This paper presents a novel practical fixed-time parameter identification algorithm and a composite learning based practical fixed-time adaptive dynamic surface control (DSC) scheme for nonlinear strict-feedback systems subject to linear-in-parameters uncertainties. The convergence of conventional parameter estimation algorithms often requires a restrictive prerequisite termed persistent excitation (PE) condition. By contrast, a new fixed-time parameter identification algorithm configured with two layer transformation technique is firstly proposed under relaxed sufficient excitation condition rather than strict PE condition. The key point of avoiding PE condition is by introducing a smooth switching function to adjust the forgetting factor in the filtered regressor dynamics. Instead of using the fractional power of the tracking errors to construct the control laws, a smooth hyperbolic tangent function based adaptive DSC scheme is designed such that the potential singular problem caused by time derivations of virtual control laws in back-stepping algorithm is avoided. Integrating the parameter identification algorithm into the adaptive DSC scheme, a composite learning based control is formed to guarantee the practical fixed-time convergence of parameter estimation errors and tracking errors. Comparative simulation results are given to illustrate the effectiveness of the proposed algorithm.

中文翻译：

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充分激励下定时参数估计的不确定非线性严格反馈系统的复合学习自适应动态曲面控制

本文针对受线性参数不确定性影响的非线性严格反馈系统，提出了一种新颖实用的固定时间参数识别算法和基于复合学习的实用固定时间自适应动态表面控制 (DSC) 方案。传统参数估计算法的收敛通常需要称为持续激励 (PE) 条件的限制性先决条件。相比之下，首次提出了一种新的固定时间参数识别算法，配置了两层变换技术，而不是在严格的PE条件下。避免 PE 条件的关键是通过引入平滑切换函数来调整过滤回归量动态中的遗忘因子。不是使用跟踪误差的分数幂来构建控制律，而是设计了基于平滑双曲正切函数的自适应 DSC 方案，以避免在反步算法中由虚拟控制律的时间推导引起的潜在奇异问题。将参数识别算法集成到自适应DSC方案中，形成了一种基于复合学习的控制，以保证参数估计误差和跟踪误差的实际固定时间收敛。给出了对比仿真结果来说明所提出算法的有效性。将参数识别算法集成到自适应DSC方案中，形成了基于复合学习的控制，以保证参数估计误差和跟踪误差的实际固定时间收敛。给出了对比仿真结果来说明所提出算法的有效性。将参数识别算法集成到自适应DSC方案中，形成了一种基于复合学习的控制，以保证参数估计误差和跟踪误差的实际固定时间收敛。给出了对比仿真结果来说明所提出算法的有效性。