Stochastic stabilization of multi‐degree‐of‐freedom nonlinear random‐time‐delay controlled systems

Abstract

AbstractThe random‐time‐delay (RTD) occurs inevitably in feedback control, caused by the utilization of a multi‐user network with random demands. This paper is devoted to the stochastic stabilization of multi‐degree‐of‐freedom (MDOF) nonlinear RTD controlled systems. Firstly, a two‐step approximated method is proposed to deal with RTD: by modeling the RTD as a Markov jump process, the RTD control is formulated as the one with discrete jump varying delay; utilizing the randomly periodic characteristic, the Markov jump delay is taken out of the control as a parameter. The stochastic averaging principle is applied to generate a less‐dimensional averaged governing equation of system's energies. Secondly, the dynamical programming principle is applied to the ergodic control problem of the average systems with an undetermined cost function, which is determined by the demand of stabilizing the averaged systems, then the optimal control law is deduced. A largest Lyapunov exponent is introduced to the averaged systems to evaluate the asymptotic stability with probability one. Finally, an example is worked out to demonstrate the application and effectiveness of the proposed method.