Distributed Model Predictive Consensus via the Alternating Direction Method of Multipliers

We propose a distributed optimization method for solving a distributed model predictive consensus problem. The goal is to design a distributed controller for a network of dynamical systems to optimize a coupled objective function while respecting state and input constraints. The distributed optimization method is an augmented Lagrangian method called the Alternating Direction Method of Multipliers (ADMM), which was introduced in the 1970s but has seen a recent resurgence in the context of dramatic increases in computing power and the development of widely available distributed computing platforms. The method is applied to position and velocity consensus in a network of double integrators. We find that a few tens of ADMM iterations yield closed-loop performance near what is achieved by solving the optimization problem centrally. Furthermore, the use of recent code generation techniques for solving local subproblems yields fast overall computation times.Comment: 7 pages, 5 figures, 50th Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA, 201

A Study On Distributed Model Predictive Consensus

We investigate convergence properties of a proposed distributed model predictive control (DMPC) scheme, where agents negotiate to compute an optimal consensus point using an incremental subgradient method based on primal decomposition as described in Johansson et al. [2006, 2007]. The objective of the distributed control strategy is to agree upon and achieve an optimal common output value for a group of agents in the presence of constraints on the agent dynamics using local predictive controllers. Stability analysis using a receding horizon implementation of the distributed optimal consensus scheme is performed. Conditions are given under which convergence can be obtained even if the negotiations do not reach full consensus.Comment: 20 pages, 4 figures, longer version of paper presented at 17th IFAC World Congres

On the Actual Inefficiency of Efficient Negotiation Methods

In this contribution we analyze the effect that mutual information has on the actual performance of efficient negotiation methods. Specifically, we start by proposing the theoretical notion of Abstract Negotiation Method (ANM) as a map from the negotiation domain in itself, for any utility profile of the parties. ANM can face both direct and iterative negotiations, since we show that ANM class is closed under the limit operation. The generality of ANM is proven by showing that it captures a large class of well known in literature negotiation methods. Hence we show that if mutual information is assumed then any Pareto efficient ANM is manipulable by one single party or by a collusion of few of them. We concern about the efficiency of the resulting manipulation. Thus we find necessarily and sufficient conditions those make manipulability equivalent to actual inefficiency, meaning that the manipulation implies a change of the efficient frontier so the Pareto efficient ANM converges to a different, hence actually inefficient, frontier. In particular we distinguish between strong and weak actual inefficiency. Where, the strong actual inefficiency is a drawback which is not possible to overcome of the ANMs, like the Pareto invariant one, so its negotiation result is invariant for any two profiles of utility sharing the same Pareto frontier, we present. While the weak actual inefficiency is a drawback of any mathematical theorization on rational agents which constrain in a particular way their space of utility functions. For the weak actual inefficiency we state a principle of Result's Inconsistency by showing that to falsify theoretical hypotheses is rational for any agent which is informed about the preference of the other, even if the theoretical assumptions, which constrain the space of agents' utilities, are exact in the reality, i.e. the preferences of each single agent are well modeled

Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability

Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices $W_k$ are often random, due to, e.g., random packet dropouts in wireless sensor networks. Key in analyzing the performance of such systems is studying convergence of matrix products $W_kW_{k-1}... W_1$. In this paper, we find the exact exponential rate $I$ for the convergence in probability of the product of such matrices when time $k$ grows large, under the assumption that the $W_k$'s are symmetric and independent identically distributed in time. Further, for commonly used random models like with gossip and link failure, we show that the rate $I$ is found by solving a min-cut problem and, hence, easily computable. Finally, we apply our results to optimally allocate the sensors' transmission power in consensus+innovations distributed detection