The Research Units (RUs) involved in this project are well known and reputed in the international control community for their past and recent contributions in EMPC [1], CG [2] and underlying Optimization Methods, which provide here the baseline concepts, ideas and solutions for the advancement envisaged. Recently Prof. Angeli, in close collaboration with leading international academics, has brought to the attention of the scientific community a new control paradigm with the potential of significant improvement in sustainability and profitability margins for industrial applications, [3-5]. The so-called Economic Model Predictive Control is an Optimization-based control design technique that allows complete freedom in the design of the cost functionals adopted by a Receding Horizon Controller so as to match (for instance) those normally employed by static Real-Time Optimization layers. This achieves the simultaneous and coherent optimization of a system's transient response and steady-state regime of operation. In summary, this approach enables achieving the maximum efficiency of an existing plant. At the same time, it opens up the possibility for plant and controller co-design to explore the limits of currently available technological solutions for any specific industrial application where advanced control systems are deployed. While traditional MPC's robustness has been thoroughly investigated and enhanced by appropriate design, analyzing and improving the resilience of Economic MPC is a major step forward needed to deliver the full potential of Economic MPC and improve its practical and reliable applicability, particularly in a distributed set-up. The CG approach has been introduced in [6] for the constraint control of linear time-invariant regulated plants.
The CG is a nonlinear device that, on the basis of future system predictions, is in charge to modify the nominal reference signal applied to a regulated system whenever its application would produce a violation of prescribed pointwise-in-time set-membership constraints on some output of interest. Since then, this concept has been extended in several directions over [2] and most of these studies have been recently surveyed in [1] along with some interesting applications. Among many, the CG studies of interest here are the non-cooperative distributed CG schemes developed for CPSs, mainly developed by the UniCAL RU of this project in recent years. In [7], a non-cooperative non-iterative game-theoretical approach was used to single-out a sequential distributed CG approach for supervising and coordinating CPSs. The sequential attribute means that a round-robin policy is adopted to orchestrate the command whereas the term non-iterative denotes the adopted local optimization scheme, which doesn’t require data exchange among the optimization iterations. The kind of optimality of the solutions has been further investigated in [8], where a non-cooperative iterative parallel distributed scheme was presented. In iterative methods, all agents interleave several optimization iterations and data exchange before arriving at the optimal solution. Finally, Plug&Play functionalities and time-varying constraints have been considered in [9].
Many fundamental problems of modern Cyber-Physical Systems can be stated as optimization problems such as estimation, decision, learning and control applications (see i.e. [10] and references therein). To solve optimization problems over CPSs, the challenges have originated a novel branch of research termed distributed optimization. Most of the distributed optimization algorithms are designed leveraging consensus-based approaches [11] and gradient tracking techniques [12]. The common assumption is that all agents cooperate to seek a minimizer. In practical scenarios of CPSs, some agents may become adversarial or faulty due to cyber or physical attacks. Therefore, a major concern is to guarantee resilience with respect to malicious agents able to attack the Cyber layer and the Physical layer [13]. This has been a driving force to the formulation of resilient consensus approaches and related distributed optimization algorithms such that, in the event of an attack in which some nodes are compromised, the remaining (healthy) nodes are still able to achieve their objective [14-17, 18]. Specifically, in the literature, distributed optimization algorithms are proposed to allow the non-adversarial nodes to converge to a certain region surrounding the true minimizer, regardless of the adversaries’ actions [12, 19]. In addition, limited node energy and computing capacity, link failures and delay variations, all make resilience and reliability more challenging for the applicability of consensus-based distributed optimization algorithms to real scenarios of CPSs [10, 13].
