Non-cooperative intelligent control agents (ICAs) with dedicated cost functions, can lead the system to poor performance and in some cases, closed-loop instability. A robust solution to this challenge is to place the ICAs at the feedback Nash equilibrium point (FNEP) of the differential game between them. This paper introduces the designation of a robust decentralized infinite horizon LQR control system based on the FNEP for a linear time-invariant system. For this purpose, two control strategies are defined. The first one is a centralized infinite horizon LQR (CIHLQR) problem (i.e. a supervisory problem), and the second one is a decentralized control problem (i.e. an infinite horizon linear-quadratic differential game). Then, while examining the optimal solution of each of the above strategies on the performance of the other, the necessary and sufficient conditions for the equivalence of the two problems are presented. In the absence of the conditions, by using the least-squares error criterion, an approximated CIHLQR controller is presented. It is shown that the theorems could be extended from a two-agent control system to a multi-agent system. Finally, the results are evaluated using the simulation results of a Two-Area non-reheat power system.

In this paper, the dual fuzzy equation modeling is considered to determine the fuzzy equilibrium point of the market. By defining three sets of solutions for the dual fuzzy equations, the minimum symmetric fuzzy price, the maximum symmetric fuzzy price and the asymmetric fuzzy price are obtained, and accordingly, the fuzzy equilibrium point of the market and fuzzy supply and demand functions are calculated, and by proposing a theorem, the conditions under which the dual fuzzy equations considered to determine the fuzzy market price always have fuzzy solutions are presented. By discussing the drawbacks of the previous method of calculating the fuzzy market price, it is demonstrated that the method proposed in this paper has resolved the disadvantages. Finally, numerical examples show the efficiency and superiority of the proposed method.

In this paper, the dual fuzzy equations modeling is considered to determine the fuzzy equilibrium point of the market. By defining three sets of solutions for the dual fuzzy equations, the minimum symmetric fuzzy price, the maximum symmetric fuzzy price and the asymmetric fuzzy price are obtained, and accordingly, the fuzzy equilibrium point of the market and fuzzy supply and demand functions are calculated, and by proposing a theorem, the conditions under which the dual fuzzy equations considered to determine the fuzzy market price always have fuzzy solutions are presented. By discussing the drawbacks of the previous method of calculating the fuzzy market price, it is demonstrated that the method proposed in this paper has resolved the disadvantages. Finally, numerical examples show the efficiency and superiority of the proposed method.

The purpose of this research is to develop the outsourcing model of the bank's electronic banking services using game theory to identify the equilibrium and win-win strategies between the bank and the applicant companies. For this purpose, an interview was held with bank and company experts. After qualitative data analysis,16 strategies were identified for the parties. According to the compatibility of the identified strategies with the marketing mix, the results were grouped into 4 product groups, price, distribution and promotion. Since the identified strategies did not have the same value for the parties, to identify the weight of the strategies. A pairwise comparison questionnaire was used and the opinions of experts from each side were collected separately. The analytical Hierarchy process was used to obtain the weight of each index and the Inconsistency Ratio index was used to check the reliability of the obtained results. After identifying the weight of the strategies, the game environment was implemented and according to the 16 identified strategies, 65536 scenarios were implemented for each side. After performing calculations, 8 scenarios with the same outcomes were identified as equilibrium scenarios or Nash Equilibrium games. The scenario that had the most consequences for the parties was introduced as the result of the game.

Based on the extragradient-like method combined with shrinking projection, we propose two algorithms, the first algorithm is obtained using sequential computation of extragradient-like method and the second algorithm is obtained using parallel computation of extragradient-like method, to find a common point of the set of fixed points of a nonexpansive mapping and the solution set of the equilibrium problem of a bifunction given as a sum of the finite number of H ̈, older continuous bifunctions. The convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for the bifunction and its summands.

Unlike perfect competitive markets, in oligopoly electricity markets due to strategic producers and transmission constraints GenCos may increase their own profit through strategic biddings. This paper investigates the problem of developing optimal bidding strategies of GenCos considering participants' market power and transmission constraints. The problem is modeled as a bi-Ievel optimization that at the first level each GenCo maximizes its payoff through strategic bidding and at the second level, in order to consider transmission constraints a system dispatch is accomplished through an OPF problem. The AC power flow model is used for proposed OPF. Here it is assumed that each GenCo uses linear supply function model for its bidding and has information about initial bidding of other-competitors. The impact of optimal biddings on market characteristics as well as GenCos' payoffs are investigated and compared with perfect competitive markets where all the participants bid with their marginal costs. Furthermore, effects of exercising market power due to transmission constraints as well as different biddings of strategic generators on GenCos' optimal bidding strategies are presented. Finally IEEE-30 bus test system is used for case study to demonstrate simulation results.

In the present work, the flash points of binary systems (ethanol+n-octane, 1 -propanol+n-octane, 1-propanol+ n-decane, and n-octane+ n-decane) were measured in atmospheric pressure. The resulting flash points data were used in NRTL, Wilson and UNIQUAC models to calculate the mixture binary parameters. The results were subsequently compared with experimentally produced VLE data, and revealed that this method is able to predict the binary interaction parameters of binary mixtures with high accuracy.