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CivilComp Proceedings
ISSN 17593433 CCP: 93
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
Paper 206
Optimal Structural Control under Stochastic Uncertainty: Stochastic Optimal OpenLoop Feedback Control K. Marti
Aerospace Engineering and Technology, Federal Armed Forces University Munich, Neubiberg/Munich, Germany K. Marti, "Optimal Structural Control under Stochastic Uncertainty: Stochastic Optimal OpenLoop Feedback Control", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 206, 2010. doi:10.4203/ccp.93.206
Keywords: active structural control under stochastic uncertainty, optimal regulators, stochastic optimal openloop feedback control, stochastic Hamiltonian, Hminimum control, twopoint boundary value problems.
Summary
Active regulator strategies are considered [1] for stabilizing dynamic mechanical
structures under stochastic applied loadings. The problem is modeled in the framework of
stochastic optimal control for minimizing the expected total costs arising from the
displacements of the structure and the regulation costs. Due to the great advantages of
openloop feedback controls, stochastic optimal openloop feedback controls are
constructed by taking into account the random parameter variations in the stochastic
structural control problem. For finding first stochastic optimal openloop controls, on
the remaining time intervals t_{b}<=t<=t_{f} with
t_{0}<=t_{b}<=t_{f}, the
stochastic Hamilton function of the control problem is considered. Then, the class
of Hminimum controls can be determined by solving a finitedimensional stochastic
optimization problem [2] for minimizing the conditional expectation of the stochastic
Hamiltonian subject to the remaining deterministic control constraints at each time point
t. Having a Hminimum control, the related twopoint boundary value problem with
random parameters is formulated for the computation of the stochastic optimal state and
adjoint state trajectory. As a result of the linearquadratic structure of the underlying control
problem, the state and adjoint state trajectory can be determined analytically to a large
extent. Inserting then these trajectories into the Hminimum control, stochastic optimal
openloop controls are found on an arbitrary remaining time interval. These controls
then immediately yield a stochastic optimal openloop feedback control law.
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