Paranormality is an observation property of a language, in which the occurrence of unobservable events never exits the closure of the language. In this paper, a synthesis method is proposed to construct a paranormal supervisor. We propose a method to construct a controllable language such that the occurrence of unobservable events does not exit the closure of the controllable language. Moreover, a new observation property, that is, Quasi Output Control Consistency (QOCC) is defined to construct the optimal (least restrictive) non-blocking decentralized supervisory control in the presence of unobservable controllable events. Using QOCC and natural observer properties, we propose a method to construct a normal supervisor such that an arbitrary pair of lookalike strings are initiated and terminated with identical observable and uncontrollable events. It is assumed that one of these strings has unobservable controllable events. An OCC property is defined in the literature as a special case of QOCC property, where none of the lookalike strings has unobservable controllable events.

Decomposition and localization of a supervisor are both reduction methods in distributed supervisory control of discrete-event systems. Decomposition is employed to reduce the number of events and localization is used to reduce the number of states of local controllers. In decomposition of a supervisor both observation and control scopes are restricted, whereas in localization only con-

Today, energy consumption and demand together with global warming are one of the most important challenges of human life. From the environmental point of view, the Heating Ventilation and Air Conditioning industry and current refrigerants are one of the important factors of global warming which need to be resolved. In terms of energy consumption, the main way is the development and use of renewable energy technologies which not only increases the efficiency of these systems but also generates diversification in energy resources. Among the various renewable energy systems, geothermal heat pumps offer significant potential to reduce energy consumption and also carbon dioxide emissions. The main purpose of this research is to select environmentally friendly refrigerants with the best performances. To assess the thermodynamic performance of organic refrigerants in geothermal heat pumps, this system is modeled using Engineering Equation Solver software. In this research, the results are compared with the results of the thermodynamic behavior of conventional refrigerants R22 and R134a for geothermal heat pumps with horizontal and vertical closed loop ground heat exchangers and also open-loop systems. Finally, R152a, R600, and R717 were introduced as substitute refrigerants to replace with synthetic refrigerants in the above-mentioned geothermal heat pump systems, resulted in an increase in 2.97–5.8 percent coefficient of performance in the cooling mode which means reducing the operating cost of the system compared to conventional artificial refrigerants.

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Distributed supervisory control is a method to synthesize local controllers without any restriction on observation of the plant. Since the set algebra preserves relationships between variables and provides a simpler way to develop theories, the observation properties are redefined and corresponding propositions are proved by set algebra, in this paper. Moreover, we define new observation properties, i.e. local normality and local relative observability for the local controllers which constructed by any localization algorithm that preserves control equivalent to monolithic supervisor w.r.t. the plant. These properties enable us to investigate the observation problem from monolithic to distributed supervisory control. Furthermore, observation equivalence property is defined corresponding to the control equivalence in distributed supervisory control with partial observation. It is proved that, providing observation equivalence of the local controllers to the monolithic supervisor w.r.t. the plant, the control equivalence is satisfied, if and only if the intersection of local events sets is a subset or equal to the global observable events set.

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