Finite-time Newton seeking control for a class of unknown static maps

This paper proposes a Newton seeking control design that achieves finite-time practical stability of the optimum of unknown multivariable static maps. The Newton seeking system is shown to yield an averaged finite-time stable Newton descent algorithm with a finite-time stable equilibrium at the optimum. A classical averaging theorem due to Krasnosel'skii and Krein is used to demonstrate that the trajectories of the Newton seeking system approximate the trajectories of the averaged finite-time stable system. The analysis shows that the finite-time Newton-seeking technique achieves finite-time practical stability of the optimum of the cost function. A simulation study is used to demonstrate the effectiveness of the design method.