Abstract
This paper provides a new framework of control allocation of over-actuated system for static optimization of inputs via dynamical extension and potential approach. The static optimization of the control allocation is performed in real-time approximately, by varying the input according to the potential. To ensure asymptotic stability of the controlled system, we extends the backstepping method to our cases where more flexible additional potential can be used. Under the conditions on the set of the minimizer, the growth rate around the set, and the unimodality of the additional potential with some auxiliary assumptions, the extended potential function becomes a control Lyapunov function of the augmented system. The effectiveness of the proposed method is demonstrated by simulations.
