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Feedback stabilization of multi‐DOF nonlinear stochastic Markovian jump systems
Author(s) -
Hu Rongchun,
Dong Hao,
Gu Xudong,
Deng Zichen
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4689
Subject(s) - nonlinear system , control theory (sociology) , mathematics , markov process , lyapunov exponent , lyapunov function , ergodic theory , computer science , mathematical analysis , control (management) , physics , statistics , quantum mechanics , artificial intelligence
Summary A feedback control strategy is designed to asymptotically stabilize a multi‐degree‐of‐freedom (DOF) nonlinear stochastic systems undergoing Markovian jumps. First, a class of hybrid nonlinear stochastic systems with Markovian jumps is reduced to a one‐dimensional averaged Itô stochastic differential equation for controlled total energy. Second, the optimal control law is deduced by applying the dynamical programming principle to the ergodic control problem of the averaged systems with an undetermined cost function. Third, the cost function is determined by the demand of stabilizing the averaged systems. A Lyapunov exponent is introduced to analyze approximately the asymptotic stability with probability one of the originally controlled systems. To illustrate the application of the present method, an example of stochastically excited two coupled nonlinear oscillators with Markovian jumps is worked out in detail.