We formulate the optimal control problem for a class of nonlinear objects that can be represented as objects with linear structure and state-dependent coefficients. We assume that the system is subjected to uncontrollable bounded disturbances. The linear structure of the transformed nonlinear system and the quadratic quality functional let us, in the optimal control synthesis, to pass from Hamilton-Jacobi-Isaacs equations to a state-dependent Riccati equation. Control of nonlinear uncertain object in the problem of moving along a given trajectory is considered using the theory of differential games. We also give an example that illustrates how theoretical results of this work can be used.