## 1 Introduction
Furthermore, classical RL algorithms require a large amount of data to obtain suitable policies. Therefore, applying RL to complex problems is not straightforward, as the combination of reinforcement learning algorithms with function approximation is currently an active field of research. A detailed description of RL methodologies in continuous state and action spaces is given in [18]. Recently, in the literature, research works have been published showing that, in particular, RL based on neural network schemes combined with other techniques can be used successfully in the control and monitoring of continuous processes. In [11; 19; 20; 21] strategies for wind turbine pitch control using RL, lookup tables, and neural networks are present. Specifically, in [11], controlling the direct angle of the wind turbine blades is considered, some hybrid control configurations are proposed. Neuro-estimators improving the controllers, together with the application of some of these techniques in a terrestrial turbine model, are shown. Other control solutions with RL algorithms and without the use of models can be found in [22], among others. In cooperative control, advances have also used RL. Thus, in [7], a cooperative wind farm control with deep reinforcement learning and knowledge-assisted learning is proposed with excellent results. In addition, in [23], a novel proposal is made for high-level control. RL based on RNAs is used for high-level agent negotiation within a distributed model predictive control (DMPC) scheme implemented in the lower layers to control a system level composed of eight interconnected tanks. Negotiation agent approaches based on reinforcement learning have advantages over other approaches, such as genetic algorithms that require multiple tests before arriving at the best strategy [24] or heuristic approaches in which the negotiation agent does not go through a learning process [25]. Negotiation approaches based on reinforcement learning often employ the Q-learning algorithm [26], based on the value function, which predicts the reward that an action will have given a state. This approach is the case in [27], in which a negotiation agent is proposed based on a Q-learning algorithm that computes the value of one or more variables shared between two MPC agents. On the other hand, there are those based on policies, a topic addressed in this work, which directly predict the action itself [28]. One of these algorithms is the Policy Gradient (PG) [17], which directly parameterizes a policy by tracing the direction of the ascending gradient [16]. In addition, PG employs a deep neural network as a policy approximation function and works in sizeable continuous state and action spaces. Local MPCs of a DMPC control make decisions based on local objectives. For this reason, consensus between local decisions is necessary to achieve global objectives to improve global index performance. In particular, in this paper, a negotiation agent based on RL manages the negotiation processes among agents of local MPCs to improve a global behavior index of a plant composed of eight interconnected tanks. Given this, the PG-DMPC algorithm within a deep neural network trained by the Policy Gradient (PG) algorithm [29] is proposed and implemented in the upper-level control layer within the control architecture. Therefore, the decision to implement the PG algorithm as a negotiation agent is based on the following advantages: not requiring knowledge of the model, the ability to adapt to handle the uncertainty of the environment, the convergence of the algorithm is assured, and few and easy understanding of tuning parameters. The remainder of this paper is organized as follows: The problem statement in Section 2. Section 3 presents the RL method, the PG-DMPC algorithm, and DMPC from the low-level control layer. Moreover, Section 4 shows the case study, negotiation framework, the training of the negotiation agent, and performance indexes. Section 5 presents the results. Finally, Section 6 provides conclusions and direction for future work.