Boundary Stabilization for Uncertain Delay Markovian Reaction-Diffusion Neural Networks With Partially Unknown Transition Rates via Sliding Mode Approach

This paper investigates the sliding mode boundary stabilization for uncertain delay Markovian reaction-diffusion neural networks with partially unknown transition rates. First, a mode-dependent sliding mode surface (SMS) and a mode-dependent sliding mode boundary controller are designed, offering enhanced adaptability to different modes. Next, the almost sure finite-time reachability of the proposed SMS is derived, despite the challenges posed by Markovian switching with partially unknown transition rates. Then, by employing the Lyapunov stability method, inequality analysis techniques, and the free-weighting matrices approach, a criterion is established to guarantee the mean-square robust exponential stability of the closed-loop system. The proposed approach effectively overcomes the challenges arising from the coexistence of partially unknown transition rates, diffusion dynamics, and boundary disturbances under Markovian switching. Finally, the proposed theoretical results are validated via application to temperature control in lithium-ion battery packs for electric vehicles, demonstrating their effectiveness. Note to Practitioners—To maintain the reliable performance of electric vehicle (EV) battery systems, it is crucial to ensure the safe and efficient operation of lithium-ion battery packs through proper temperature control, as uncontrolled temperatures not only risk overheating and reduced battery life, but also threaten overall vehicle safety. This work tackles the challenge by designing control methods adaptive to different EV operating modes (discharging, balancing, charging), maintaining thermal stability despite external disturbances such as ambient temperature fluctuations or airflow variations. A key advantage of this approach is its ability to operate under real-world uncertainties while simplifying implementation. However, this approach is limited to series-connected battery packs based on a specific radial diffusion model and requires adaptation for more complex configurations. Future research could combine it with battery degradation predictive models or integrate it into broader vehicle energy management systems. Beyond EVs, this method also applies to systems with distributed, uncertain dynamicsłsuch as thermal control for industrial furnaces or temperature management for large-scale energy storagełoffering a flexible solution for addressing complex thermal control challenges in dynamic, uncertain environments.