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# Distributed on-the-fly control of multi-agent systems with unknown dynamics: Using limited data to obtain near-optimal control

*Proceedings of the 6th Annual Learning for Dynamics & Control Conference*, PMLR 242:1440-1451, 2024.

#### Abstract

We propose a method called ODMU for “on-the-fly control of distributed multi-agent systems with unknown nonlinear dynamics” and with (a)synchronous communication between the agents where data from a single finite-horizon trajectory is used, possibly in conjunction with side information. ODMU can be applied to real-time scenarios when the dynamics of the system are unknown or suddenly change such that a priori known model cannot be applied. In our proposed algorithm, the agents communicate their states using (a)synchronous communication and exploit the side information, e.g., regularities of the system, states, agents’ communication scheme, algebraic limitations, and coupling in the system states. We provide ODMU for over-approximating the reachable sets and to control the agents under conditions with severely limited data. ODMU creates differential inclusion sets that calculate the over approximations of the reachable sets containing the unknown vector field. We show that ODMU calculates the near-optimal control and calculates an upper bound (suboptimality bound) for the error between the optimal trajectory and the trajectory calculated by ODMU. We use convex-optimization-based control to obtain the guaranteed near-optimal solution. We demonstrate the effect of side information on obtaining smaller bounds on suboptimality by applying ODMU on a system of unicycles. Additionally, we present a case study where a multi-agent system of unicycles with unknown dynamics is controlled via ODMU. Moreover, we have developed two baselines, SINDYcMulti and CGP-LCBMulti to compare our method with them.