Must it be the case that increasingly deep levels of strategic iterated reasoning by humans give increasingly close approximations of normative economic rationality? And if not, what might they do instead? We argue that human higher-level reasoning processes may support non-equilibrium, non-convergent "flocking" behavior. Flocking in the physical world is the sustained convergence of both the p...

In some applied models (of flocking or of the crowd control) it is more natural to deal with elements a metric space (as for instance family subsets vector endowed Hausdorff metric) rather than vectors in normed space. We consider an optimal control problem involving so called morphological system whose trajectories are time dependent tubes RN and show that theory Hamilton-Jacobi-Bellman inequa...

Thang Nguyen1, Hung La2, Vahid Azimi1, and Thanh-Trung Han3 1 Department of Electrical Engineering and Computer Science, Cleveland State University, 2121 Euclid Ave., Cleveland, OH 44115-2214, USA (email:[email protected];[email protected]); 2 Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam (e-mail: [email protected]); 3 Advan...

We study the problem of distributed velocity alignment among a group of nonholonomic agents in 2 and 3 dimensions. Inspired by social aggregation phenomena such as flocking and schooling in birds and fish, we develop vision based control laws for velocity alignment and motion coordination. The proposed control laws are distributed, in the sense that only information from neighboring agents are ...

We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary c...

The safe flocking problem requires a collection of N mobile agents to (a) converge to and maintain an equi-spaced lattice formation, (b) arrive at a destination, and (c) always maintain a minimum safe separation. Safe flocking in Euclidean spaces is a well-studied and difficult coordination problem. Motivated by real-world deployment of multi-agent systems, this paper studies one-dimensional sa...