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| Generalized density evolution equation based structural stochastic optimal control |
| Received:December 22, 2008 Revised:November 06, 2009 |
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| DOI：10.7511/jslx20106004 |
| KeyWord:general density evolution equation Pontryagin’s maximum principles LQG control weighting matrices choices structural performance |
| Author | Institution |
| 李杰 |
同济大学 土木工程学院,上海 |
| 彭勇波 |
同济大学 土木工程学院,上海 ;同济大学上海防灾救灾研究所,上海 |
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| Abstract: |
| The celebrated Pontryagin’s maximum principles is employed in this paper to conduct the physical solutions of the state vector and the control force vector of stochastic optimal controls of closed-loop systems by synthesizing deterministic optimal control solutions of a collection of representative excitation driven systems using the generalized density evolution equation. The optimal control scheme extends the classical stochastic optimal control methods, which is practically useful to general nonlinear systems driven by non-stationary and non-Gaussian stochastic processes, and can govern the evolution details of stochastic dynamical systems, while the classical stochastic optimal control methods, such as the LQG control, essentially hold the system statistics, and cannot govern the desirable evolution details. Further, the selection strategy of weighting matrices of stochastic optimal controls is discussed to construct optimal control policies based on the control criterion of system second-order statistics assessment. The stochastic optimal control of an active tendon control system, subjected to the random ground motion represented by the physical stochastic earthquake model is investigated. Numerical investigations reveal that the structural seismic performance is significantly improved when the optimal control strategy is applied. The LQG control, however, using the nominal Gaussian white noise as the external excitation cannot design the reasonable control system for civil engineering structures. It is indicated that the developed physical stochastic optimal control methodology has the validity and applicability. |
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