Attacking the V: On the Resiliency of Adaptive-Horizon MPC

Abstract

Abstract. We introduce the concept of a V-formation game between a controller and an attacker, where controller's goal is to maneuver the plant (a simple model of flocking dynamics) into a V-formation, and the goal of the attacker is to prevent the controller from doing so. Controllers in V-formation games utilize a new formulation of model-predictive control we call Adaptive-Horizon MPC (AMPC), giving them extraordinary power: we prove that under certain controllability assumptions, an AMPC controller is able to attain V-formation with probability 1. We define several classes of attackers, including those that in one move can remove R birds from the flock, or introduce random displacement into flock dynamics. We consider both naive attackers, whose strategies are purely probabilistic, and AMPC-enabled attackers, putting them on par strategically with the controllers. While an AMPC-enabled controller is expected to win every game with probability 1, in practice, it is resourceconstrained : its maximum prediction horizon and the maximum number of game execution steps are fixed. Under these conditions, an attacker has a much better chance of winning a V-formation game. Our extensive performance evaluation of V-formation games uses statistical model checking to estimate the probability an attacker can thwart the controller. Our results show that for the bird-removal game with R = 1, the controller almost always wins (restores the flock to a V-formation). For R = 2, the game outcome critically depends on which two birds are removed. For the displacement game, our results again demonstrate that an intelligent attacker, i.e. one that uses AMPC in this case, significantly outperforms its naive counterpart that randomly executes its attack.

Distributed adaptive-neighborhood control for stochastic reachability in multi-agent systems

“…The result presented in [13] applied to our distributed model, together with Theorem 1, ensure the validity of the following corollary.…”

“…The average convergence duration, horizon, and neighbors, respectively, increase monotonically when we consider more birds, as one would expect. The average neighborhood size is smaller than the number of birds, indicating that we improve over AMPC [13] where all birds need to be considered for synthesizing the next action. We also observe that the average number of for good runs until convergence 3.69 5.32 6.35 5.00 7.00 9.00 for good runs over m steps 3.35 4.86 5.58 5.00 7.00 9.00 for good runs after convergence 4.06 5.79 6.75 5.00 7.00 9.00 for bad runs 4.74 6.43 6.99 5.00 7.00 9.00 neighbors for good runs until convergence is larger than the one for bad runs, except for 5 birds.…”

“…Beyond this horizon, however, PSO is allowed to freely choose the accelerations, that is, the MDP M is fully controllable again. The result now follows from convergence of AMPC (Theorem 1 from [13]).…”

“…4) ensuring convergence to a global optimum. If h max is reached before the cost of the flock was decreased by ∆, the size of the neighborhood will be increased by one, and eventually it would reach B. Consequently, using Theorem 1 in [13], there exists a horizon h max that ensures global convergence. For this choice of h max and for maximum neighborhood size, the cost is guaranteed to decrease by ∆, and we are bound to proceed to the next level in DAMPC.…”

“…Recent work on V-formation has shown that the problem can be viewed as one of optimal control, model-predictive control (MPC) in particular. In [13], we introduced adaptive-horizon MPC (AMPC), a highly effective control algorithm for multi-agent cyber-physical systems (CPS) modeled as a Markov decision process (MDP). Traditional MPC uses a fixed prediction horizon, i.e.…”