quadratic nature of LQG control-performance measure cumulant. Inf. Control 32(3), 276–305 (1976) · Zbl 0341.93028 · doi:10.1016/S0019-9958(76)90264-3
[9]Zyskowski, M.J.: Cost density-shaping for stochastic optimal control. Ph.D. thesis, University of Notre Dame (2010)
[10]Spencer, B.F., Dyke, S., Deoskar, H.: Benchmark problems in structural control: Part I–Active mass driver system. Earthquake Eng. Struct. Dyn. 27, 1127–1139 (1998) · doi:10.1002/(SICI)1096-9845(1998110)27:11<1127::AID-EQE774>3.0.CO;2-F