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Feedback stabilization of multi‐DOF nonlinear stochastic Markovian jump systems
Ist Teil von
International journal of robust and nonlinear control, 2019-11, Vol.29 (16), p.5654-5667
Ort / Verlag
Bognor Regis: Wiley Subscription Services, Inc
Erscheinungsjahr
2019
Link zum Volltext
Quelle
Wiley Online Library - AutoHoldings Journals
Beschreibungen/Notizen
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.