Abstract While the asymptotic output tracking property has been proven for many nonlinear adaptive control systems, their higher-order output tracking property has not been reported. In this paper, the higher-order derivative convergence of the output tracking error e ( t ) is studied for nonlinear adaptive control systems using the feedback linearization design. It is proven that not only each error component e j ( t ) from e ( t ) = [ e 1 ( t ) , e 2 ( t ) , … , e m ( t ) ] T converges to zero asymptotically but also its up to k th-order time-derivative e j ( k ) ( t ) converges to zero, for k = 1 , 2 , … , ρ j , where ρ j , j = 1 , 2 , … , m , are the control relative degrees of the nonlinear system with m inputs.

中文翻译：

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非线性自适应控制系统的高阶跟踪特性

摘要 虽然渐近输出跟踪特性已被证明适用于许多非线性自适应控制系统，但其高阶输出跟踪特性尚未见报道。在本文中，使用反馈线性化设计研究非线性自适应控制系统的输出跟踪误差 e ( t ) 的高阶导数收敛。证明了不仅来自 e ( t ) = [ e 1 ( t ) , e 2 ( t ) , … , em ( t ) ] T 的每个误差分量 ej ( t ) 都渐近收敛到零，而且直到 k三次时间导数 ej ( k ) ( t ) 收敛到零，对于 k = 1 , 2 , … , ρ j ，其中 ρ j , j = 1 , 2 , … , m 是控制相对度具有 m 个输入的非线性系统。