LAUSR

Abstract This manuscript aims at investigating the neural adaptive control of drug dosage regimens in cancer treatment. The goal of the treatment is to get an appropriate scheme for the drug dosage in order to reduce the tumor cells. To obtain a controller presenting good performances, the cancer immunotherapy system is first described by Caputo fractional differential equations. Second, Nussbaum functions and neural networks are introduced to deal with the unknown control directions and the uncertain nonlinear dynamics, respectively. Then, the backstepping dynamic surface control method is deployed to regulate the updating laws and the control signals, simultaneously. Through rigorous analysis based on the Lyapunov stability theory, it is shown that by means of the proposed adaptive controller, the boundedness of all variables in the closed-loop system and the semi-global asymptotic tracking are well ensured for any bounded initial conditions. It is also demonstrated that the performances of the drug treatment based on our proposed adaptive neural control scheme are better than a number of existing schemes. Finally, simulation results are given to demonstrate the feasibility of the proposed control scheme in the diminution of the number of tumor cells in the cancer model.