AI 中文总结
本文针对Vlasov-Maxwell系统，提出算子理论方法构建依赖参数的控制器与观测器，通过Lyapunov算子、算子微分LMIs及Galerkin投影实现稳定分析与数值综合，经基准问题验证了收敛性。
AI 中文摘要
本文针对Vlasov-Maxwell系统的依赖参数控制器与观测器综合，提出了一种算子理论公式。将线性化动力学建模为非自治演化系统，其生成元依赖于可测量的等离子体量。建立了相关演化族的适定性及一致增长界；依赖参数的Lyapunov算子可得到算子微分线性矩阵不等式（LMIs），确保一致指数稳定性与观测器收敛性。H∞扩展提供了与耦合Vlasov-Maxwell方程固有能量结构一致的干扰衰减条件。Galerkin投影得到与算子不等式兼容的有限维LMIs，可在保留原始模型解析结构的同时实现可靠的数值综合。在简化的Vlasov-Maxwell基准问题上的数值结果验证了所预测的收敛特性。
英文摘要
An operator--theoretic formulation is developed for the synthesis of parameter-dependent controllers and observers for the Vlasov--Maxwell system. The linearized dynamics are modeled as a non-autonomous evolution system whose generators depend on measurable plasma quantities. Well-posedness of the associated evolution family is established together with uniform growth bounds. Parameter-dependent Lyapunov operators yield operator differential LMIs ensuring uniform exponential stability and observer convergence. An $H_\infty$ extension provides disturbance attenuation conditions consistent with the intrinsic energy structure of the coupled Vlasov--Maxwell equations. Galerkin projections lead to finite-dimensional LMIs consistent with the operator inequalities, enabling reliable numerical synthesis while preserving the analytical structure of the original model. Numerical results on a reduced Vlasov--Maxwell benchmark confirm the predicted convergence properties.
Comments17 pages, 4 figures
