Vulnerabilities in Lagrange‐based distributed model predictive control

Abstract

Summary In this paper, we present an analysis of the vulnerability of a distributed model predictive control scheme. A distributed system can be easily attacked by a malicious agent that modifies the reliable information exchange. We consider different types of so‐called insider attacks. In particular, we analyze a controller that is part of the control architecture that sends false information to others to manipulate costs for its own advantage. We propose a mechanism to protect or, at least, relieve the consequences of the attack in a typical distributed model predictive control negotiation procedure. More specifically, a consensus approach that dismisses the extreme control actions is presented as a way to protect the distributed system from potential threats. Two applications are considered as case studies, ie, an academic example involving the control of a distributed system with a single coupled input and a distributed local electricity grid of households. The results are presented via simulations to illustrate both the consequences of the attacks and the defense mechanisms.

Resilient distributed model predictive control for energy management of interconnected microgrids

“…Note that the step of the dual-ascent method for computing the decision variables is carried out in step 4 and the step of the dual-ascent method for updating the Lagrange multipliers is carried out in step 6. Based on Lemma 1, since (10b) forms a compact polyhedral set and (10a) is strictly convex, the solutions coming from Algorithm 1, which are denoted by u ⋆ i, |k , for all i ∈  and ∈ {k, … , k + h p − 1}, converge to the optimal solution of Problem (10). Note that, in order to implement the algorithm (performing steps 3 and 5), it has been assumed that there exists a bidirectional communication between two neighboring agents, ie, for all i and j, where (i, ) ∈ .…”

“…Noncompliance of some agents in a network that applies a distributed approach has been discussed in some papers. 10,11 For instance, a secure dual-decomposition-based DMPC, in which each agent should monitor two neighbors that provide extreme control input values and disregard these extreme values, has been proposed. 10 Furthermore, a cyber-attack problem of a consensus-based distributed control scheme for distributed energy storage systems has also been addressed, 11 where the approach involves a fuzzy-logic-based detection and a consensus-based leader-follower distributed control scheme.…”

“…10,11 For instance, a secure dual-decomposition-based DMPC, in which each agent should monitor two neighbors that provide extreme control input values and disregard these extreme values, has been proposed. 10 Furthermore, a cyber-attack problem of a consensus-based distributed control scheme for distributed energy storage systems has also been addressed, 11 where the approach involves a fuzzy-logic-based detection and a consensus-based leader-follower distributed control scheme. Related to the cyber-security issue of cyber-physical systems, the work of Pasqualetti et al 12 provides a mathematical framework for attack detection and monitoring, particularly for deterministic systems.…”

“…Moreover, in this paper, we also provide a convergence analysis of the attack identification and mitigation method. Since the control approach considered in this paper is based on MPC, it is more related to the work of Velarde et al 10 than that of Sharma et al 11 However, different from the method proposed by Velarde et al, 10 our methodology deals with the attacks by computing control inputs that are robust with respect to such attacks. Furthermore, our approach is also able to identify the adversarial agents in certain cases and can also deal with more general systems in which there are more than one adversarial agent in the network.…”

Resilient Distributed Energy Management for Systems of Interconnected Microgrids

“…However, the methodology that we propose in this paper is different than that proposed in [7], in a way that it is more specific for the aforementioned problem and particularly for power systems. Moreover, unlike [7], our approach can deal with more than one adversarial agent in a network. This paper is structured as follows.…”