Constrained distributed optimization : A population dynamics approach

Large-scale network systems involve a large number of states, which makes the design of real-time controllers a challenging task. A distributed controller design allows to reduce computational requirements since tasks are divided into different systems, allowing real-time processing. This paper proposes a novel methodology for solving constrained optimization problems in a distributed way inspired by population dynamics. This methodology consists of an extension of a population dynamics equation and the introduction of a mass dynamics equation. The proposed methodology divides the problem into smaller sub-problems, whose feasible regions vary over time achieving an agreement to solve the global problem. The methodology also guarantees attraction to the feasible region and allows to have few changes in the decision-making design when a network suffers the addition/removal of nodes/edges. Then, distributed controllers are designed with the proposed methodology and applied to the large-scale Barcelona Drinking Water Network (BDWN). Some simulations are presented and discussed in order to illustrate the control performance.Peer ReviewedPostprint (author's final draft

Distributed MPC with time-varying communication network: A density-dependent population games approach

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This work addresses distributed control design by using density-dependent population dynamics. Furthermore, stability of the equilibrium point under this proposed class of population dynamics is studied, and the relationship between the equilibrium point of density-dependent population games (DDPG) and the solution of constrained optimization problems is shown. Finally, a distributed predictive control is designed with the proposed density-dependent dynamics, and contemplating a time-varying communication network.Peer ReviewedPostprint (author's final draft

Distributed formation control of multiple unmanned aerial vehicles over time-varying graphs using population games

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a control technique based on distributed population dynamics under time-varying communication graphs for a multi-agent system structured in a leader-follower fashion. Here, the leader agent follows a particular trajectory and the follower agents should track it in a certain organized formation manner. The tracking of the leader can be performed in the position coordinates x; y; and z, and in the yaw angle phi. Additional features are performed with this method: each agent has only partial knowledge of the position of other agents and not necessarily all agents should communicate to the leader. Moreover, it is possible to integrate a new agent into the formation (or for an agent to leave the formation task) in a dynamical manner. In addition, the formation configuration can be changed along the time, and the distributed population-games-based controller achieves the new organization goal accommodating conveniently the information-sharing graph in function of the communication range capabilities of each UAV. Finally, several simulations are presented to illustrate different scenarios, e.g., formation with time-varying communication network, and time-varying formationPeer ReviewedPostprint (author's final draft

Time-varying partitioning for predictive control design: density-games approach

The design of distributed optimization-based controllers for large-scale systems (LSSs) implies every time new challenges. The fact that LSSs are generally located throughout large geographical areas makes dicult the recollection of measurements and their transmission. In this regard, the communication network that is required for a centralized control approach might have high associated economic costs. Furthermore, the computation of a large amount of data implies a high computational burden to manage, process and use them in order to make decisions over the system operation. A plausible solution to mitigate the aforementioned issues associated with the control of LSSs consists in dividing this type of systems into smaller sub-systems able to be handled by independent local controllers. This paper studies two fundamental components of the design of distributed optimization-based controllers for LSSs, i.e., the system partitioning and distributed optimization algorithms. The design of distributed model predictive control (DMPC) strategies with a system partitioning and by using density-dependent population games (DDPG) is presented.Peer ReviewedPostprint (author's final draft

On controllability of neuronal networks with constraints on the average of control gains

Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently

Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem and to the constrained mean field charging control problem for large populations of plug-in electric vehicles.Comment: IEEE Trans. on Automatic Control (cond. accepted