不確かなモデルに対する分布ロバスト最適化による安全で安定な制御合成
Safe and Stable Control Synthesis for Uncertain System Models via Distributionally Robust Optimization
モデルパラメータの不確かさを有限個のサンプルから捉え、制御バリア関数と制御リアプノフ関数の制約を分布ロバストチャンス制約として扱い、二次錐計画に帰着して安全と安定を両立する制御入力を効率的に計算する手法を提案した。
著者: Kehan Long, Yinzhuang Yi, Jorge Cortes, Nikolay Atanasov
分類: math.OC, cs.RO
原文アブストラクト
This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. Safety and stability constraints may be specified using a control barrier function (CBF) and a control Lyapunov function (CLF), respectively. To take model uncertainty into account, robust and chance formulations of the constraints are commonly considered. However, this requires known error bounds or a known distribution for the model uncertainty, and the resulting formulations may suffer from over-conservatism or over-confidence. In this paper, we assume that only a finite set of model parametric uncertainty samples is available and formulate a distributionally robust chance-constrained program (DRCCP) for control synthesis with CBF safety and CLF stability guarantees. To facilitate efficient computation of control inputs during online execution, we present a reformulation of the DRCCP as a second-order cone program (SOCP). Our formulation is evaluated in an adaptive cruise control example in comparison to 1) a baseline CLF-CBF quadratic programming approach, 2) a robust approach that assumes known error bounds of the system uncertainty, and 3) a chance-constrained approach that assumes a known Gaussian Process distribution of the uncertainty.
