## 1 Introduction  
Industry requires optimal operation procedures and advanced control systems to cope with the different factors that affect plant economics and process performance. The two-layer real time optimization strategy (RTO) has been successfully and widely applied in chemical processes for the economic optimization of plant operation. This process control architecture consists of the steady state real time optimization (RTO) of the trajectories for the regulated variables in terms of costs, in an upper level, followed by a model predictive controller (MPC) that executes the direct control actions on shorter time-scales, in a lower level [1; 2; 3]. Nevertheless, the steady state RTO approach may not be satisfactory in some cases leading to sub-optimal economic plant performance [4; 5; 6; 7; 8]. An important weakness of this approach is the inconsistency between the nonlinear steady-state models used in the RTO layer and the usual linear dynamic models used in the regulatory MPC layer. Another drawback is the delay in the optimization associated with the steady-state assumption in the RTO layer; because, it can produce an incorrect prediction of the operational point in the presence of frequent disturbances. The Dynamic Real Time Optimization (D-RTO) has been proposed to overcome the limitations of the stationary RTO for the dynamic nonlinear behavior of processes [9; 10]. In this context, the integration of RTO into model predictive controllers (MPCs) is an interesting alternative. The Model Predictive Control (MPC) technique has been successfully used in advanced control of chemical processes. The MPC algorithm translates the control problem into an optimization one. At each sampling time, the MPC algorithm calculates the appropriated sequence of future manipulated variable adjustments, carrying out an on-line optimization of the future plant behavior [11; 12]. An explicit process model is used to estimate the future response of the plant within a specific time horizon. A standard quadratic regulatory cost function is typically used, but it can be modified to quantify economic and/or operational objectives within the dynamic optimization problem [4; 13; 14; 15]. Moreover, constraints can be imposed not only on the admissible range of the inputs and control variables, but also, on decisions related to product quality, economic efficiency and general operating requirements. These particular characteristics of MPCs algorithm allow for the consideration of cost effectiveness criteria and optimal operation policies in the control problem formulation, leading to economic oriented MPCs [9]. The optimization of plant economic performance based on the integration of RTO and MPC has been addressed by in single level and two level strategies [7; 10]. In the single level strategies the economic optimization and control objectives are included in a single MPC algorithm in order to improve both economic and control performance in a cohesive manner. In Zanin [15], an optimizing MPC is defined to achieve both tasks by adding an economic objective term to the standard MPC objective function, observing that the one-layer procedure could react to frequent disturbances faster than the multilayer approach. However, a disadvantage of this procedure is that the incorporation of the economic objective turns the optimization problem, into a Nonlinear Programming (NLP) problem, where the objective function is nonlinear and there are nonlinear constraints corresponding to the steady-state model of the process system. Consequently, the expected computational effort required to compute the control sequence can be much higher than in the conventional MPC. As a solution, [PERSON] et al. [16] proposed a simplified version of the one-layer optimizing MPC. In their approach, the objective function of the MPC controller is also modified to include a term related to the economic objective, but the economic information is restricted to an estimation of the gradient of the economic objective.