Control (management)

Step response

Engineering

Control engineering

Real-time computing

Theoretical computer science

Bipartite graph

Settling

Computer science

Mathematical optimization

Time synchronization

Distributed computing

Settling time

Environmental engineering

Graph

Mathematics

Synchronization (alternating current)

Artificial intelligence

Combinatorics

Topology (electrical circuits)

Control theory (sociology)

Automatica

This paper mainly delves into the fixed-time bipartite synchronization problems of multi-agent networks embedded single- and double-integrator over directed graphs with cooperative–antagonistic interactions. Firstly, by introducing Pontryagin’s maximum principle in distributed fashions, a new kind of distributed fixed-time bipartite synchronization protocols is developed. Then, through multi-step motion planning techniques, the designed protocols can ensure that the states of agents converge to values with the same module but different sign at a pre-appointed settling time. Compared with existing results, an important contribution of this paper is that it is over directed networks that fixed-time bipartite synchronization problems are solved. Meanwhile, the fixed settling time can be appointed in advance. Finally, the application to formation problems with a pre-appointed settling time is further considered to indicate the utility of proposed protocols.

Fixed-time bipartite synchronization with a pre-appointed settling time over directed cooperative–antagonistic networks