確率論的入力状態安定性
Input-to-State Stability in Probability
有界な外乱に対する入力状態安定性(ISS)を、非有界な確率的外乱を持つ離散時間系に拡張した「確率的ISS(ISSp)」を提案し、マルチンゲール理論に基づくリアプノフ条件を与え、二足歩行ロボットの段差外乱に適用した。
著者: Preston Culbertson, Ryan K. Cosner, Maegan Tucker, Aaron D. Ames
分類: eess.SY, cs.RO, cs.SY
原文アブストラクト
Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an equilibrium of the undisturbed system. This graceful degradation of stability in the presence of disturbances describes a variety of real-world control implementations. Despite its utility, this property requires the disturbance to be bounded and provides invariance and stability guarantees only with respect to this worst-case bound. In this work, we introduce the concept of ``ISS in probability (ISSp)'' which generalizes ISS to discrete-time systems subject to unbounded stochastic disturbances. Using tools from martingale theory, we provide Lyapunov conditions for a system to be exponentially ISSp, and connect ISSp to stochastic stability conditions found in literature. We exemplify the utility of this method through its application to a bipedal robot confronted with step heights sampled from a truncated Gaussian distribution.
