Adaptive backstepping controller design for MIMO cancer immunotherapy using Laguerre polynomials

This paper focuses on designing an efficient adaptive backstepping controller for multi-input multi-output (MIMO) cancer immunotherapy system. The proposed controller takes the advantage of the backstepping control and the property of universal approximation of the Laguerre polynomials. In this structure; the Laguerre polynomials, whose weights are adjusted online according to some adaptive laws, approximate the nonlinear part of the system that simplifies the design of backstepping controller. The proposed adaptive backstepping controller structure has simple but yet efficient structure for the control of MIMO cancer immunotherapy system when compared to the classical backstepping method. The main advantage of the proposed control scheme is that it is not only a model-free control structure but also it has a significantly low number of adaptive parameters to be tuned on-line. Moreover, it is proven that all the signals in the closed-loop system are bounded based on the Lyapunov stability theory. The simulation results confirm that only after short days of drug treatment the number of tumor cells is reduced to zero.