A population dynamics approach for the water distribution problem

Advances in Water Resources

Escobar³

et al. 2015

197

113

Urban drainage systems (UDS) may be considered large-scale systems given their large number of associated states and decision actions, making challenging their real-time control (RTC) design. Moreover, the complexity of the dynamics of the UDS makes necessary the development of strategies for the control design. This paper reviews and discusses several techniques and strategies commonly used for the control of UDS. Moreover, the models to describe, simulate, and control the transport of wastewater in UDS are also reviewed.

Section: Population Dynamics-based Control (Pd)mentioning

confidence: 99%

Section: Population Dynamics-based Control (Pd)mentioning

confidence: 99%

Modeling and real-time control of urban drainage systems: A review

Garcia¹,

Advances in Water Resources

Escobar³

et al. 2015

197

113

“…Other per-spective is the evolutionary game approach [20,24]. For instance in [2,3,14,[17][18][19], a population dynamics approach has been presented for control and/or optimization purposes. Motivated by all the applications of this game-theoretical approach in control systems, this work uses the evolutionary game theory as a learning approach to propose a dynamical tuning strategy for multi-objective MPC controllers.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Game-Based Dynamical Tuning for Multi-objective Model Predictive Control

Developments in Model-Based Optimization and Control

Ocampo‐Martínez

Quijano

2015

Self Cite

Model predictive control (MPC) is one of the most used optimizationbased control strategies for large-scale systems, since this strategy allows to consider a large number of states and multi-objective cost functions in a straightforward way. One of the main issues in the design of multi-objective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has time-varying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially improves the closed-loop performance. In order to adapt in a dynamical way the weights in the MPC multi-objective cost function, an evolutionary-game approach is proposed. This approach allows to vary the prioritization weights in the proper direction taking as a reference a desired region within the Pareto front. The proper direction for the prioritization is computed by only using the current system values, i.e., the current optimal control action and the measurement of the current states, which establish the system cost function over a certain point in the Pareto front. Finally, some simulations of a multi-objective MPC for a real multi-variable case study show a comparison between the system performance obtained with static and dynamical tuning.

“…Then, a data-driven dynamic resource allocation problem is solved at each sub-system by converging to a Nash equilibrium. The stability of the closed-loop system, composed of the flow-based distribution network and the population games, is analyzed by using passivity theory as in [1][8] [30] [32]. Moreover, this paper proposes a different way to compute the Shapley value for a specific characteristic function in the cooperative game in order to reduce the computational burden, which is one of the main issues when using this game-theoretical approach.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, the considerable reduction in the computational cost also allows computing the Shapley value in a distributed way. Finally, in order to show the performance of the proposed methodology based on cooperative and non-cooperative games, a resource allocation problem in a water system treated in [32] is presented. Different from the preliminary work presented in [2], this paper includes analysis regarding invariant-set properties that guarantee a limitation resource constraint, and the stability of the whole closed-loop system.…”

Section: Introductionmentioning

confidence: 99%

Non-centralized control for flow-based distribution networks: A game-theoretical insight

Journal of the Franklin Institute

Ocampo‐Martínez

Quijano

et al. 2017

Self Cite

This paper solves a data-driven control problem for a flow-based distribution network with two objectives: a resource allocation and a fair distribution of costs. These objectives represent both cooperation and competition directions. It is proposed a solution that combines either a centralized or distributed cooperative game approach using the Shapley value to determine a proper partitioning of the system and a fair communication cost distribution. On the other hand, a decentralized noncooperative game approach computing the Nash equilibrium is used to achieve the control objective of the resource allocation under a non-complete information topology. Furthermore, an invariant-set property is presented and the closed-loop system stability is analyzed for the non-cooperative game approach. Another contribution regarding the cooperative game approach is an alternative way to compute the Shapley value for the proposed specific characteristic function. Unlike the classical cooperative-games approach, which has a limited application due to the combinatorial explosion issues, the alternative method allows calculating the Shapley value in polynomial time and hence can be applied to large-scale problems.