A solution for the cooperative formation-tracking problem in a network of completely unknown nonlinear dynamic systems without relative position information

In this paper, a solution of the formation-tracking problem is provided for a network that contains nonlinear agents with completely unknown dynamics and working under unknown disturbances. By the combination of a cooperative observer and an adaptive model-free controller, the requirement of inter-agent relative position information in the network is eliminated. Here, a cooperative observer is designed to estimate the time-varying reference trajectory and the time-varying parameters of the desired formation topology at each agent in the network. The stability of the proposed cooperative observer is analysed using Lyapunov analysis. Utilising the cooperative observer, the formation-tracking problem in the network of dynamic agents is transformed to a tracking problem in a single agent system. Moreover, an adaptive model-free control policy is applied to each agent for providing the tracking objective. Utilising the algebraic connectivity originating from graph theory, this model-free control algorithm is formulated to scale-up for a network of multi-agents. The proposed decentralised controller includes two model-free adaptive laws for online estimating of the completely unknown dynamics at each agent in the network. The application of the proposed solution is simulated for a network of four quadrotors with unknown internal dynamics and unknown external disturbances.