  This paper proposes a finite-time Newton seeking control design for systems
described by unknown multivariable static maps. The Newton seeking system has
an averaged system that implements a Newton continuous-time algorithm. The
averaged Newton seeking system is shown to achieve finite-time stability of the
unknown optimum of the static map. An averaging analysis demonstrates that the
proposed Newton-seeking achieves finite-time practical stability of the
optimum. A simulation study is used to demonstrate the effectiveness of the
design method.
