## 1 Introduction
### Joint Applications of FC and RL  
Several applications where FC and some sort of learning or self-tuning procedures are applied synergistically have been found. However, this synergy does not seem to be often exploited in energy systems. A few non-exhaustive examples of the joint application of the two techniques are: the optimization of the data traffic in a wireless network [52]; the tuning of a fuzzy navigation system for small robots [53]; the robust control of robotic manipulators [54]; and the PI and PD controllers' tuning [55; 56]. All these papers refer to an adaptation of the Q-learning algorithm called Fuzzy Q-learning [57; 58]. [PERSON] et al. [59] applied this algorithm also to manage energy flows in micro-grids. Other applications where fuzzy logic is coupled to other self-learning approaches are: Reference [60], where actor-critic learning, neural networks, and fuzzy inference mechanism are used to design an adaptive goal-regulation mechanism for future manufacturing systems; Reference [61], where RL and the adaptive neural fuzzy inference system (ANFIS) are used to implement a non-arbitrage algorithmic trading system; the inspiring work of [PERSON] et al. [62], where an on-line learning procedure is implemented to adapt the number and shape of input linguistic terms and the position of the output singletons of a vehicle cruise control system FC; and Reference [63], where an iterative procedure called iterative learning tuning, based on minimization of a cost function, is used to tune the singletons output membership functions of a monocycle controller. Integration of reinforced learning and fuzzy logic at high level is found in the work of [PERSON] et al. [64], where these techniques are used to demonstrate the feasibility of what is called artificial cognitive control architecture. The paper describes the design of the architecture and its implementation to an industrial micro-drilling process. The work is an excellent example of how the tools and concept of theoretical computer science and cognitive sciences can be applied to the control of complex industrial systems. Details about the design of the reinforced learning component of the cognitive controller are found in the Reference [65].  
In the field of energy systems for buildings, an interesting work by [PERSON] and [PERSON] [66] appeared, where the authors present the application of RL to tune a supervisory fuzzy controller for a low-energy building. In this work, the authors showed an application of online learning scheme based on pre-generated fuzzy rule-based. Here, the learning process is accelerated with the use of the Q(\(\lambda\)) algorithm with a fuzzy state variable and eligibility traceback. The successful application of RL to the supervisory control of buildings is strongly dependent on reducing the state space and action space of the controller. As reported in other papers, the importance of off-line learning is underlined, included in this case in the knowledge used to devise the fuzzy controller rules. The approach based solely on the online learning takes an unacceptably long training time.  
The above discussion suggests that despite its potentiality, the application of an FL control and RL to thermal energy systems is lacking (Table 1). It seems, therefore, reasonable to investigate their application to this type of system.