Title: Nested signal temporal logic specifications of nonlinear systems via time-varying high order control barrier functions

Authors: Shenyang Wang; Yazhou Wang; Lijun Long

Addresses: College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China ' College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China ' Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, 200240, China; State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China

Abstract: This paper addresses a control synthesis problem for a class of nonlinear systems with disturbances under nested signal temporal logic (STL) specifications. While most existing literature on control synthesis using control barrier functions (CBFs) to satisfy STL specifications does not address nested temporal operators and often assumes nominal (disturbance-free) systems, we propose a control framework based on STL incremental (STLInc), disturbance observers (DOBs), and time-varying high-order control barrier functions (HOCBFs) to address these gaps. Specifically, the proposed control framework uses STLInc, an incremental planning framework, to decompose nested STL formulas into a series of sub-specifications through two steps: flattening and scheduling. Then, control strategies are synthesised by using DOBs and time-varying HOCBFs to satisfy these sub-specifications. Also, the nested STL specifications are satisfied even when the system is disturbed. Finally, a 2D robot navigation example is presented to demonstrate the effectiveness of the proposed control framework.

Keywords: STL; signal temporal logic; CBF; control barrier functions; control synthesis; DOB; disturbance observer.

DOI: 10.1504/IJSCIP.2025.150922

International Journal of System Control and Information Processing, 2025 Vol.4 No.4, pp.273 - 290

Received: 25 Dec 2024
Accepted: 27 Mar 2025
Published online: 05 Jan 2026 *

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