A Bregman Nonlinear Proximal Point Algorithm for Adaptive Control

A nonlinear proximal point algorithm is proposed in the setting of adaptive control. Based on the Bregman generalized distance induced by a convex function, forward non-orthogonal projections provide a more general approach to classic optimization algorithms. In this paper convergence theorems are provided for the application of the Bregman algorithm to the adaptive control of both linear systems and nonlinear control-affine systems. It is shown that the proposed algorithm is particularly suited for adaptive control applications because it outperforms the gradient algorithm for on-line parameter estimation. Simulations on an autonomous underwater vehicle and a robotic manipulator show the benefits of the proposed adaptive control scheme when compared to the classic ones.