文脈トリガー型ロバストMPCによる時相論理仕様の満足化
Context-Triggered Robust MPC for Temporal Logic Specifications
離散時間線形システムに対し、外乱下で文脈依存の線形時相論理仕様を満たすロバストなフィードバック制御器を合成する問題を扱い、ロバストMPCと局所不変制御器を組み合わせたスイッチング制御アーキテクチャを提案した。
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著者: Arash Bahari Kordabad, Satya Prakash Nayak, Sadegh Soudjani, Anne-Kathrin Schmuck
分類: eess.SY, math.OC
原文アブストラクト
We consider the problem of synthesizing robust feedback controllers for discrete-time linear systems that ensure the satisfaction of context-dependent linear temporal logic specifications in the presence of additive bounded disturbances. Building on existing results that reduce context-triggered temporal logic synthesis to the realization of context-dependent reach-avoid-stay (cRAS) objectives, we focus on the corresponding low-level control synthesis problem. We first employ certificate-based conditions for the almost-sure satisfaction of RAS specifications. Based on these conditions, we propose a switching control architecture that combines robust model predictive control (MPC) with a local invariant controller, and show that the resulting MPC value function serves as a reachability certificate while avoidance is enforced through robust constraints and the stay is enforced via the local controller. To obtain computationally tractable formulations for the resulting robust optimizations, we employ convex duality to reformulate the robust constraints into equivalent deterministic optimization problems, yielding convex quadratic and second-order cone programs for relevant geometric settings. The proposed framework is demonstrated on a robot navigation problem with context-triggered logical switches in both static and moving environments. The results show significantly larger feasible sets than Lyapunov-based approaches, while naturally accommodating dynamic environments and online task reconfiguration.
