Stochastic stabilization of quasi integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitation

Abstract

A stochastic stabilization control strategy is proposed for multi-degree-of-freedom (MDOF) quasi integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitation. At first, the averaged Itô stochastic differential equations (SDEs) for controlled first integrals are derived from the system motion equations by using the stochastic averaging method. Second, the dynamical programming equation of the averaged system with undetermined cost function is established based on the dynamical programming principle. The optimal control law is given through solving the dynamical programming equation. Third, the asymptotic Lyapunov stability with probability one of the controlled system is analyzed approximately by evaluating the largest Lyapunov exponent of the averaged system. Finally, the cost function and optimal control forces are determined based on the requirement of stabilizing the system. An example is delivered to illustrate the application and effectiveness of the proposed stochastic stabilization control strategy.