Finite-Time Resilient Formation Control with Bounded Inputs

Abstract

In this paper we consider the problem of a multiagent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents can converge to a formation with respect to a set of leaders. The controller employs a norm-based filtering mechanism, and unlike most prior algorithms, also incorporates input bounds. In addition, the controller is shown to guarantee convergence in finite time. A sufficient condition for the controller to guarantee convergence is shown to be a graph theoretical structure which we denote as Resilient Directed Acyclic Graph (RDAG). Further, we employ our filtering mechanism on a discrete time system which is shown to have exponential convergence. Our results are demonstrated through simulations.

Finite-Time Consensus-Based Clock Synchronization Under Deception Attacks

“…In other words, a communication link (i, j) is said to be compromised by the deception attack if the message sent by node i is different from the message received by node j in the time iteration. Considering the fact that the adversary has limited capability in practice (i.e., the adversary does not have the complete capability to compromise all the communication links of the underlying networks), a widely adopted attack model is so called "F -local model" in the previous literature on multiagent consensus problems, for example, [13], [17], [23], [33]. In this work, we also consider that there exists an upper bound F on the number of compromised links of each node's incoming links.…”

“…The authors in [22] studied the attack tolerant finite-time consensus problems for continuous-time multi-agent networks under directed topologies. The authors in [23] studied the both continuous time and discrete time systems in the presence of misbehaving agents, and proposed a norm-based filtering mechanism which guarantees convergence in finite-time even with bounded inputs. However, it is important to remark that the convergence rates of consensus-based synchronization algorithms proposed by [19]- [23] can be influenced by the network connectivity, i.e., the second-smallest eigenvalue of the interaction graph Laplacian matrix.…”

“…Recently, iterative learning control (ILC) is regarded as an effective control strategy, which can give an alternate solution to solve the finite-time consensus problem. Different from existing works [19]- [23], the ILC-based consensus algorithm which fully utilizes the past control experience to improve the performance of consensus processes in the current iteration, not only has better robust to the connectivity of the inter-connection topology, but also has prescribed terminal time as desired [24]. Owing to its simplicity and effectiveness, ILCbased consensus has generated considerable interest over the past years [25]- [29].…”

Formally verified asymptotic consensus in robust networks

“…This algorithm provides asymptotic consensus in the presence of malicious agents. We have chosen to formalize this algorithm since it is a widely-used algorithm for resilient consensus [39,38,43,42]. From the perspective of practical applications, enabling resilient consensus in the presence of misbehaving or faulty nodes is desirable for many applications in autonomous systems and robotics, e.g., for coordinated control of multi-robot systems.…”

Resilient fixed-time bipartite consensus of multi-agent systems with nonlinear dynamics and directed graphs

“…38–40 In some research, the finite-time consensus of multi-agent systems in the presence of malicious nodes has been studied. 41–43 The resilient adaptive and H ∞ controls of multi-agent systems have been considered under sensor and actuator faults. 44 Some control strategies have been investigated for the networks with leader-following 45 and switching topology 46 in the presence of misbehaving nodes.…”