Analyzing controllability of neural networks

In recent years, due to the relation between cognitive control and mathematical concept of control dynamical systems, there has been growing interest in the descriptive analysis of complex networks with linear dynamics, permeating many aspects from everyday life, obtaining considerable advances in the description of their structural and dynamical properties. Nevertheless, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems is of interest to study the exact controllability, this measure is defined as the minimum set of controls that are needed to steer the whole system toward any desired state. In this paper, a revision of controllability concepts is presented and provides conditions for exact controllability for the multiagent systemsPostprint (author's final draft

Position and Orientation Based Formation Control of Multiple Rigid Bodies with Collision Avoidance and Connectivity Maintenance

This paper addresses the problem of position- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in a $3$D workspace with obstacles. More specifically, we design a decentralized control protocol such that each agent achieves a predefined geometric formation with its initial neighbors, while using local information based on a limited sensing radius. The latter implies that the proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance as well as collision avoidance with the obstacles and the boundary of the workspace. The proposed controllers employ a novel class of potential functions and do not require a priori knowledge of the dynamical model, except for gravity-related terms. Finally, simulation results verify the validity of the proposed framework

Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators