Multi-task learning for fast online adaptation under signal temporal logic specifications: An air traffic management application

Multi-task learning (MTL) seeks to improve the generalized performance during new testing tasks by exploiting useful information incorporated in related tasks. This paper developed an MTL-based control framework that considers signal temporal logic (STL) specifications applied to air traffic management. MTL settings involve both training and testing stages. In the training stage, an ensemble of tasks is generated by perturbing STL specifications considering the spatiotemporal features, ensuring a diverse yet structured task distribution. Task compliance is measured using the robustness degree, which is computed through STL semantics to quantify how well a state variables trajectory satisfies a set of specifications. Furthermore, robustness degree expressions are inherently non-convex due to log-sum exponential (LSE) terms used to approximate min and max operators, making direct optimization challenging. To address this, we employed sequential convex programming (SCP) with dynamically updated trust regions, which iteratively refine solutions to ensure convergence and stability in the optimization process. In the testing stage, new unseen tasks were introduced, requiring adaptation based on prior knowledge. The optimal solution obtained from the training phase served as a warm start, enabling rapid/few-shot adaptation to new, more perturbed tasks. Experimental validation was performed on two different dynamical systems. The first system corresponds to the spring-mass-damper system. The second system corresponds to a more comprehensive application within the air traffic control problem, scaled down to the context of quad-rotor dynamics. The results demonstrate that the proposed framework successfully satisfies new tasks' specifications within only a few SCP iterations, even under significant perturbations, highlighting the efficiency and adaptability of our approach.