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Brief description of the proposal

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 and Command Governors, 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 underlying the online command computation with respect to adversarial behaviors and, more in general, to 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.

All these complex systems have, as a common characteristic, the fact that they consist of a variety of spatially distributed interactive nodes representing sensors, actuators and subsystems, possibly dynamically coupled and connected via communication links, which need to be controlled and coordinated in order to accomplish their overall objective. The evolutions of the subsystems are typically subjected to safety, operative and coordination constraints that usually take the form of pointwise-in-time set-membership constraints on relevant variables of the subsystems, to be fulfilled during the CPS evolutions. The communication network is typically subject to latency, which is usually modeled abstractly as a time-varying time delay, and also packet dropouts may result in some adverse situations that make the distributed optimization and control problems challenging. Moreover, adversarial behaviors can disturb the systems. 

Amongst many, the one of main interest here is referred to in the literature as non-compliance. In particular, in the case of cooperative optimization, this might happen when one or more agents in the network do not cooperate because they selfishly want to have better performance. In other words, the adversarial agents might optimize a local cost with the goal to steer the iterates to a point that serves their own interest despite possible global performance worsening. Thus, the properties of the cooperative distributed schemes in supervising and coordinating the nodes of a constrained CPS will be investigated and, in particular, its ability to detect and isolate the malicious agent whenever possible.