Sliding Mode Control for the Hes1 Biochemical Reaction System Using RBF Neural Networks

Abstract

This paper presents a Sliding Mode Control (SMC) strategy based on Radial Basis Function Neural Network (RBFNN), the trajectory tracking problem of Res1 biochemical reaction system is introduced. The control task is realized by combining the superiority of RBFNN control and SMC. The sliding mode controller is used as input of RBFNN, the concentration of Res1 mRNA is used as its output, which can be seemed as a SISO system, this could facilitate the design and realization of the controller, and the output is designed to track the reference signal in finite time. The update formulas of the network weights are deduced from the Lyapunov method so that the controlled system is not only robust with respect to nonlinear dynamics, but also possesses the asymptotically stable ability. In order to prove the stability of the biochemical reaction system, a Lyapunov function is constructed. Simulation results indicate that the feasibility of this control approach, which is obtained by the control of the Res1 biochemical reaction system, and the proposed method can quickly track the given command signal. In addition, the effectiveness of this control method has been confirmed by the control of the model of tumor growth. Both theoretical analysis and two practical examples illustrate the effectiveness of the proposed strategy.