Quantitative measure for nonlinear unstable systems based on the region of attraction and its application to designing parameter optimization – inverted pendulum example

Quantitative stability measures for mechanical systems are highly needed. However, only a few such measures have been proposed for nonlinear systems. In this paper, a quantitative measure of stability for nonlinear systems based on the region of attraction (ROA) is proposed, and the measure is applied to parameter optimization of mechanical systems: multi-link inverted pendulum example. Recently, some techniques for calculating ROAs have been suggested; however, obtaining an accurate estimate of a ROA remains computationally demanding. We illustrate two techniques for efficiently estimating the proposed measure and apply them to the design parameter optimization problem for maximizing the stability measure. A number of simulations show the effectiveness of the proposed method.