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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.

Recent works have shown that Markov chain theory can be used to model and realistically describe road network dynamics. Properties of the Markov transition matrix such as the Perron eigenvector, the second eigenvalue, and the Kemeny constant have nice corresponding interpretations in the road network counterparts. Our objective in this paper is to use this modelling paradigm to develop new traffic management applications. In particular, our framework is particularly suited to routing algorithm development, offering new approaches to this old problem. This is the focus of the present paper.

Polyhedral Lyapunov functions are convenient to solve the constrained stabilization problem of linear systems as non-conservative estimates of the domain of attraction can be obtained. Alternatively, truncated ellipsoids can be used to find an under-estimate of the feasible region, with a considerably reduced number of parameters. This paper reformulates classic geometric intersection operators in terms of R-functions, leading to a new family of smooth Lyapunov functions. This approach can be used to smooth both polyhedral and truncated ellipsoids Lyapunov functions improving control performances, as shown in several benchmark examples.