Exact Prescribed-Time Distributed Optimization for Second-Order Multi-Agent Systems: A Time-Switching Control Strategy

This paper addresses the exact prescribed-time distributed optimization problem (PT-DOP) for second-order multiagent systems (MASs) with a global optimization objective. Some bounded time-varying functions are introduced into controller gains to avoid the numerical implementation problem of unbounded time-varying control gains and ensure that the global optimization objective is reached within a prescribed time. A time-switching centralized optimization controller containing a virtual controller is developed. The exact PT-DOP of the secondorder MASs under the time-switching centralized optimization controller is solved in three phases: [0, T<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q1</sub>), [<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_Q1</i>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_Q2</i>), and [<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_Q2</i>, T). First, the second-order MASs are transformed into a first-order form by the time-switching centralized optimization controller during [0, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_Q1</i>). Next, the transformed first-order MASs based on the virtual controller reach the consensus in their positions at T<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q2</sub>. Finally, the global optimization objective is exactly solved by the virtual controller during [<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_Q2</i>, T). To avoid each agent utilizing the global gradient information of the MASs, a time-switching distributed optimization controller containing a virtual controller is also introduced, and it can guarantee the exact PT-DOP of the MASs. Three numerical simulation examples are provided to confirm the effectiveness of the proposed controllers.