Optimal Control of Stochastic Parametrically and Externally Excited Nonlinear Control Systems

[+] Author and Article Information
G. E. Young, R. J. Chang

School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Okla. 74078

J. Dyn. Sys., Meas., Control 110(2), 114-119 (Jun 01, 1988) (6 pages) doi:10.1115/1.3152660 History: Received October 29, 1987; Online July 21, 2009


A sub-optimal nonlinear controller which is synthesized by using the external linearization approach is applied to the optimal control of stochastic parametrically and externally excited nonlinear systems with complete state information. Algebraic necessary conditions are derived for the minimization of the quadratic cost function through the concepts of equivalent external excitation. The concepts and applications of the statistical linearization approach for the externally excited nonlinear systems are extended to the nonlinear systems subjected to both stochastic parametric and external excitations. Two examples which include a first-order nonlinear and a second-order Duffing type stochastic system are used to illustrate the performance of the present design. The applications of the statistical linearization approach to the optimal control of a stochastic parametrically and externally excited Duffing type system is illustrated and compared with the present approach by using Monte Carlo simulation.

Copyright © 1988 by ASME
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