Distributed Prescribed-Time Optimization for Multi-Agent Systems Over Switching Networks

The main focus of this work is on deriving a prescribed-time optimization control solution for a family of networked systems with uncertain nonlinearities and local time-varying cost functions. The underlying problem becomes much more challenging if the communication topology is not only local but also frequently switching. To overcome the technique difficulty arising from the local and switching network, a casted observer is introduced into the proposed distributed prescribed-time optimization control scheme, which allows the necessary non-local information to be localized within a prescribed time under the switching topology. Furthermore, the proposed prescribed-time optimization control algorithm is based on finite time-varying gain, avoiding excessive control input (especially excessive initial control input) caused by sustained high gain based method, without which the prescribed-time optimization result can not be derived. In addition, the gain switching time in the switching controller can be pre-assigned, distinguishing itself from most existing finite gain based prescribed-time control methods. Finally, the effectiveness of the method is validated through both numerical simulation and real-world experiment, demonstrating its potential for practical applications in networked control systems. Note to Practitioners—In real-world networked systems, such as multi-vehicle coordination and distributed robotics, achieving consensus while optimizing performance metrics poses complex challenges due to nonlinear and uncertain dynamics as well as switching communication topology. Existing control strategies often struggle to guarantee both control precision and optimal performance metrics within the desired time. This paper introduces a distributed prescribed-time optimization control algorithm that ensures consensus while achieving desired performance metrics within a user-assigned time. Both numerical simulation and real-world experiment confirm the feasibility and practical applicability of the proposed method.