Title :
Application of pseudospectral method in stochastic optimal control of nonlinear structural systems
Author :
Wei Song ; Dyke, S.J.
Author_Institution :
Sch. of Civil Eng., Purdue Univ., West Lafayette, IN, USA
fDate :
June 29 2011-July 1 2011
Abstract :
This paper presents the results of numerical study on the optimal control strategy of nonlinear stochastic systems. The systems under investigation are mechanical oscillators and a damping device. The numerical approach to obtain the optimal control strategy involves solving a nonlinear partial differential equation - the Hamilton-Jacobi-Bellman equation. Since civil engineering structural systems usually exhibit nonlinear hysteretic behavior under extreme loading conditions, the potential application of the obtained control strategy could provide an optimal feedback control law to reduce the system response under the random excitations (such as earthquakes, wind load and sea waves). Several numerical examples are presented to verify optimality and demonstrate the efficacy of the proposed optimal control solution. First, a linear oscillator is used to verify that the obtained solution is indeed the optimal solution by comparing it to the closed form solution. Then the proposed method is applied to several nonlinear systems. In each case, optimality is demonstrated by comparing the system responses and costs under optimal control with those obtained using linearized optimal control.
Keywords :
feedback; nonlinear control systems; nonlinear differential equations; optimal control; partial differential equations; stochastic systems; structural engineering; Hamilton-Jacobi-Bellman equation; civil engineering structural systems; damping device; mechanical oscillators; nonlinear hysteretic behavior; nonlinear partial differential equation; nonlinear stochastic systems; nonlinear structural systems; optimal feedback control; pseudospectral method; stochastic optimal control; Equations; Indexes; Manifolds; Mathematical model; Optimal control; Oscillators; Stochastic systems;
Conference_Titel :
American Control Conference (ACC), 2011
Conference_Location :
San Francisco, CA
Print_ISBN :
978-1-4577-0080-4
DOI :
10.1109/ACC.2011.5991279