Feedback Control Algorithms for Some Classes of Nonlinear Systems with a Parameter at Finite Interval

An efficient numerical algorithm is proposed to determine the feedback control for systems on a finite interval with a parameter at the control matrix that takes either small or large values and a small parameter that connects the subsystems in large dimension control problems. The algorithm is based on the construction of asymptotic expansions of the state-dependent differential Riccati equation in the SDRE approach by a small parameter or its inverse value. The resulting expansions are used as a basis for tuning of two-point Padé approximations of the gain matrices.