Game theory based distributed model predictive control: an approach to large-scale systems control

Los sistemas de gran escala son sistemas conformados por diferentes elementos interactuando entre sí. Cada uno de estos elementos tiene asignado un controlador local encargado de de-cidir las acciones de control locales que deben ser aplicadas con el fin de alcanzar un objetivo. Por lo general, estas acciones son tomadas sin tener en cuenta su efecto en el comportamiento de los demás elementos ni en el desempeño global del sistema. Este comportamiento puede llevar al sistema a puntos de operación indeseables. Con el ´animo de resolver este problema, el control de sistemas de gran escala se ha venido formulando como un problema de optimización con restricciones, siendo el control predictivo basado en modelos la estrategia de control más promisoria para el control de este tipo de sistemas. Sin embargo, debido a que el control predictivo basado en modelos es una estrategia de control basada en optimización, no es posible su aplicación directa a sistemas de gran escala, ya que típicamente el control predictivo se implementa de forma centralizada y esto requiere la transmisión de grandes volúmenes de información y el uso de un alto poder computacional. Por tales motivos, los métodos de control distribuido basados en controladores predictivos surgen como una alternativa para su implementación en sistemas de gran escala. A pesar de los esfuerzos dedicados al diseño de estrategias de control distribuido basadas en control predictivo, la cooperación entre subsistemas sigue siendo un problema de investigación abierto. Con el fin de superar este problema, la teoría de juegos surge como un marco teórico alternativo para formular y caracterizar el problema de control predictivo distribuido. La teoría de juegos es una rama de las matemáticas aplicadas dedicada a identificar patrones de comportamiento en situaciones estratégicas, donde el beneficio percibido por cada uno de los individuos involucrados está determinado tanto por sus decisiones como por las decisiones que toman los demás individuos. En esta tesis, se propone una estrategia de control predictivo distribuida basada en juegos de negociación. Sin entrar en detalles, un juego de negociación es una situación en la que varios individuos deciden, conjuntamente, que estrategia es la mejor para alcanzar un beneficio mutuo. El uso de este tipo de juegos como marco de referencia permite tratar el problema de cooperación entre subsistemas usando control predictivo distribuido. Adicionalmente, este marco de referencia permite formular soluciones para el problema de control distribuido en las que los subsistemas no tienen que resolver más de un problema de optimización, facilitando la reducción de la carga computacional asociada a cada problema de optimización local. En el caso particular de esta tesis, tal solución fue propuesta a partir de una caracterización axiomática. Para esta solución, las condiciones para la estabilidad en lazo cerrado también se discuten./Abstarct. Large-scale systems are systems composed of several interacting components. Each component has a local controller with a local control objective, designed to take local decisions without considering the effect of their local control actions into the whole system performance. This issue may drive the system to undesirable closed-loop performance due to the "competition"\ among controllers. In order to overcome this issue, the control of large-scale systems has been formulated as a constrained optimization problem. In this way, model predictive control schemes have been arising as a promising alternative for controlling large-scale systems. Since model predictive control is an optimization based control scheme its centralized application in large-scale systems may become impractical because it may require the exchange of large amounts of information and the usage of high computational power. Therefore, distributed model predictive control schemes arise as an alternative for the implementation of model predictive control schemes in large-scale systems. Despite of the efforts dedicated to design methods for distributed model predictive control, the cooperation among subsystems still remains as an open research problem. In order to overcome this issue, game theory arises as an alternative to formulate and characterize the distributed model predictive problem. Game theory is a branch of applied mathematics used to capture behaviors in strategic situations where the outcome of a player is function not only of his choices but also depends on the choices of others. In this thesis, a bargaining game based distributed model predictive control scheme is proposed. Roughly speaking, a bargaining game is a situation where several players jointly decide which strategy is best with respect to their mutual benefit. This allows to deal with the cooperation issues of the distributed model predictive control problem. Additionally, the bargaining game framework allows to formulate solutions for the distributed model predictive control problem where the subsystems do not have to solve more than one optimization problem at each time step. This, also allows to reduce the computational burden of the local optimization problems. In the particular case of this thesis, such solution is proposed based on an axiomatic characterization. For the proposed solution, the conditions for the closed-loop stability are also discussed.Doctorad

