Distributed time-varying optimization with prescribed-time approach

This work focuses on distributed time-varying optimization algorithms that can converge in a prescribed time period, both single-integrator systems and double-integrator systems are considered. A nested structure is proposed for applying prescribed-time approach to distributed time-varying optimization problems in this work. For single-integrator systems, the prescribed time interval is divided into three sub-intervals, then the average consensus estimation, the state consensus, and the optimized trajectory tracking are achieved sequentially through the time-scale function in the three sub-time intervals. This nested structure and the properties of the time-scale function ensure that the first-order algorithm is continuous and bounded. Therefore, the algorithm can be extended to double integrator systems by tracking the virtual first-order input signal. The validity of the proposed first-order and second-order algorithms is verified through optimal dynamic trajectory tracking experiments for indoor UAV clusters.