1,721,081 research outputs found
Consensus via multi-population robust mean-field games
Full text linkIn less prescriptive environments where individuals are told ‘what to do’
but not ‘how to do’, synchronization can be a byproduct of strategic thinking,
prediction, and local interactions. We prove this in the context of multipopulation
robust mean-field games. The model sheds light on a multi-scale
phenomenon involving fast synchronization within the same population and
slow inter-cluster oscillation between different populations
Boolean-controlled systems via receding horizon and linear programing.
Full text linkWe consider dynamic systems controlled by boolean signals or decisions. We show that in a number of cases, the receding horizon formulation of the control problem can be solved via linear programing by relaxing the binary constraints on the control. The idea behind our approach is conceptually easy: a feasible control can be forced by imposing that the boolean signal is set to one at least one time over the horizon. We translate this idea into constraints on the controls and analyze the polyhedron of all feasible controls. We specialize the approach to the stabilizability of switched and impulsively controlled systems
Distributed Consensus Protocols for Coordinating Buyers
Full text linkIn this paper, we introduce a distributed consensus protocol for coordinating orders of a network of buyers also called agents/decision makers. Each buyer chooses a different threshold strategy, defining its intention to place an order only if at least other l buyers will do the same. We prove that consensus is reached asymptotically globally and coordination is the same that if the decision making process would be centralized, namely, any decision maker (DM) has access to the thresholds of all other DMs and chooses to order or not. The proposed distributed protocol has the advantage that buyers do not have to communicate their threshold strategy in advance, and consensus is reached without exploring all the possible threshold values
Robust control in uncertain multi-inventory systems and consensus problems
No full textWe consider a continuous time linear multi-inventory system with unknown demands bounded within ellipsoids and controls bounded within polytopes. We address the problem of epsilon-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which epsilon-stabilizability is possible through a saturated linear state feedback control. The idea of this approach is similar to the consensus problem solution for a network of continuous time dynamic agents, where each agent evolves according to a first order dynamics has bounded control and it is subject to unknown but bounded disturbances. In this context, we derive conditions under which consensus can be reached. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations
Generalized person-by-person optimization in team problems with binary decisions
Full text linkIn this paper, we extend the notion of person by person optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where the Decision Makers (DMs) make decisions sequentially in groups of m, we call it mbm optimization. The main contribution are certain sufficient conditions, verifiable in polynomial time, under which a pbp or an mbm optimization algorithm leads to the team-optimum. We also show that there exists a subclass of sub-modular team problems, recognizable in polynomial time, for which the convergence is guaranteed if the pbp algorithm is opportunely initialized
Altitude alignment of a team of UAVs under decentralized information structure
No full textIn this paper, we discuss nonlinear centralized and decentralized information protocols enabling a team of unmanned air-vehicles (UAVs) to reach consensus regarding the attitude of the formation center. The last is averaged over all UAV's attitudes and not known a-priori. The maneuver consists of an horizontal alignment starting at different attitudes while keeping the formation center constant. During the maneuver, each vehicle controls the vertical rate of climb based on sensed information about the relative attitude of only the nearest vehicles. The rate is bounded by the performance capabilities of the vehicles
Adaptation, coordination, and local interactions via distributed approachability
Full text linkThis paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent
systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework
of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability
theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for
the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local
information and interaction structure. The game model turns into a nonlinear differential inclusion, which after a proper design
of the control and disturbance policies, presents a consensus term and an exogenous adversarial input. Local interactions enter
in the model through a graph topology and the corresponding graph-Laplacian matrix. Given the above model, we turn the
original questions on cooperation, competition, and local interactions, into convergence properties of the differential inclusion.
In particular, we prove convergence and exponential convergence conditions around zero under general Markovian strategies.
We illustrate our results in the case of decentralized organizations with multiple decision-makers
Optimal impulse control problems and linear programming.
Full text linkOptimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the optimal impulse control problem via a binary linear programming problem with a totally unimodular constraint matrix. Hence, solving the binary linear programming problem is equivalent to solving its linear relaxation. It turns out that any solution of the linear relaxation is a feasible solution for the optimal impulse control problem. Then, given the feasible solution, obtained solving the linear relaxation, we find the optimal solution via local search
A Polynomial algorithm solving a special class of hybrid optimal control problems
No full textHybrid optimal control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions [5]. In this paper, we identify a special class of hybrid optimal control problems which are easy to solve. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the hybrid optimal control problem via an integer-linear programming reformulation. The integer-linear programming problem is a Set-covering one with a totally unimodular constraint matrix and therefore solving the Setcovering problem is equivalent to solving its linear relaxation. It turns out that any solution of the linear relaxation is a feasible solution for the hybrid optimal control problem. Then, given the feasible solution, obtained solving the linear relaxation, we find the optimal solution via local search
Challenging aspects in Consensus protocols for networks
No full textRecent results on Consensus protocols for networks are presented. The basic tools and the main contribution available in the literature are considered, together with some of the related challenging aspects: estimation in networks and how to deal with disturbances is considered. Motivated by applications to sensor, peer-to-peer, and ad hoc networks, many papers have considered the problem of estimation in a consensus fashion. Here, the Unknown But Bounded (UBB) noise affecting the network is addressed in details. Because of the presence of UBB disturbances convergence to equilibria with all equal components is, in general, not possible. The solution of the ∈-consensus problem, where the states converge in a tube of ray ∈ asymptotically or in finite time, is described. In solving the ∈-consensus problem a focus on linear protocols and a rule for estimating the average from a compact set of candidate points, the lazy rule, is shown
- …
