Designing a Resilient Controller for Cancer Immunotherapy: Application to a Fractional-Order Tumour-Immune Model.

In this paper, we propose a robust control method for the automatic treatment of targeted anti-angiogenic molecular therapy based on multi-input multi-output (MIMO) nonlinear fractional and non-fractional models using the backstepping (BS) approach. This protocol aims to eradicate tumour cells while preserving high levels of the body's natural effector cells and maintaining drug dosage within safe limits. The exponential stability of the controlled system is mathematically demonstrated using the Lyapunov theorem. Consequently, the tumour volume's convergence rate can be precisely controlled-a critical factor in cancer treatment. To fine-tune the controller gains, a soft actor-critic (SAC) algorithm within the framework of deep reinforcement learning (DRL) is employed, with a reward function designed based on the specific requirements of the system. Additionally, the Lyapunov theorem is used to mathematically verify the system's robustness against parametric uncertainty. Compared to state-of-the-art approaches, the proposed scheme demonstrates superior long-term performance, achieving complete tumour eradication and drug delivery convergence to zero within 50 days while preserving high effector cell levels.