Leader selection for minimum-time consensus in multi-agent networks

• Published in: CDC : 2017 IEEE 56th annual Conference on Decision and Control : 12-15 December 2017 pp. 1036 - 1041
• Main Authors: Mulla, Ameer K., Anand, Deepak, Chakraborty, Debraj, Belur, Madhu N.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2017
• Subjects: Controllability; Convergence; Eigenvalues and eigenfunctions; Laplace equations; Multi-agent systems; Optimal control; Robustness
• DOI: 10.1109/CDC.2017.8263793

Leader selection for a single-leader, continuous-time multi-agent system, with single-integrator agents, is considered. A network of single integrator agents interact with each other according to the well studied asymptotic consensus law proposed by Olfati-Saber and Murray. In addition to the input prescribed by this consensus law, it is assumed that a bounded external input is allowed to act on only one (called the leader) of the agents. For each choice of leader, this bounded external input can be optimized to drive all the agents to a consensus state in the minimum possible time. This paper presents an algorithm for selecting a leader such that the time taken to reach consensus is the least among the minimum consensus times achievable by each leader. Recently developed Groebner basis based algorithms are used to calculate explicit set of polynomials which partitions each hyper-sphere in the statespace, centered at the origin; where each partition is identified with a particular leader node. The Groebner basis needs to be computed only once. To select the minimum time leader, these demarcating polynomials need to be evaluated at given initial condition exactly one time.