A study of the control problem of the shoot side environment delivery system of a closed crop growth research chamber

The details of our initial study of the control problem of the crop shoot environment of a hypothetical closed crop growth research chamber (CGRC) are presented in this report. The configuration of the CGRC is hypothetical because neither a physical subject nor a design existed at the time the study began, a circumstance which is typical of large scale systems control studies. The basis of the control study is a mathematical model which was judged to adequately mimic the relevant dynamics of the system components considered necessary to provide acceptable realism in the representation. Control of pressure, temperature, and flow rate of the crop shoot environment, along with its oxygen, carbon dioxide, and water concentration is addressed. To account for mass exchange, the group of plants is represented in the model by a source of oxygen, a source of water vapor, and a sink for carbon dioxide. In terms of the thermal energy exchange, the group of plants is represented by a surface with an appropriate temperature. Most of the primitive equations about an experimental operating condition and a state variable representation which was extracted from the linearized equations are presented. Next, we present the results of a real Jordan decomposition and the repositioning of an undesirable eigenvalue via full state feedback. The state variable representation of the modeling system is of the nineteenth order and reflects the eleven control variables and eight system disturbances. Five real eigenvalues are very near zero, with one at zero, three having small magnitude positive values, and one having a small magnitude negative value. A Singular Value Decomposition analysis indicates that these non-zero eigenvalues are not results of numerical error

Decision Support System for Urbanization of the Northern Part of the Volga-Akhtuba Floodplain (Russia) on the Basis of Interdisciplinary Computer Modeling

There is a computer decision support system (CDSS) for urbanization of the northern part of the Volga-Akhtuba floodplain. This system includes subsystems of cognitive and game-theoretic analysis, geoinformation and hydrodynamic simulations. The paper presents the cognitive graph, two-level and three-level models of hierarchical games for the cases of uncontrolled and controlled development of the problem situation. We described the quantitative analysis of the effects of different strategies for the spatial distribution of the urbanized territories. For this reason we conducted the territory zoning according to the level of negative consequences of urbanization for various agents. In addition, we found an analytical solution for games with the linear dependence of the average flooded area on the urbanized area. We numerically computed a game equilibrium for dependences derived from the imitational geoinformation and hydrodynamic modeling of flooding. As the result, we showed that the transition to the three-level management system and the implementation of an optimal urbanization strategy minimize its negative consequences.Comment: 14 pages, 5 figures; Conference: Creativity in Intelligent Technologies and Data Science. CIT&DS 201

Interpolatory Weighted-H2 Model Reduction

This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an optimal reduced-order model. The H2 norm representation also provides an error expression that motivates a new weighted-H2 model reduction algorithm. Several numerical examples illustrate the effectiveness of the proposed approach

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

Improving the quality of the industrial enterprise management based on the network-centric approach

The article examines the network-centric approach to the industrial enterprise management to improve the ef ciency and effectiveness in the implementation of production plans and maximize responsiveness to customers. A network-centric management means the decentralized enterprise group management. A group means a set of enterprise divisions, which should solve by joint efforts a certain case that occurs in the production process. The network-centric management involves more delegation of authority to the lower elements of the enterprise’s organizational structure. The industrial enterprise is considered as a large complex system (production system) functioning and controlled amidst various types of uncertainty: information support uncertainty and goal uncertainty or multicriteria uncertainty. The information support uncertainty occurs because the complex system functioning always takes place in the context of incomplete and fuzzy information. Goal uncertainty or multicriteria uncertainty caused by a great number of goalsestablished for the production system. The network-centric management task de nition by the production system is formulated. The authors offer a mathematical model for optimal planning of consumers’ orders production with the participation of the main enterprise divisions. The methods of formalization of various types of uncertainty in production planning tasks are considered on the basis of the application of the fuzzy sets theory. An enterprise command center is offered as an effective tool for making management decisions by divisions. The article demonstrates that decentralized group management methods can improve the ef ciency and effectiveness of the implementation of production plans through the self-organization mechanisms of enterprise divisions.The work has been prepared with the financial support from the Russian Ministry of Education and Science (Contract No. 02.G25.31.0068 of 23.05.2013 as part of the measure to implement Decision of the Russian Government No. 218)