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

Abstract

The 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.

Observer‐based critically damped feedback systems for nonlinear roll‐to‐roll printing machine applications under decentralized strategy

“…The full‐state feedback multi‐loop controller was used to solve the system nonlinearities and parameter dependence problems by incorporating a combination of active damping and a disturbance observer (DOB), 3 which is an advanced solution to the flatness‐technique‐based feedback linearization controller 2 . However, this recent development does not guarantee ideal performance during actual implementation owing to the uncertain time delays between the local agents and main controller, which can be alleviated by incorporating additional time‐delay compensation mechanisms (as in References 8–10) in the main control loop.…”