Construction of control for nonlinear system with quasi-constant regulator parameters

The synthesis method is considered of non-linear object control with quadratic quality functional, based on the technique of “extended linearization” of initial mathematic model of the object. Non-linear controller parameters are determined by the solution of matrix equation of Riccati type with parameters dependent on the object state. Noted is that the main problem of such controller realization is the difficulty of finding the solution of this equation at a same speed as object operate. The decision method is suggested, based on finding the controller parameters for each time step of a control interval. The developed method of synthesis and realization of a non-linear object control is suggested to be tested by building the strategy of drug injection while cancer treatment with the use of the mathematical model of cancerous tissue growth dynamics and its interaction with normal and immune cells. The results are given of mathematical modeling, conducted to test the effectiveness of the solutions obtained.