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

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

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

A differential game approach to urban drainage systems control

© 20xx 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.Urban drainage systems (UDSs) are complex large-scale systems that carry stormwater and wastewater throughout urban areas. During heavy rain scenarios, UDSs are not able to handle the amount of extra water that enters the network and flooding occurs. Usually, this might happen because the network is not being used efficiently, i.e., some structures remain underused while many others are overused. This paper proposes a control methology based on differential game theory that aims to efficiently use the existing network elements in order to minimize overflows and properly manage the water resource. The proposed controller is tested on a typical UDS and is compared with a centralized MPC achieving similar results in terms of flooding minimization and network usage, but only using local information on distributed controllers.Peer ReviewedPostprint (author's final draft

Distributed population dynamics : optimization and control applications

© 2017 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.Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well-mixed populations, which limits the applications where this theory can be implemented. In this paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controllers.Peer ReviewedPostprint (author's final draft

Decentralized control for urban drainage systems using replicator dynamics

This paper proposes a decentralized control scheme that mitigates floods in urban drainage systems (UDSs). First, we develop a partitioning algorithm of the UDS relying on a graph model of the system. Once this is done, we design a local controller for each partition based on the replicator dynamics model (a set of differential equations that describes the evolution of a population of players involved in a strategic game). The decentralized nature of the proposed strategy makes it suitable for applying it in large-scale systems. Stability of the closed-loop system is proved by using Lyapunov theory. Furthermore, we simulate the performance of the decentralized control scheme in two case studies. One of them models part of the Bogotá (Colombia) stormwater UDS. Finally, we compare the proposed technique with two widely used methods for-real time control of UDSs, i.e., constrained linear quadratic regulator (LQR) and model predictive control (MPC).Peer ReviewedPostprint (published version

A class of population dynamics for reaching epsilon-equilibria : engineering applications

© 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 worksThis document proposes a novel class of population dynamics that are parameterized by a nonnegative scalar . We show that any rest point of the proposed dynamics corresponds to an -equilibrium of the underlying population game. In order to derive this class of population dynamics, our approach is twofold. First, we use an extension of the pairwise comparison revision protocol and the classic mean dynamics for well-mixed populations. This approach requires full-information. Second, we employ the same revision protocol and a version of the mean dynamics for non-well-mixed populations that uses only local information. Furthermore, invariance properties of the set of allowed population states are analyzed, and stability of the -equilibria is formally proven. Finally, two engineering examples based on the -dynamics are presented: A control scenario in which noisy measurements should be mitigated, and a humanitarian engineering application related to wealth distribution in poor societies. © 2016 American Automatic Control Council (AACC).Peer ReviewedPostprint (author's final draft

Dynamical tuning for MPC using population games: a water supply network application

ISA Transactions Best Paper Award 2018Model predictive control (MPC) is a suitable strategy for the control of large-scale systems that have multiple design requirements, e.g., multiple physical and operational constraints. Besides, an MPC controller is able to deal with multiple control objectives considering them within the cost function, which implies to determine a proper prioritization for each of the objectives. Furthermore, when the system has time-varying parameters and/or disturbances, the appropriate prioritization might vary along the time as well. This situation leads to the need of a dynamical tuning methodology. This paper addresses the dynamical tuning issue by using evolutionary game theory. The advantages of the proposed method are highlighted and tested over a large-scale water supply network with periodic time-varying disturbances. Finally, results are analyzed with respect to a multi-objective MPC controller that uses static tuning.Peer ReviewedAward-winningPostprint (author's final draft

Dynamical tuning for MPC using population games: a water supply network application

ISA Transactions Best Paper Award 2018Model predictive control (MPC) is a suitable strategy for the control of large-scale systems that have multiple design requirements, e.g., multiple physical and operational constraints. Besides, an MPC controller is able to deal with multiple control objectives considering them within the cost function, which implies to determine a proper prioritization for each of the objectives. Furthermore, when the system has time-varying parameters and/or disturbances, the appropriate prioritization might vary along the time as well. This situation leads to the need of a dynamical tuning methodology. This paper addresses the dynamical tuning issue by using evolutionary game theory. The advantages of the proposed method are highlighted and tested over a large-scale water supply network with periodic time-varying disturbances. Finally, results are analyzed with respect to a multi-objective MPC controller that uses static tuning.Peer ReviewedAward-winningPostprint (author's final draft

On the communication discussion of two distributed population-game approaches for optimization purposes

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Population games have become a powerful tool for solving resource-allocation problems in a distributed manner, and for the design of non-centralized optimization-based controllers. The aim of this paper is to illustrate the advantages of two recently introduced population-game approaches in comparison to other classical optimization methods. More specically, the discussion is mainly devoted to the communication requirements. Finally, an illustrative example shows with more detail the advantages highlighted throughout the comparative discussion, i.e., fewer communications links are required for resource allocation problems, and there is not need of additional computation stages to solve the problem in a distributed manner.Peer ReviewedPostprint (author's final draft