Reliability-Based Approach to Linear Covariance Control Design
Publication: Journal of Engineering Mechanics
Volume 124, Issue 2
Abstract
An extension to classical covariance control methods introduced by Skelton and coworkers, is proposed specifically for application to the control of civil engineering structures subjected to random dynamic excitations. The covariance structure of the system is developed directly from specification of its reliability via the assumption of independent (Poisson) outcrossings of its stationary response process from a polyhedral safe region. This leads to a set of state covariance controllers, each of which guarantees that the closed-loop system will possess the specified level of reliability. Several example problems are considered.
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References
1.
Belyaev, Y. K.(1968). “On the number of exits across the boundary of a region by a vector stochastic process.”Theory of Probability Applications, 13, 320–324.
2.
Chung, L., Reinhorn, A., and Soong, T.(1988). “Experiments on active control of seismic structures.”J. Engrg. Mech., ASCE, 114(2), 241–256.
3.
Cramér, H.(1966). “On the intersections between the trajectories of a normal stationary stochastic process and a high level.”Arkiv. Mat., 6, 337.
4.
Ditlevsen, O.(1983). “Gaussian outcrossings from safe convex polyhedrons.”J. Engrg. Mech., ASCE, 109(1), 127–148.
5.
Grace, A. (1992). MATLAB;rm optimization toolbox. The MathWorks, Inc., Natick, Mass.
6.
Hotz, A., and Skelton, R. (1985). “A covariance control theory.”Proc., 24th Conf. on Decision and Control, IEEE, Ft. Lauderdale, Fla., 552–557.
7.
Kaspari, D. Jr., Spencer, B. Jr., and Sain, M. (1995). “Optimal structural control: a reliability-based approach.”Proc., 1995 ASME Des. Engrg. Tech. Conf., 15th Biennial Conf. on Mech. Vibration and Noise, ASME DE-8401, ASME, New York, N.Y., 855–862.
8.
Meirovitch, L. (1990). Dynamics and control of structures. John Wiley & Sons, Inc., New York, N.Y.
9.
Rice, S.(1944). “Mathematical analysis of random noise.”Bell Sys. Tech. J., 23, 282–332.
10.
Rice, S.(1945). “Mathematical analysis of random noice.”Bell Sys. Tech. J., 24, 46–156.
11.
Skelton, R., and Ikeda, M.(1989). “Covariance controllers for linear continuous-time systems.”Int. J. Control, 49(5), 1773–1785.
12.
Skelton, R., Iwasaki, T., and Grigoriadis, K. (1995). A unified algebraic approach to linear control design, preprint.
13.
Soong, T., and Grigoriu, M. (1993). Random vibration of mechanical and structural systems. Prentice-Hall, Inc., Englewood Cliffs, N.J.
14.
Spencer, B. Jr., Kaspari, D. Jr., and Sain, M. (1994a). “Structural control design: a reliability-based approach.”Proc., of the Am. Control Conf., Baltimore, Md., 1062–1066.
15.
Spencer, B. Jr., Kaspari, K. Jr., and Sain, M. (1994b). “Reliability based active structural control.”Proc., 5th U.S. Nat. Conf. on Earthquake Engrg., Chicago, Il., 703–712.
16.
Veneziano, D., Grigoriu, M., and Cornell, C.(1977). “Vector-process models for system reliability.”J. Engrg. Mech., ASCE, 103(3), 441–460.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 124 • Issue 2 • February 1998
Pages: 193 - 199
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Feb 1, 1998
Published in print: Feb 1998
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