The Hamilton-Jacobi equation (HJE) plays an essential role in both classical mechanics and nonlinear H∞ control theory. In this paper, we propose a detailed successive algorithm for finding an approximate solution of the HJE by solving linear equations. A scalar example is given to compare the computational procedures and the accuracy for the proposed approach with some other methods. In addition, the nonlinear H∞ controller design for the inverted pendulum is also included to show the superiority of the nonlinear H∞ controller, as compared with the linear H∞ controller, in the aspect of the robust performance/stability.
Hu, Shr-Shiung; Yang, Pao-Hwa; and Juang, Jeng-Yih
"On a Computational Algorithm to the HJE in Nnlinear H∞ Control,"
Journal of Marine Science and Technology: Vol. 9:
2, Article 4.
Available at: https://jmstt.ntou.edu.tw/journal/vol9/iss2/4