Receding Horizon Control in Deep Structured Teams: A Provably Tractable Large-Scale Approach with Application to Swarm Robotics

In this paper, a deep structured tracking problem is introduced for a large number of decision-makers. The problem is formulated as a linear quadratic deep structured team, where the decision-makers wish to track a global target cooperatively while considering their local targets. For the unconstrained setup, the gauge transformation technique is used to decompose the resultant optimization problem in order to obtain a low-dimensional optimal control strategy in terms of the local and global Riccati equations. For the constrained case, however, the feasible set is not necessarily decomposable by the gauge transformation. To overcome this hurdle, we propose a family of local and global receding horizon control problems, where a carefully constructed linear combination of their solutions provides a feasible solution for the original constrained problem. The salient property of the above solutions is that they are tractable with respect to the number of decision-makers and can be implemented in a distributed manner. In addition, the main results are generalized to cases with multiple sub-populations and multiple features, including leader-follower setup, cohesive cost function and soft structural constraint. Furthermore, a class of cyber-physical attacks is proposed in terms of perturbed influence factors. A numerical example is presented to demonstrate the efficacy of the results.