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— In this paper we propose a novel smooth vector field whose trajectories globally converge to the saddle point of the Lagrangian associated with a convex and constrained optimization problem. Under suitable assumptions, we prove global convergence of the trajectories for the class of strictly convex problems and we propose a vector field for linear… (More)

— In this paper we consider two examples of synchronization problems, i.e., a network of oscillators and a network of rigid bodies. We propose a controller that requires only the knowledge of the relative distances among the neighboring systems in the network. The controller is based on an extremum seeking controller, that steers the overall system to the… (More)

Extremum seeking is a powerful control method to steer a dynamical system to an extremum of a partially unknown function. In this paper, we introduce extremum seeking systems on submanifolds in the Euclidian space. Using a trajectory approximation technique based on Lie brackets, we prove that uniform asymptotic stability of the so-called Lie bracket system… (More)

—We consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems.

— The problem of autonomously steering a vehicle to a destination point, while avoiding obstacles, is considered. The vehicle is modeled as a single-integrator in the plane and it is assumed that the obstacles are unknown a priori. The control law is an extremum seeking algorithm, which steers the vehicle to the minimum of a navigation function. In this… (More)

In this paper, we consider convex optimization problems with constraints. By combining the idea of a Lie bracket approximation for extremum seeking systems and saddle point algorithms, we propose a feedback which steers a single-integrator system to the set of saddle points of the Lagrangian associated to the convex optimization problem. We prove practical… (More)

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