AI 中文总结
本文针对带点观测的边界控制扩散系统，解析研究了三类正相关问题，提出原创观测器反馈镇定策略，对其空间离散化形式做严格对比并推导了易实现的解。
AI 中文摘要
本文对带点观测的通用边界控制扩散系统的正镇定、正状态估计以及基于观测器的正镇定问题开展了完整的分析研究。特别地，通过解析方法求解了最优设计问题，并提出了一种基于观测器的反馈镇定的原创策略。同时针对标称PDE系统的任意阶空间离散化形式研究了上述三类问题，以实现数值计算，并与标称解进行了严格对比。在连续和离散两种场景下，均推导得到了明确且易于实现的解。
英文摘要
This paper provides a complete analytical study of the positive stabilization, positive state estimation, and observer-based positive stabilization problems for a generic boundary control diffusion system with point observation. In particular, optimal design problems are solved analytically, and an original strategy for observer-based feedback stabilization is proposed. The three problems are also investigated for an arbitrary-order spatial discretization of the nominal PDE system enabling numerical implementation together with rigorous comparisons with the nominal solutions. In both the continuous and discretized settings, explicit and readily implementable solutions are derived.
