(709h) Feasibility Governor for Economic Model Predictive Control

The performance of chemical industries is typically assessed using economic-oriented criteria, such as profit, energy consumption, yields, and sustainability [1]. These economic criteria are usually affected by market fluctuation due to frequent changes in energy prices, costs, and production demands [1][2]. The conventional model predictive controller (MPC), which typically drives the system states to operate at a pre-defined steady-state, may not suffice to adapt to consistently changing economic criteria and achieve economically optimal operation [3]. To address this limitation, the economic model predictive controller (EMPC), which incorporates the economic criteria in the optimal control framework, has emerged as a promising framework. By leveraging the economic cost as the objective function, EMPC enables systems to operate in a consistently dynamic and transient way.

The stability of EMPC can be ensured by using a point-wise terminal constraint [4] or a terminal region constraint [3][5][6], both of which rely on the pre-calculation of an economically optimal equilibrium. Specifically, the point-wise terminal constraint requires the terminal state to be the pre-calculated equilibrium, while the terminal region constraint relaxes this requirement and allows the terminal state to lie in a region containing the equilibrium. However, the economically optimal equilibrium suffers from frequent changes due to the change of economic criteria caused by market fluctuation. In this case, when the current system states are far from the target equilibrium, the EMPC may become infeasible. To address this issue, several approaches have been proposed to improve the feasibility of EMPC with changing economic criteria. In [2][5], the point-wise terminal constraint was relaxed, which allows the terminal state to be any admissible equilibrium rather than a fixed, economically optimal equilibrium. [6] further extended the approach in [5] and proposed the generalized terminal region constraint, which allows the terminal state to lie in a terminal region around any equilibrium. In [7], a robust EMPC was proposed to account for changing economic criteria. In this method, the optimal equilibria in the terminal inequality constraints are treated as decision variables and jointly determined with optimal control input. It is noted that the above approaches require a redesign of the EMPC formulation.

Another promising framework to address the feasibility of EMPC is to leverage the feasibility governor (FG) [8][9][10]. Different from the methods in [2][5][6][7], the FG is an add-on scheme, which does not require modifications to the EMPC design. FG was initially introduced in [8] to address the feasibility of MPC. The key idea of FG is to modify the reference at each sampling instant to ensure that the terminal set of MPC remains reachable within the control horizon. The FG design was extended in [9], where the FG is designed by leveraging the information of the terminal set of MPC instead of the feasible set utilized in [8]. In [10], the terminal set FG was utilized to address the feasibility of preview. It is noted that the FG designs in [8][9][10] rely on the feasibility set or terminal set computation, which is challenging to obtain for nonlinear systems. To account for the nonlinear systems, [12] proposed a new FG design by leveraging the formulation of the explicit reference governor [11]. To the best of our knowledge, the feasibility of EMPC is typically addressed through modifications to its formulation [2][5][6][7]. The incorporation of FG with EMPC remains an unexplored direction.

Based on the above considerations, we address the feasibility of EMPC by proposing a feasibility governor-based EMPC (FG-EMPC). Our objective is three-fold: 1) to ensure the feasibility of EMPC with changing economic criteria using FG; 2) to guarantee the constraint satisfaction; 3) to achieve cost-effective system operation. The proposed FG-EMPC is applied to a simulated chemical process to demonstrate the effectiveness of the proposed FG-EMPC approach.

References
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