  We present recent results that demonstrate the power of viewing the problem
of V-formation in a flock of birds as one of Model Predictive Control (MPC).
The V-formation-MPC marriage can be understood in terms of the problem of
synthesizing an optimal plan for a continuous-space and continuous-time Markov
decision process (MDP), where the goal is to reach a target state that
minimizes a given cost function. First, we consider ARES, an approximation
algorithm for generating optimal plans (action sequences) that take an initial
state of an MDP to a state whose cost is below a specified (convergence)
threshold. ARES uses Particle Swarm Optimization, with adaptive sizing for both
the receding horizon and the particle swarm. Inspired by Importance Splitting,
the length of the horizon and the number of particles are chosen such that at
least one particle reaches a next-level state. ARES can alternatively be viewed
as a model-predictive control (MPC) algorithm that utilizes an adaptive
receding horizon, aka Adaptive MPC (AMPC). We next present Distributed AMPC
(DAMPC), a distributed version of AMPC that works with local neighborhoods. We
introduce adaptive neighborhood resizing, whereby the neighborhood size is
determined by the cost-based Lyapunov function evaluated over a global system
state. Our experiments show that DAMPC can perform almost as well as
centralized AMPC, while using only local information and a form of distributed
consensus in each time step. Finally, inspired by security attacks on
cyber-physical systems, we introduce controller-attacker games (CAG), where two
players, a controller and an attacker, have antagonistic objectives. We
formulate a special case of CAG called V-formation games, where the attacker's
goal is to prevent the controller from attaining V-formation. We demonstrate
how adaptation in the design of the controller helps in overcoming certain
attacks.
