Probabilistic bounded non-linear control algorithm for linear structures

Non-linear control algorithms with limited control force has been widely explored and has shown promising results, but the probabilistic analysis of such control algorithms has been made restrictively due to their non-linear nature and corresponding difficulty in obtaining analytical solution of the joint probability density function (PDF). In this paper, the method for the probabilistic analysis on the bounded non-linear control algorithm is proposed based on the equivalent non-linear system method and additional regression analysis. Numerical examples show that the proposed approximate joint PDF of the closed-loop system subjected to a Gaussian white noise and a Kanai-Tajimi filtered Gaussian white noise matches closely with the joint PDF obtained statistically. The effectiveness of the bounded non-linear control is also investigated utilizing the calculated approximate joint PDF. Time history analysis results indicate that the same control performance level as the linear controller is achieved when 50% of the maximum control force of the linear controller is used for the non-linear controller.