Containment Control of Multi-agent Systems with Uniform Quantization

In this paper, the problem of containment control is investigated for a class of multi-agent systems with second-order integrator dynamics. A directed graph is considered, and a pair of matrix norm and vector norm is designed. Accounting for the limitation of the finite bandwidth channels, quantized communication topology based on the encoding-decoding strategy is designed, in which the quantizers only have finite quantization levels and it is independent of the initial state of agents. Moreover, the quantizer and controller are jointly designed only using the estimated value of the neighbors' state information to ensure the system stability with less communication resource. The relationship between the quantization levels and sampling interval is established to guarantee that all the quantizers are not saturated, and thus ensure the asymptotic stability of the system. And a vector norm induced by a constructed matrix norm is applied to reduce the lower boundary of the communication data rate which is free from the dimension and number of agents. Finally, simulation examples are given to show the effectiveness of the new designed techniques.