Feedback Maximization For Reliability Of Strongly Nonlinear Systems With Multi-degrees-of-freedom

The main task of stochastic optimal control is to study the feedback control of thediffusion Markovian processes. In this paper, the problem of feedback maximization forreliability (stochastic optimal control for first-passage failure) of strongly nonlinearsystems with multi-degrees-of-freedom (MDOF) is studied. The excitations are classifiedas Gaussian white, combined harmonic and Gaussian white noise (or wide-band noise).For the weakly controlled systems, the original equation of motions are reduced totime-homogeneous diffusion processes, which are described by partially averaged It stochastic differential equations (SDEs). The dynamical programming equations for thecontrol problems of maximizing the conditional reliability and maximizing the meanfirst-passage time (MFPT) are formulated from the partially averaged It stochasticdifferential equations．The optimal control1aw is determined by using the principle ofdynamical programming. The completely averaged It SDEs are obtained by inserting theoptimal control law into the partially averaged It SDEs and averaging the termscontaining the control force. The backward Kolmogorov equation and the Pontryaginequation，which govern the conditional reliability function and the MFPT of the optimallycontrolled system, are established and solved respectively. The typical strongly nonlinearMDOF systems, such as coupled Duffing-van der Pol oscillators are taken as the examplesto illustrate the proposed procedures. All the theoretical results are verified by MonteCarlo simulation．...