On asymptotic stability of a receding horizon control scheme

The stability of the receding horizon control scheme is investigated. A finite time quadratic optimization criterion is considered with a variable end-point penalty of the final state. For inner systems, a class of end-point weights is characterized that guarantee asymptotic stability of the system when controlled with a receding horizon optimal controller. In particular, it is shown that the receding horizon optimal controller stabilizes the system with an arbitrary small end-point penalty, provided the control horizon is sufficiently large.