Inverse-Optimal Consensus Control of Fractional-Order Multiagent Systems
研究了分数阶多智能体系统的逆最优一致性控制问题，分别针对连续时间和离散时间系统推导了最优状态反馈增益矩阵，并证明其能实现一致性。
In this article, the problems of inverse-optimal consensus control (IOCC) for single-integral dynamics in Caputo continuous-time and Grunwald–Letnikov (G-L) discrete-time fractional-order multiagent systems (FOMASs) are investigated. For continuous-time FOMASs, by virtue of the variational method, the optimal solution under the constraint of the global performance index function is presented, and then the optimal state-feedback gain matrix (OSFGM) is derived through the Laplace transform and the inverse transform of fractional order. For discrete-time FOMASs, the OSFGM based on the algebraic Riccati equation (ARE) is computed, then it is shown that the OSFGM is a (asymmetric) Laplace matrix which has a zero eigenvalue and the corresponding network structure is a complete graph. Moreover, we rigorously prove that consensus can be achieved under the optimal state-feedback gain matrices. Finally, two simulation examples are shown to check the validity of the proposed theorems.