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 project aims at providing methodological advancements on a class of distributed optimization-based control and supervisory design methodologies referred to in the literature as Economical Model Predictive Control (EMPC) [1] and Command Governors (CGs) [2], which have been proved to be suitable for addressing constrained supervisory and control problems for Cyber-Physical Systems (CPSs). These advancements will concern especially the resilience of the Optimization Algorithms [3] underlying the online command computation with respect to the uncertainty in the shared data arising naturally for different causes in the distributed context of CPSs. The latter system paradigm, where cyber and physical aspects coexist and influence each other, has received in the last years increasing interest from the international control community for its ability to describe complex phenomena arising in modern engineering systems, applications and services as large-scale industrial plants, power grids, water distribution infrastructures and intelligent transportation systems to name a few, collectively giving rise to the so-called Smart-World [20].
Task 1.1 Resilient Cooperative Distributed Iterative CG Schemes
The goal of this task is the study and development of a cooperative distributed CG scheme for the supervision of constrained CPSS. Each cooperative node supervises a physical subsystem and computes the commands by solving, with local and other data provided by the neighboring nodes, an optimization problem that reflects the global performance of the whole CPS and not only that of the local node. Typically, the optimization is performed cooperatively and iteratively by the involved nodes and requires performing some data exchange with the neighbors, where the privacy issues can be prevalent in some applications. The optimization procedure has to be proved to converge to a suitable global optimal solution and the applications of the corresponding optimal commands have to ensure the global stability of the CPS. The problem is complicated by the presence of malicious nodes that can adversely affect the solution and the CPS performance.
Task 2.1: Resilience in distributed Economic MPC
We aim to design distributed EMPC protocols that are robust with respect to exogenous attacks and/or corrupted information across communication channels. Many emerging applications entail a multitude of agents which interact with each other and need to coordinate in order to improve the overall system's performance. While this could be achieved under standard operating conditions, the use of distributed protocols exposes the agents to the possibility of attacks or faults which could significantly deteriorate the system's performance or even compromise the safety of operation. State-of-the-art distributed EMPC algorithms assume perfect information and neglect the possibility of exogenous disturbances or malicious attacks.
Task 3.1: Mean Subsequence Reduced (MSR) Algorithms for Resilient Distributed Optimization
Most of the resilient protocols proposed in the literature leverage the so-called mean subsequence reduced (MSR) algorithm, mainly known for its simplicity and scalability [18]. MSR algorithms simply order solution estimations in ascending (or descending order) and remove F top and lowest values from the ordered list, where F is an a-priori fixed bound to the number of malicious agents. Then, the average among the remaining values is computed and a standard linear consensus update equation is applied. The key idea in most of these existing algorithms is to avoid utilizing malicious states broadcast by adversarial agents to guarantee that the final state is within the interval of the smallest initial state and the largest one.
Task 4.1: Distributed Scheduling of Flexible Demand in Smart Grids
In recent years, following environmental concerns and technological developments, power systems have been undergoing significant changes, moving from a traditional centralized structure towards the distributed and decentralized concept of the “smart grid”. As a consequence, in the near future, energy generation will be subject to an increasing level of uncertainty and decentralization. In order to guarantee a reliable operation of the grid and achieve efficient utilization of its current assets, it will be necessary to rethink the current centralized approach and involve other entities, such as storage or flexible demand, in the network’s operation. This case study aims at designing decentralized control strategies for the efficient integration of flexible demand in power systems.
This WP will be devoted to disseminating the results of the project and coordinating its activity. A website associated with the project will be developed for the wide diffusion of its activities. The website will have a restricted area through which the research units can exchange and archive the material (e.g. software, reports, etc.) during the course of the project. Several workshops on the topics of the project will be organized during international conferences in order to stimulate the research activities and to make the community aware of the project developments. The activities of the project will be extensively documented in peer-reviewed journals and presented at international conferences. The models, algorithms and data used in the case studies will be freely released on the website of the project for providing benchmarks to the research community and allowing a public assessment of the performance and further investigations. Regular (at distance) meetings will take place frequently to make the research units aware of the project developments. General project meetings will take place at the end of each year hosted by each RU.
