University of Guilan Journal of Mathematical Modeling 2345-394X 14 1 2026 03 01 Design of an optimal learning sliding mode control for linear systems 191 206 9327 10.22124/jmm.2025.30152.2694 EN Majid Yarahmadi Address: Iran, Lorestan, Khorramabad, Lorestan University Tahereh Azizpour Department of Mathematics and Computer, Lorestan university, Lorestan, Iran Journal Article 2025 03 18 In this paper, a new learning robust controller based on the sliding mode control method and reinforcement learning approach is designed for a class of SISO linear systems with a relative degree of uncertainty ‎$ r$‎. For this purpose, a hybrid controller that including equivalent controller and learning robust controller, is designed. The proposed controller guarantees asymptotic stability, sliding condition, finite reaching time, elimination of chattering phenomenon and tracking of desired output in an optimally approach. For online approximation of the value function and design of an optimal policy a new robust optimal learning controller is designed. For analytical facilitation and stability analysis, three theorems are proved and a new algorithm is designed. Finally, a simulation example is presented to demonstrate the advantages of the proposed method. The simulation results show the optimality of the controls, the elimination of chattering phenomenon and the tracking of the desired ‎output.‎‎ https://jmm.guilan.ac.ir/article_9327_a00db244aaadd9edae34648d4a3904fd.pdf