Disturbance Rejection Control under Nested Signal Temporal Logic Specifications: A Recursive Design Approach
For control systems with complex temporal specifications, this work addresses the challenge of nested STL under uncertainty, offering a computationally feasible solution that outperforms existing methods in applicability and assumptions.
This paper proposes a recursive control barrier function (CBF) design for uncertain continuous-time systems under nested signal temporal logic (STL) specifications, enabling disturbance rejection without prior knowledge of disturbances. The approach guarantees STL satisfaction and relaxes initial safety assumptions, validated through simulations.
This paper investigates the control synthesis for continuous-time uncertain systems under nested Signal Temporal Logic (STL) specifications containing nested temporal operators. Control Barrier Functions (CBFs) are utilized herein to encode STL formulas into system constraints. However, traditional CBF designs fail to encode nested STL formulas, whereas recent reachability analysis-based methods capable of handling such formulas are inapplicable to uncertain systems and suffer from a severe computational burden. To overcome these challenges, a novel recursive CBF design procedure based on a modified STL tree (sTLT) is proposed to yield explicit parameterized CBFs. Within this framework, sliding window variables are introduced to capture complex temporal relationships. Crucially, satisfying the resulting CBF constraints is proven to guarantee the fulfillment of the STL specifications. To render the proposed recursive CBF design applicable to systems subject to uncertain disturbance, a novel controller based on reconstructed CBF using quadratic programming (QP) is proposed, ensuring strict CBF constraint satisfaction under disturbances. In contrast to existing methods, the proposed reconstructed CBF approach requires no prior knowledge of the disturbances while relaxing initial safety assumptions. Simulation results validate the efficacy of the proposed approach.