Fixed-Time and Prescribed-Time Consensus Control of Multiagent Systems and Its Applications: A Survey of Recent Trends and Methodologies

Fixed-time and prescribed-time consensus control can bring an explicit estimate of the settling time without dependence on initial conditions, which is important in providing control engineers <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> system information. This article aims at presenting a survey of recent trends and methodologies of fixed-time and prescribed-time consensus control in multiagent systems. First, some typical fixed-time consensus results are reviewed. Despite the advantage in deriving a fixed settling time bound, fixed-time consensus controllers usually result in a conservative estimate of the bound and a large magnitude of initial control input, which in turn show the necessity of designing prescribed-time consensus controllers. Second, characteristics and controller design of (practical, respectively) prescribed-time consensus are provided in detail. Particularly, representative time-varying function-based controllers are presented, by which (practical, respectively) consensus can be achieved in prescribed time. Third, applications of fixed-time and prescribed-time consensus control in mobile robots and smart grids are illustrated in case studies. Finally, several challenging issues in prescribed-time consensus control are discussed for future research.