Stability of dynamical distribution networks with arbitrary flow constraints and unknown in/outflows

A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. We analyze the dynamics of the system in closed-loop with a distributed proportional-integral controller structure, where the flow inputs are constrained to take value in closed intervals. Results from our previous work are extended to general flow constraint intervals, and conditions for asymptotic load balancing are derived that rely on the structure of the graph and its flow constraints.Comment: published in proceeding of 52nd IEEE Conference on Decision and Control (CDC 2013). arXiv admin note: text overlap with arXiv:1403.5198, arXiv:1403.520

A graphic condition for the stability of dynamical distribution networks with flow constraints

We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. In [1] we showed how a distributed proportionalintegral controller structure, associating with every edge of the graph a controller state, regulates the state variables of the vertices, irrespective of the unknown constant inflows and outflows, in the sense that the storage variables converge to the same value (load balancing or consensus). In many practical cases, the flows on the edges are constrained. The main result of [1] is a sufficient and necessary condition, which only depend on the structure of the network, for load balancing for arbitrary constraint intervals of which the intersection has nonempty interior. In this paper, we will consider the question about how to decide the steady states of the same model as in [1] with given network structure and constraint intervals. We will derive a graphic condition, which is sufficient and necessary, for load balancing. This will be proved by a Lyapunov function and the analysis the kernel of incidence matrix of the network. Furthermore, we will show that by modified PI controller, the storage variable on the nodes can be driven to an arbitrary point of admissible set.Comment: submitted to MTNS 201

Constrained proportional integral control of dynamical distribution networks with state constraints

This paper studies a basic model of a dynamical distribution network, where the network topology is given by a directed graph with storage variables corresponding to the vertices and flow inputs corresponding to the edges. We aim at regulating the system to consensus, while the storage variables remain greater or equal than a given lower bound. The problem is solved by using a distributed PI controller structure with constraints which vary in time. It is shown how the constraints can be obtained by solving an optimization problem.Comment: CDC201

On the modeling of neural cognition for social network applications

In this paper, we study neural cognition in social network. A stochastic model is introduced and shown to incorporate two well-known models in Pavlovian conditioning and social networks as special case, namely Rescorla-Wagner model and Friedkin-Johnsen model. The interpretation and comparison of these model are discussed. We consider two cases when the disturbance is independent identical distributed for all time and when the distribution of the random variable evolves according to a markov chain. We show that the systems for both cases are mean square stable and the expectation of the states converges to consensus.Comment: submitted to IEEE CCAT 201