F. J. Muros

An Iterative Design Method for Coalitional Control Networks with Constraints on the Shapley Value

Abstract In this work, we introduce a new iterative design method for a coalitional control scheme for linear systems recently proposed. In this scheme, the links in the network infrastructure are enabled or disabled depending on their contribution to the overall system performance. As a consequence, the local controllers are divided dynamically into sets or coalitions that cooperate in order to attain their control tasks. The new design method allows the control system designer to include new constraints regarding the game theoretical tools of the control architecture, while optimizing the matrices that define the controller.

Coalitional control: An irrigation canal case study

We present a hierarchical distributed control scheme for large-scale systems in which the network topology is adjusted to fit to the dynamic coupling among the subsystems, considering the cost of data transmission. Each group of linked subsystems forms a coalition controlled by a closed-loop MPC scheme at the lower layer. The goal is to find a trade-off between the control performance and a reduced communicational cost. To set the proposed approach in a real scenario, the control scheme is tested on a model of an existing irrigation canal.

An application of the Shapley value to perform system partitioning

We introduce a new method to perform the partitioning of non-centralized dynamical linear systems based on the relevance of the possible interconnections among the smallest components of the system. In particular, we analyze the importance of the interconnections using game theoretical tools, so that they can be arranged as a function of their expected contribution to the overall system performance. In addition, this method allows to identify unnecessary interconnections and highlights the most appropriate communication links facing the application of distributed control schemes. The effectiveness of the proposed method is shown at the end of this work by means of a numerical example.

Constraints on the shapley value for a coalitional control system

We introduce several refinements in the design method of a coalitional control scheme for linear systems recently proposed. In this scheme, the network topology is modified in order to attain a trade-off between communication burden and overall system performance. In particular, all the communication links with low contribution to the overall performance are disconnected. Likewise, the control law is adapted to these changes. Given that the coalitional control scheme can be described as a cooperative game, it is possible to apply classical game theory results to gain insight into the distributed control problem. In this work, we show how the design method can be modified in order to include constraints regarding the game theoretical properties of the aforementioned scheme.

An assessment of coalitional control in water systems

The evolution of distributed control techniques has led to the development of schemes where the communication burden is adapted dynamically: when the overall system is far from the control goal, the communication burden is augmented to improve the performance; when the system is close to its goal and there is no need of coordination, the distributed control scheme tends to behave as a decentralized one. As a result of this policy, local controllers are divided into dynamical groups or coalitions where the communication is essential to ensure the cooperation. In this paper, the application of coalitional control schemes for water systems is assessed. In addition, a software tool implemented in Matlab® for testing coalitional control schemes is proposed and tested in a water network.

Networked control design for coalitional schemes using game-theoretic methods

Abstract In this work, we present an iterative design method for a coalitional networked control scheme for linear systems. In this scheme, the links in the communication network are enabled or disabled depending on their contribution to the overall system performance. Likewise, the control law is adapted to these changes. In particular, new conditions are included at the design phase, in order to consider constraints on the links and the agents regarding the game theoretical tools utilized while optimizing the matrices that define the controller.

An algorithm with low computational requirements to constrain the Shapley value in coalitional networks

In this paper, we deal with a distributed control scheme for linear systems in which the local controllers work cooperatively whenever the benefits from a control perspective are higher than the corresponding communication requirements. To this end, the network topology may vary with time so that all the communication links with a minor contribution to the overall performance are disconnected. Hence, there is also a change in the overall control law, which must be adapted to the information flows enabled by the network topology. This whole framework can be modeled as a cooperative game, which allows us to apply tools such as the Shapley value to gain an insight into the distributed control problem. In particular, we show an alternative way to impose restrictions on this value by using a more computationally efficient design procedure.

Distributed MPC Based on a Team Game

In this chapter we present a distributed scheme based on a team game for the particular case in which the system is controlled by two agents. The main features of the proposed scheme are the limited amount of global information that the agents share and the low communication burden that it requires. For this reason, this scheme is a good candidate to be implemented in systems with reduced capabilities, for example in wireless sensor and actuator networks.

Cooperative game theory tools to detect critical nodes in distributed control systems

In this work, we deal with the identification of critical nodes in distributed control systems by means of game theoretical tools. This detection is addressed taking into consideration different factors such as the control performance under different topologies, the communication costs, and the centrality of the nodes in the network under study. In this sense, a generalization of the solution concept known as position value is considered to obtain a payoff for each node. A method that captures relevant information of the nodes using probability density functions of their payoffs is given and tested through an academic example.

Harsanyi Power Solutions in Coalitional Control Systems

In coalitional control the connections among the different parts of a control network evolve dynamically to achieve a trade-off between communication burden and control performance, and the coalition choices are made by selecting the network topology with minimal payoff. This work analyzes how Harsanyi power solutions for games in coalitional control schemes, which generalize the Shapley value in this context, can be used to quantify the value of the communication links under different control topologies. To this end, a game among these links is considered, and the payoff that each link receives is determined by the Harsanyi power solutions, which take into account the communication costs and the predicted infinite-horizon costs for these topologies. The concept of link power measure as a centrality index to configure the communication costs is also introduced. As a result, a more computationally efficient design method with respect to previous works has been proposed.