Distributed Modifier-Adaptation Schemes for the Real-Time Optimization of Interconnected Systems in the Presence of Structural Plant-Model Mismatch

The desire to operate chemical processes in a safe and economically optimal way has motivated the development of so-called real-time optimization (RTO) methods [1]. For continuous processes, these methods aim to compute safe and optimal steady-state setpoints for the lower-level process controllers. A key challenge for this task is plant-model mismatch. For example, in the case of a model that is assumed to be structurally identical with the plant but has unknown parameters, the so-called two-step approach [2-4] has been proposed. It repeats two steps: In the first step, plant measurements are used to identify the parameters of the model. In the second step, the economically optimal setpoints for the updated process model are determined by solving an optimization problem. Unfortunately, a structurally correct process model is rarely available in practice. In that case, the optimal setpoints for the model determined by the two-step approach may not be optimal for the plant. To overcome this problem, the so-called modifier-adaptation (MA) methods have been developed [5]. In MA, no structurally correct model is required. Instead, plant measurements are used to formulate and solve a modified optimization problem at each iteration, such that, upon convergence, the first-order optimality conditions of the plant are guaranteed to be satisfied [5]. These and other available RTO methods usually treat the plant as a single entity, and compute the optimal setpoints in a centralized manner. However, this approach may be suboptimal or even infeasible for an increasing number of applications involving so-called interconnected systems. Interconnected systems are here defined as systems composed of subsystems that exchange material, energy or information, such as compressor networks, teams of autonomous vehicles or large industrial parks, in which different business units of a chemical company share certain resources. In these cases, distributed RTO methods can be employed, which utilize the available interconnection variables and exploit the inherent interconnection structure of the particular system. Only a few distributed RTO methods have been reported in the literature, including the methods proposed by Brdys and Tatjewski [6]. Just as in the two-step approaches, structurally correct models are assumed. In addition to identifying the model parameters, the methods also try to estimate the values of the interconnection variables. Consequently, these methods may not yield the plant optimum in the presence of structural plant-model mismatch. In this contribution, we propose a set of distributed RTO methods based on the modifier-adaptation framework for interconnected systems in the presence of structural plant-model mismatch. Thanks to the modifier-adaptation framework, all proposed distributed RTO methods are able to reach the plant optimum upon convergence despite possible plant-model mismatch. The proposed schemes employ differen