Discrete sliding mode control for robust temperature regulation in 2D magnetic hyperthermia

• Presents a novel Discrete Sliding Mode Control (DSMC) framework for robust temperature regulation in magnetic hyperthermia cancer treatment. • Develops a complete 2D model of tumor tissue, addressing a more complex and realistic scenario than common 1D approximations. • Provides the first complete control solution for 2D hyperthermia that explicitly manages both external disturbances and system uncertainties. • Employs a finite difference method to effectively discretize the governing heat equation (PDE) into a state-space model suitable for control design. • Demonstrates exceptional controller performance through simulations, confirming high effectiveness and robustness in maintaining the target temperature of 316.15 K. Hyperthermia is a cancer treatment method that can be administered through multiple techniques. One recent technique that has gained attention involves using magnetic nanoparticles exposed to an external magnetic field to increase tissue temperature to a range of 315.15 to 318.15 K, which results in the destruction of cancer cells. To design a model-based controller for the thermal system, the governing heat equation a partial differential equation (PDE) - must be addressed. To implement model-based control, the governing PDE must be discretized into a finite-dimensional system. In this study, we leverage this approach to develop a discrete sliding mode control (DSMC) for regulating the tumor temperature to 316.15 K. To the best of our knowledge, this paper presents the first complete solution for controlling the temperature of 2D tumor tissue in the presence of disturbances and uncertainties. Simulation results demonstrate that the proposed controller is highly effective and robust against these challenges.