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Economic instruments, behaviour and incentives in groundwater management
Published in Karen G. Villholth, Elena López-Gunn, Kirstin I. Conti, Alberto Garrido, Jac van der Gun, Advances in Groundwater Governance, 2017
Phoebe Koundouri, Ebun Akinsete, Nikolaos Englezos, Xanti I. Kartala, Ioannis Souliotis, Josef Adler
In a river basin scale, several hydro-economic models were used to integrate riparian zones and wetlands (Hattermann et al., 2006) and optimize the conjunctive management of surface and groundwater systems (Pulido-Velazquez et al., 2007, 2008, Safavi et al., 2010, Wu et al., 2015, and Nasim & Helfand, 2015), as well as under uncertainty analysis (Wu et al., 2014). The conflict-resolution issues on water scarcity and infrastructure operations concerning river basin management in transboundary water resources allocation, i.e. the river is a common water resource to multiple countries, is addressed by the game theoretic approach. Wu and Whittington (2006) investigated the incentive structure of both cooperative and no cooperative policies for different riparian countries that share an international river basin. Eleftheriadou & Mylopoulos (2008) quantified the consequences caused by water flow decrease for different scenarios to estimate compromising solutions acceptable by two countries. Under the effects of climate change, Bhaduri et al. (2011) presented a stochastic noncooperative differential game to obtain sustainable transboundary water allocation by linking transboundary flows to hydropower exports, whereas Girard et al. (2016) compared cooperative game theory and social justice approaches with respect to cost allocation of adaptation measures at the river basin scale.
Linear Continuous‐Time Stochastic H2/H∞ Control
Published in Weihai Zhang, Lihua Xie, Bor-Sen Chen, 2/H∞ Control, 2017
Weihai Zhang, Lihua Xie, Bor-Sen Chen
In this chapter, we study linear continuous‐time stochastic H2/H∞ control of Itôtype systems based on the Nash game approach, which can be viewed as an extension of the deterministic H2/H∞ control in [113]. To this end, we have to develop SBRLs, generalized Lyapunov‐type theorems, and indefinite stochastic LQ theory. It turns out that the solvability of the finite‐time (respectively, infinite‐time) stochastic H2/H∞ control is equivalent to the solvability of some cross‐coupled GDREs (respectively, GAREs). A relationship between the solvability of the stochastic H2/H∞ control and the existence of an equilibrium point of a two‐person non‐zero sum Nash game is revealed. A unified treatment for the finite‐time H2, H∞ and mixed H2/H∞ control is presented, which shows that the pure H2 or H∞ control can be treated as special cases of the mixed H2/H∞ control. The results of this chapter contribute not only to the stochastic H2/H∞ control but also to multiple decision making [135] and differential game theory [136].
Optimal Control and Differential Game Modeling of a Systems Engineering Process for Transformation
Published in Kenneth C. Hoffman, Christopher G. Glazner, William J. Bunting, Leonard A. Wojcik, Anne Cady, Enterprise Dynamics Sourcebook, 2013
Leonard A. Wojcik, Kenneth C. Hoffman
Large- scale, complex systems engineering efforts involving multiple stakeholders often have been problematic, so there is keen interest in both government and private industry in understanding how to improve the systems engineering process for such systems. This chapter presents an approach to modeling the systems engineering (SE) process, originally inspired by the highly optimized tolerance (HOT) framework for understanding complexity in designed systems. Here, high- level, optimal control- theoretic and differential- game models of the systems engineering process represent in a simplified way the cost, schedule, and performance tradeoffs inherent in systems engineering. Although the modeling is in an exploratory research stage and is not predictive, it is suggested that high- level models can be used to communicate risks inherent in new and ongoing systems engineering programs, as well as the potential effects of management and governance mitigation approaches. Key areas for further exploration include high- level modeling for systems engineering program diagnostics and early- stage assessment.
Adaptive dynamic surface-based differential games for a class of pure-feedback nonlinear systems with output constraints
Published in International Journal of Control, 2020
During the past decades, differential game as a mathematical tool for dealing with the problems of continuous dynamic conflict, competition or cooperation with two or more control actions has attracted increasing attention for researchers. Especially, the control has been formulated as a zero-sum differential game, where the control strategy is designed satisfying that the control input attempts to minimising a cost function, while the disturbance attempts to maximising the cost function. For nonlinear systems, the bottleneck of designing a differential game strategy is to find the Nash equilibrium solution of the associated Hamilton–Jacobi–Isaacs (HJI) equation that can be reduced as an algebraic Riccati equation for linear systems. Since the HJI equation is actually a partial derivative equation, it is usually intractable or impossible to find its analytical solution. Therefore, several methods have been developed to obtain the approximate solution of HJI equation.
Nash equilibrium and bang-bang property for the non-zero-sum differential game of multi-player uncertain systems with Hurwicz criterion
Published in International Journal of Systems Science, 2022
Xi Li, Qiankun Song, Yurong Liu, Fuad E. Alsaadi
Differential games involve multi-player multi-objective decisions in the context of dynamic systems. Isaacs (1965) made a pioneering work of differential games, and his work has inspired many researchers and has been developed over the years (Cappello et al., 2021; Gromova et al., 2021; Martin-Herran & Rubio, 2021). Non-zero-sum game, in which the sum of the gains or losses of all the players is not identically zero, plays a crucial role in differential game theory (Odekunle et al., 2020). Because of widespread applications in economics and finance, many researchers have carried out in-depth research focussing on the non-zero-sum differential game (Sadana et al., 2021; J. N. Zhang et al., 2021).
Quality control in food supply chain with dynamic quality characteristics
Published in Journal of Control and Decision, 2022
In game theory, differential games are a group of problems related to the modelling and analysis of conflict in the context of a dynamical system. Differential game model has been widely used in the field of supply chain management from different angles, such as goodwill, dynamic advertising, and carbon emission (Hu & Xu, 2019). Different from previous studies, our research establishes a differential game model to solve the quality control issue present in the food supply chain. For the coordination and dynamic quality control of the food supply chain, our study uses the Stackelberg game theory to establish the Stackelberg dynamic game model of the food supply chain.