Approximate Solution of the Target Control Problem with a Nonlinearity Depending on One State Variable

We consider a target control problem for a system of differential equations of a special form in which the nonlinear terms depend on a single state variable. The solution is based on the passage from the original problem to an auxiliary problem for a piecewise linear system as well as on an application of the comparison principle and "smoothed" piecewise quadratic value functions. We also propose a feedback control and derive an a priori estimate for the deviation from the target set in the closed-loop original system. In addition, we present a numerical method whose efficiency is confirmed by two sample computations.