Although adaptive parameter estimation (APE) has been studied for decades, quantifying the transient estimation error convergence performance (e.g., overshoot and convergence rate) that is essential for system safety and reliability is more difficult than the steady-state convergence analysis. To address this issue, a new APE method with prescribed convergence performance is proposed in this paper. The main idea is to incorporate a prescribed performance function (PPF) into the design of adaptive laws to predefine the estimation error convergence boundary. For this purpose, a filtering approach is first introduced to extract the estimation error by using the measured system input and output. An estimation error transformation is then introduced to derive intermediate variables for establishing the adaptive law. With the well-recognized persistent excitation (PE) condition, it is proved that the estimation error for constant parameters can be strictly guaranteed within a predefined boundary. The robustness against bounded disturbances is also examined. With this framework, the PE condition can be verified by examining the positive definiteness of an induced intermediate matrix. A simulation example is given to show the effectiveness of the proposed algorithm.

尽管自适应参数估计（APE）已经研究了数十年，但量化稳态估计误差对系统安全性和可靠性至关重要的收敛性能（例如，过冲和收敛速率）比稳态收敛分析更加困难。为了解决这个问题，本文提出了一种新的具有规定收敛性能的APE方法。主要思想是将规定的性能函数（PPF）纳入自适应定律的设计中，以预先定义估计误差的收敛边界。为此，首先引入了一种滤波方法，以通过使用测得的系统输入和输出来提取估计误差。然后引入估计误差变换以导出用于建立自适应定律的中间变量。利用公认的持续激励（PE）条件，证明了可以在预定的边界内严格保证恒定参数的估计误差。还研究了针对有界干扰的鲁棒性。在此框架下，可以通过检查诱导中间矩阵的正定性来验证PE条件。仿真例子表明了该算法的有效性。