## 1 Introduction  
Wastewater treatment plants (WWTPs) are a very complex process operated to obtain an effluent from the wastewater that can be returned to the water cycle with a minimal impact on the environment. An efficient operation of WWTPs should also guarantee minimization of the operational costs and the sludge production. The control systems used to achieve these goals have a strong impact on the efficiency and operation of the WWTP. A conventional WWTP is composed of different treatment stages and processes linked to each other. Usually these treatment stages are as follows: pre-treatment, primary, secondary and tertiary treatment [1]. In the pre-treatment stage, large debris is removed from the raw wastewater. In the primary treatment stage, smaller particles such as the settable solids and floatable materials from the effluent are removed. Secondary treatment involves complex biological processes that are used to remove refractory solids, such as sludge, that were not removed during primary treatment. Some WWTPs provide only secondary treatment and when this treatment ends, the effluent is disinfected and released to the environment. If the WWTP provides tertiary treatment process, once the secondary effluent is transferred, additional unwanted constituents (for instance, phosphorus or nitrogen) are removed to meet some regulatory requirements. Sludge removed in the secondary treatment is further treated in a separate sludge digestion process. This process is very important during the design and operation of all WWTPs. It is fundamental to reduce its volume and to stabilize the organic materials. Stabilized sludge can be better manipulated and a volume reduction implies a decrease in the costs of pumping and storage. Different types of biological WWTPs treatments can be found [2]. However, each treatment can be classified as aerobic, anaerobic, or anoxic treatment depending on whether oxygen is used or not. The most typical secondary wastewater treatment plant is the activated sludge process (ASP). It uses microbial degradation for the digestion of soluble organic constituents within primarily treated effluent. In our paper, the BSM1 is used as the benchmark scenario to implement the control strategies [3], as it is one of the most popular in the literature for WWTPs. The plant layout represents the ASP, one of the most demanding process in a WWTP with nitrification/denitrification stages [4]. It is composed of activated sludge reactors in series, followed by a clarifier. The first two reactors are non-aerated and the other three are aerobic tanks [3]. WWTPs operate by controlling the values of certain variables that are returned by sensors located in the plant. In the ASP, several variables are considered [5; 6; 7]: dissolved oxygen concentration, ammonia concentration, internal recycle flow rate, sludge recycle flow rate or external carbon dosing. Among all these variables, dissolved oxygen concentration (DO) is the one in charge of the most expensive cost of the plant [5; 8]. In aerobic treatment, blow oxygen is supplied in the aeration tank to speed up the degradation process, which implies an important energy demand. Therefore, the DO content in the aeration tank is an essential control test. The most widely used approach to control different variables in WWTPs is PID controllers [9; 10; 11; 12]. However, due to the complexity of WWTP processes and the big differences in external conditions, the performance of PIDs is not optimal [13], especially when operational cost is a major concern [14]. More advanced control techniques have also been proposed for WWTPs, such as model predictive control or fuzzy-logic control [15; 16]. In fact, artificial intelligence approaches such as artificial neural networks [17; 18; 19; 20; 21] or reinforcement learning [22] have been applied in the last decade [23; 24]. In addition, among artificial intelligence techniques for industrial applications, deep learning techniques are increasing in popularity.