Abstract
A controlled quasi partially integrable Hamiltonian system with pure parametric stochastic excitations is first reduced to averaged Itô equations by using the stochastic averaging method for quasi-Hamiltonian systems. A dynamical programming equation is then established for the ergodic control problem and solved to yield the optimal control law. The expression for the largest Lyapunov exponent is derived and the necessary and sufficient condition for the asymptotically Lyapunov stability with probability one of optimally controlled system is obtained. The system is stabilized by feedback control with proper choosing of the cost function and weighting matrix in the performance index for ergodic control problem.
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© 2003 Springer Science+Business Media Dordrecht
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Zhu, W.Q., Huang, Z.L. (2003). Lyapunov Exponent and Stability of Optimally Controlled Quasi Partially Integrable Hamiltonian Systems. In: Namachchivaya, N.S., Lin, Y.K. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics. Solid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0179-3_24
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DOI: https://doi.org/10.1007/978-94-010-0179-3_24
Publisher Name: Springer, Dordrecht
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