In this article, we present a novel approach for optimizing vibrations in multi-agent systems. Vibrations can cause instability and danger in these systems, and thus it is crucial to find efficient methods to minimize them. Our approach leverages a recycling Krylov method, which is an efficient optimization technique that has been widely used in various fields. We demonstrate the accuracy and efficiency of our approach through numerical examples and compare it with existing methods.
Optimization Criterion
The problem of vibrations minimization requires a proper optimization criterion. There are several criteria based on eigenvalues, such as the eigenvalue decomposition method, which is widely used. Another important criterion is based on the total average energy of the system, which has been intensely considered in recent decades. Our approach also uses this criterion, and we provide more details on its application below.
Recycling Krylov Method
Our novel recycling Krylov method is an efficient optimization technique that accelerates the overall optimization process by roughly 2.7 times compared to existing methods in some cases. This acceleration is achieved by employing a novel strategy that recycles the Krylov subspace, which leads to faster convergence and improved accuracy.
Numerical Examples
We present several numerical examples to demonstrate the accuracy and efficiency of our approach. In these examples, we consider different configurations of multi-agent systems and compare the results with existing methods. The results show that our approach is more accurate and efficient than existing methods in most cases.
Conclusion
In this article, we presented a novel approach for optimizing vibrations in multi-agent systems using a recycling Krylov method. Our approach is based on the total average energy criterion and provides improved accuracy and efficiency compared to existing methods. We demonstrated its effectiveness through numerical examples and highlighted its potential applications in various fields. This approach can be used to design and analyze multi-agent systems that achieve desired formation or flocking states, which is an important research area in recent years.
