ノルム依存収縮率による打ち切りmRPI集合のハウスドルフ距離の明示的評価
Explicit Bounds on the Hausdorff Distance for Truncated mRPI Sets via Norm-Dependent Contraction Rates
打ち切り最小ロバスト正不変集合と無限ホライズン極限のハウスドルフ距離の上界を、外乱サイズとシステム行列の収縮率から閉形式で導出し、反復計算なしで所望の近似精度を保証するホライズン選択則を提案した。
著者: Jiaxun Sun, Hengyu Xue, Yuyang Zhao
分類: cs.RO, cs.SY, eess.SY, math.DS
原文アブストラクト
We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an induced-norm contraction factor of the system matrix, and it yields an explicit, fully analytic horizon-selection rule that guarantees a prescribed approximation tolerance without iterative set computations. The choice of vector norm enters as a design lever: norm shaping -- through diagonal or Lyapunov-based weighting -- tightens both the contraction factor and the resulting certificate, with direct consequences for robust invariant-set approximation and tube-based model predictive control (MPC) constraint tightening. Numerical examples illustrate the accuracy, scalability, and practical impact of the proposed bound.