Research on Destabilization of Nonlinear Systems by Assigning Instantaneous Lyapunov Exponent

2015 Fiscal Year Final Research Report

• Project/Area Number: 25420445
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Control engineering/System engineering
• Research Institution: Oita University
• Principal Investigator: Matsuo Takami 大分大学, 工学部, 教授 (90181700)
• Co-Investigator(Kenkyū-buntansha): SUEMITSU HARUO 大分大学, 工学部, 助教 (50162839)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 非線形制御理論 / リアプノフ関数 / リアプノフ指数 / 適応オブザーバ / フォワーディング手法

Outline of Final Research Achievements

In this study, we deal with the control method for rotational movements of a pendulum using a separatrix. We design a controller that attains a homoclinic motion or a heteroclinic motion of the pendulum and the asymptotic stability of the cart by using a kind of forwarding control design. First, we derive a controller that converges to a homoclinic orbit via a Lyapunov function of the pendulum subsystem. Next, we give a nonlinear stabilizing controller via another Lyapunov function of the cart subsystem. Moreover, using the third Lyapunov function and adding a complementary control input, we guarantee that the pendulum converges to the homoclinic orbit and the cart is stabilized. The simulation and the experiment using the rapid controller prototyping system are performed to demonstrate the forward upward circling and the giant swing of the pendulum. Moreover, we propose an estimation method for the Malthus parameter to calculate the instantaneous Lyapunov exponent.

Free Research Field

制御理論