The controlled system \[ \frac{dx}{dt} = f(x,t) B(x)u(x,t)\tag{1} \] is considered, where \(x\in R^n\), \(f\in C(R^n\times R_+,R^n)\), \(B\in C(R^n,R^m)\), \(u\in R^m\) is a vector of controlling forces. It is assumed that for \(u(x,t)\equiv 0\) the first integrals are known for the system (1). Under this assumption the control \(u^0(x,t)\) is found transferring system (1) from the state \(x_0\) into the state \(x_T\) and minimizing the functional \[ J\left[x(\cdot),u(\cdot)\right] = \frac 12 \int_0^T \sum_{j=1}^m\left[\frac{u_j(x,t)}{k _j}\right]^2dt, \] where \(k_j\) are constants.