  This paper presents a complementary approach to establish stability of finite
receding horizon control with a terminal cost. First a new augmented stage cost
is defined by rotating the terminal cost. Then a one-step optimisation problem
is defined based on this augmented stage cost. It is shown that a slightly
modified Model Predictive Control (MPC) algorithm is stable if the value
function of the augmented one-step cost (OSVF) is a control Lyapunov function.
The proposed stability condition is completely complementary to the existing
terminal cost based MPC stability conditions in the sense that they are
mutually excluded with each other. By using this approach, we are able to
establish stability for MPC algorithms with zero terminal cost or even negative
terminal cost as special cases. Combining this new approach with the existing
MPC stability theory, we are able to significantly relax the stability
requirement on MPC and extend the design space where stability are guaranteed.
The proposed approach will help to further reduce the gap between stability
theory and practical applications of MPC and other optimisation based control
methods.
