Nonlinear stochastic optimal control strategy of hysteretic structures

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

[1]  M. Shefer,et al.  Estimation and control with cubic nonlinearities , 1983, 1983 American Control Conference.

[2]  Fereidoun Amini,et al.  Optimal structural active control force, number and placement of controllers , 2005 .

[3]  Mohammad Noori,et al.  Random Vibration of Degrading, Pinching Systems , 1985 .

[4]  James T. P. Yao,et al.  CONCEPT OF STRUCTURAL CONTROL , 1972 .

[5]  H. Zhang,et al.  Parameter Analysis of the Differential Model of Hysteresis , 2004 .

[6]  Jianbing Chen,et al.  Dynamic response and reliability analysis of non-linear stochastic structures , 2005 .

[7]  R. Clough.  Effect of stiffness degradation on earthquake ductility requirements , 1966 .

[8]  Thomas T. Baber,et al.  Random Vibration Hysteretic, Degrading Systems , 1981 .

[9]  D. Bernstein.  Nonquadratic cost and nonlinear feedback control , 1993 .

[10]  Yongbo Peng,et al.  Probabilistic criteria of structural stochastic optimal controls , 2011 .

[11]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[12]  M. Sain,et al.  Non-linear optimal control of a Duffing system , 1992 .

[13]  Yongbo Peng,et al.  A physical approach to structural stochastic optimal controls , 2010 .

[14]  Jintai Chung,et al.  A new family of explicit time integration methods for linear and non‐linear structural dynamics , 1994 .

[15]  Zexiang Li,et al.  Aseismic hybrid control of nonlinear and hysteretic structures. II , 1992 .

[16]  Anil K. Agrawal,et al.  OPTIMAL POLYNOMIAL CONTROL FOR SEISMICALLY EXCITED NON‐LINEAR AND HYSTERETIC STRUCTURES , 1996 .

[17]  Greg Foliente,et al.  Hysteresis Modeling of Wood Joints and Structural Systems , 1995 .

[18]  Zexiang Li,et al.  Stochastic hybrid control of hysteretic structures , 1994 .

[19]  Weiqing Liu,et al.  Stochastic Seismic Response and Reliability Analysis of Base-Isolated Structures , 2007 .

[20]  R. Bouc.  Forced Vibration of Mechanical Systems with Hysteresis , 1967 .

[21]  Om P. Malik,et al.  Optimization technique for the design of a linear optimal power system stabilizer , 1992 .

[22]  Yi-Qing Ni,et al.  OPTIMAL NONLINEAR STOCHASTIC CONTROL OF HYSTERETIC SYSTEMS , 2000 .

[23]  Jianbing Chen,et al.  Strategy for selecting representative points via tangent spheres in the probability density evolution method , 2008 .

[24]  Michael S. Eldred,et al.  DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's reference manual. , 2010 .