Adaptive Formation Tracking Control of Directed Networked Vehicles in a Time-Varying Flowfield Yang-Yang Chen * Southeast University, Nanjing, 210096, China, Kaiwen Chen † Imperial College London, London, SW7 2AZ, U.K. Alessandro Astolfi ‡ Imperial College London, London, SW7 2AZ, U.K. University of Rome, Tor Vergata, 00133 Rome, Italy Nomenclature R = the set of real numbers R n×m = the set of n × m matrices with real entries I = the identity matrix 0 = the zero matrix of appropriate dimension T = the one-torus k·k = the Euclidean norm |M | = the determinant of matrix M N = the Kronecker product p i = the position of vehicle i p xi = the position abscissa of vehicle i p yi = the position ordinate of vehicle i u i = the control input of vehicle i u xi = the control input of vehicle i along the abscissa u yi = the control input of vehicle i along the ordinate f i = the flow velocity at position p i and time t λ i = the path following error of vehicle i Ω i = an open set associated with vehicle i f αi = the flow amplitude at λ i f βi = the basis flow function evaluated at position p i and time t * Associate Professor, School of Automation and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, yychen@seu.edu.cn. † PhD Student, Department of Electrical and Electronic Engineering, kaiwen.chen16@imperial.ac.uk. ‡ Professor, Department of Electrical and Electronic Engineering and Department of Civil Engineering and Computer Science Engineering, a.astolfi@imperial.ac.uk