{"ID":2868471,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.16746","arxiv_id":"2509.16746","title":"On the System Theoretic Offline Learning of Continuous-Time LQR with Exogenous Disturbances","abstract":"We analyze offline designs of linear quadratic regulator (LQR) strategies with uncertain disturbances. First, we consider the scenario where the exogenous variable can be estimated in a controlled environment, and subsequently, consider a more practical and challenging scenario where it is unknown in a stochastic setting. Our approach builds on the fundamental learning-based framework of adaptive dynamic programming (ADP), combined with a Lyapunov-based analytical methodology to design the algorithms and derive sample-based approximations motivated from the Markov decision process (MDP)-based approaches. For the scenario involving non-measurable disturbances, we further establish stability and convergence guarantees for the learned control gains under sample-based approximations. The overall methodology emphasizes simplicity while providing rigorous guarantees. Finally, numerical experiments focus on the intricacies and validations for the design of offline continuous-time LQR with exogenous disturbances.","short_abstract":"We analyze offline designs of linear quadratic regulator (LQR) strategies with uncertain disturbances. First, we consider the scenario where the exogenous variable can be estimated in a controlled environment, and subsequently, consider a more practical and challenging scenario where it is unknown in a stochastic setti...","url_abs":"https://arxiv.org/abs/2509.16746","url_pdf":"https://arxiv.org/pdf/2509.16746v2","authors":"[\"Sayak Mukherjee\",\"Ramij R. Hossain\",\"Mahantesh Halappanavar\"]","published":"2025-09-20T17:14:27Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"cs.LG\"]","methods":"[]","has_code":false}