Search for: All records

In this paper, we consider a discrete ensemble of linear, scalar control systems driven by a common single input. Assuming that all the individual systems are unstable, we investigate whether there exists a linear static feedback control law that can asymptotically stabilize the ensemble system. We provide necessary/sufficient conditions for feasibility of pole placement in the left half plane and for feedback stabilizability of the ensemble system. 

We propose a data synthesis pipeline for generating realistic traffic scenes and safety-critical rare events under natural language instructions while providing agent relation annotations. The pipeline structurally comprises the scene planner, agent generator, waypoint filter, event reasoner, and trajectory refiner, while incorporating a language model backend for controlled inference. By decomposing high-level semantic reasoning and low-level scene execution, our framework is able to produce physically grounded agent trajectories that satisfy the social relation specifications. The pipeline is used to generate a dataset of 370 traffic scenes based on an urban traffic intersection, featuring agent relations such as collision and yielding, which are safety-critical but challenging to specify in real world traffic data. We evaluate the quality of the synthesized agent trajectories by the simulation-to-reality gaps, where the pipeline achieves an 84% of instruction satisfaction rate equipped with the Claude3.5-Sonnet backend. We further showcase the usage of the synthesized dataset by testing traffic scene perception and precognition using a simple agentic pipeline, both outperforming non-LLM baselines by a noticeable margin. 

We investigate the H-property for step-graphons. Specifically, we sample graphs G_n on n nodes from a step-graphon and evaluate the probability that G_n has a Hamiltonian decomposition in the asymptotic regime as n goes to infinity. It has been shown in our earlier work that for almost all step-graphons, this probability converges to either zero or one. We focus in this paper on the residual case where the zero-one law does not apply. We show that the limit of the probability still exists and provide an explicit expression of it. We present a complete proof of the result and validate it through numerical studies.