University of Guilan Journal of Mathematical Modeling 2345-394X 14 1 2026 03 01 Dynamic adaptation strategies for optimal control in unknown linear time-invariant system 1 17 8876 10.22124/jmm.2025.30264.2716 EN Homa Pouyanfar Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran Sohrab Effati Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran Amin Mansoori Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran Journal Article 2025 04 04 This paper presents a framework for online adaptive optimal control of continuous-time linear systems with unknown dynamics. The approach uses approximate and adaptive dynamic programming to learn the optimal control policy and value function in real-time, without prior knowledge of the system matrices. We introduce two algorithms based on policy iteration and value iteration, providing proofs the convergence and stability. Our value iteration method is robust against  from  exploration noise. The effectiveness of these control strategies is demonstrated through two examples, highlighting their ability to achieve near-optimal performance despite unknown dynamics.  https://jmm.guilan.ac.ir/article_8876_121fae0e0bfcfd9f477de65a53e5cff7.pdf