Optimal Feedback Control Problem for a Singularly Perturbed Discrete System

The article proposes an asymptotic method for constructing an optimal control in a linear singularly perturbed discrete system with feedback. The optimal control is constructed for an equivalent system obtained by separating the state variables of the original system. Since in the feedback problem the optimal control depends on the solution of the nonlinear difference matrix Riccati equation, this equation is transformed to three linear singularly perturbed difference equations and the asymptotics of the solutions of these equations are constructed.