Specified-time consensus for multi-agent systems

This paper constructs a novel consensus framework for continuous-time multi-agent systems by using motion planning approaches. In this framework, a novel notion, specifiedtime consensus, is raised. Specified-time consensus means that the consensus of multi-agent systems is achieving with a finite settling time, which can be accurately and arbitrarily pre-specified according to task requirements. In order to achieve specified-time consensus, we firstly focus on asymptotic consensus problems. By using finite-time optimal control approaches, a class of sampled-data based consensus algorithms are developed. The sampling periods can be arbitrarily designed according to the requirements of consensus convergence rate, which means that the sampling period of the consensus algorithms is decoupled and independent. Thus, one can design a time-varying sampling sequence that is convergent to a specified settling time. Then, specified-time consensus can be solved under the sampled-data based consensus algorithms with the designed time-varying sampling sequence. Besides, since the sampling periods, communication topologies and control gains are decoupling and can be separately designed in this framework, the specified-time consensus can be solved under directed switching topologies that have a joint spanning tree.