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.
In the approach we envision, the distributed algorithms should be able to operate optimally when attacks are not present, but should react to anomalous situations by means of suitable corrective actions when the signals received by neighboring agents appear to be incompatible with a priori modeling assumptions. We recently developed filters that can enforce compatibility of gradient information communicated through a channel with a priori unknown convex cost functionals. We plan to adopt such filters in the context of EMPC and complement this with further recently developed tools in resilient optimization.
Task 2.2: Self-interested agents in Economic MPC
When multiple systems operate in a shared environment while executing complex tasks, coupling and interaction among them open up the need and opportunity for simultaneous optimization of several, possibly conflicting, objectives. This is a shift from centralized optimization (with a unique objective) to a distributed setting where individual agents need to assess and devise strategies to pursue their individual objectives directly cooperating or competing with other agents which may have similarly aligned or conflicting goals. Our research aims at addressing the following issues:
- Coalition formation: it is known that Nash equilibria may result in highly suboptimal overall performance, (the price of anarchy). Coalitional game theory allows studying the formation of coalitions of self-interested agents to devise rational distributed decisions. These concepts will be used to bridge the gap between competitive equilibria and altruistic socially optimal behaviors that, on the other hand, challenge our notion of fairness. We aim to adopt virtual side payments and transferable utilities, so that agents might willingly sacrifice their own level of performance through suitable compensations from “allied” agents, whenever beneficial for the coalition they belong to. This will enhance the system’s performance by enlarging the region of feasible operation.
- Distributed mechanism design: distributed social optimization among heterogeneous agents that lack trust in each other is a challenging research question, as standard distributed optimization exposes the system's performance to greedy agents which inflate individual costs in order to distort the social optimum towards their individual preferences.
Realignment of societal and individual interests can be achieved through contracts that bind agents to payments in proportion to the damage their individual preferences cause to society. The so-called VCG mechanism achieves this realignment but is normally formulated in a centralized context and as a one-shot game. Recasting it in a decentralized scenario and within a receding horizon approach is an open problem that could greatly enhance the security and trust in distributed optimization protocols, thus expanding their applicability.
