非可微分関数を含むフィードバック制御系設計 : バックステッピング法からのアプローチ

概要

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Based on the backstepping method, we present a new design method for nonlinear feedback systems with nondifferentiable functions. Making use of the Clarke's generalized directional deriva tive, we generalize the differentiable backstepping into nondifferentiable one. First, we derive a virtual subsystem with relative degree one, where a Lyapunov function is given. Next we introduce a new virtual subsystem which includes the previous subsystem. Then, with the help of the Clarke's derivative, we construct a new Lyapunov function based on the previous Lyapunov function, which contains nondifferentiable functions. The nondifferentiable backstepping consists of the recursive process. Last, we demonstrate the effectiveness of the proposed method by numerical simulation.
1999-04-25