Control barrier functions (CBFs) have recently become a powerful method for rendering desired safe sets forward invariant in single-agent and multiagent systems. In the multiagent case, prior literature has considered scenarios where all agents cooperate to ensure that the corresponding set remains invariant. However, these works do not consider scenarios where a subset of the agents are behaving adversarially with the intent to violate safety bounds. In addition, prior results on multiagent CBFs typically assume that control inputs are continuous and do not consider sampled-data dynamics. This article presents a framework for normally behaving agents in a multiagent system with heterogeneous control-affine, sampled-data dynamics to render a safe set forward invariant in the presence of adversarial agents. The proposed approach considers several aspects of practical control systems including input constraints, clock asynchrony and disturbances, and distributed calculation of control inputs. Our approach also considers functions describing safe sets having high relative degree with respect to system dynamics. The efficacy of these results are demonstrated through simulations.

This article presents a novel method for a class of multirobot networks to resiliently propagate vector messages from a set of leaders to all followers within the network in the presence of faulty or adversarially behaving robots. It is shown that the proposed method can operate under heterogeneous communication rates between robots and perturbations of the leaders’ propagated information. As a case study, the proposed method is applied to the problem of time-varying trajectory tracking; more specifically, time-varying reference trajectories in the form of Bezier curves are encoded into vectors of static parameters, which, in turn, are resiliently propagated from the leaders to the followers.

Several algorithms in prior literature have been proposed, which guarantee the consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the convex hull of initial normal agents’ states, with the exact consensus value possibly being unknown. In leader-follower consensus problems, however, the objective is for normally behaving agents to track a reference state that may take on values outside of this convex hull. In this paper, we present methods for agents in time-varying graphs with discrete-time dynamics to resiliently track a reference state propagated by a set of leaders, despite a bounded subset of the leaders and followers behaving adversarially. Our results are demonstrated through simulations.

There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of r- and (r,s)-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers and are sufficiently large. However, determining an arbitrary graph’s robustness is a highly nontrivial problem. This paper introduces a novel method for determining the r- and (r,s)-robustness of digraphs using mixed integer linear programming; to the best of the authors’ knowledge it is the first time that mixed integer programming methods have been applied to the robustness determination problem. The approach only requires knowledge of the graph Laplacian matrix, and can be formulated with binary integer variables. Mixed integer programming algorithms such as branch-and-bound are used to iteratively tighten the lower and upper bounds on r and s. Simulations are presented which compare the performance of this approach to prior robustness determination algorithms.