反推
控制理论(社会学)
非线性系统
有界函数
跟踪误差
数学
控制器(灌溉)
趋同(经济学)
符号函数
功能(生物学)
维数(图论)
自适应控制
应用数学
数学优化
计算机科学
控制(管理)
数学分析
人工智能
生物
纯数学
经济
物理
进化生物学
量子力学
经济增长
农学
作者
Chen Liu,Dong Shen,JinRong Wang
摘要
Summary This paper studies the iteration varying trail lengths problem for high‐order continuous‐time nonlinear systems, where the initial state may deviate from the desired value and the sign of input gain is unknown. First, to deal with the general nonlinear systems, a fuzzy approximation technique is applied for each dimension of the nonlinear function and the backstepping technique is then used for controller design and performance analysis. Moreover, to deal with the randomly varying trial length problem, we introduce a novel composite energy function for the asymptotic convergence analysis. Furthermore, the initial state deviation issue is resolved by introducing an initial state learning protocol such that the initial state tracking error converges to zero asymptotically. Last but not least, the unknown control direction is regulated by applying a Nussbaum function and the analysis in the presence of nonuniform trial lengths is strictly established. Based on these treatments, we prove that the tracking error converges to zero as iteration number increases and all signals are bounded. The effectiveness of the proposed framework is verified by numerical simulations.
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