Feasibility of Optimal Formation Under Multiplicative Noise With Energy and Time Constraints

We investigate the problem of distributed optimal formation control in Multi-Agent Systems (MAS) affected by multiplicative noise, with energy and time constraints. We develop a globally optimal distributed formation control algorithm to achieve the expected formation while minimizing a comprehensive cost function that includes formation errors, energy consumption, and network costs. Additionally, we derive lower bounds for the achievable completion time and the required energy levels, expressed in terms of the convergence error, and the second smallest and largest eigenvalues of the Laplacian matrix. These bounds set practical criteria for formation tasks with constraints on energy and time. Finally, we provide simulation results to validate the effectiveness of the proposed approach.