Network-based deployment of multi-agents without communication of leaders with multiple followers: a PDE approach

Recently, a PDE-based deployment of multi-agents was suggested that employed transmission of control signals from leaders to other agents which may be expensive and not secure. In this paper we propose a solution to the deployment problem that avoids the latter transmission. In our consideration, only two boundary agents (leaders) measure their absolute positions that they send through communication network to the controller and receive their control signals from the controller via communication network. Our design employs network-based finite-dimensional control of 1D heat equation under two Neumann actuations by using two boundary measurements.