An estimation law of unknown parameters vector is proposed for one class of nonlinearly parameterized regression equations . We restrict our attention to parameterizations that are widely obtained in practical scenarios when polynomials in are used to form . For them we introduce a new “linearizability” assumption that a mapping from overparameterized vector of parameters to original one exists in terms of standard algebraic functions. Under such assumption and necessary and sufficient identifiability condition, on the basis of dynamic regressor extension and mixing technique we propose a procedure to reduce the nonlinear regression equation to the linear parameterization without application of singularity causing operations and the need to identify the overparameterized parameters vector. As a result, an estimation law with exponential convergence rate is derived, which, unlike known solutions, () does not require a strict -monotonicity condition to be met and information about to be known, () ensures elementwise monotonicity for the parameter error vector. The effectiveness of our approach is illustrated with both academic example and 2-DOF robot manipulator control problem.

中文翻译：

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无过度参数化的一类非线性参数化回归的单调参数估计

针对一类非线性参数化回归方程，提出了一种未知参数向量估计律。我们将注意力限制在使用多项式 来形成 时在实际场景中广泛获得的参数化。对于它们，我们引入了一种新的“线性化”假设，即从参数的过度参数化向量到原始向量的映射以标准代数函数的形式存在。在这样的假设和充分的可辨识性条件下，基于动态回归量扩展和混合技术，我们提出了一种将非线性回归方程简化为线性参数化的过程，而不需要应用引起奇异性的操作和识别超参数化参数向量。由此推导出具有指数收敛速度的估计律，与已知解不同，()不需要满足严格的单调性条件和已知信息，()保证了参数误差向量的元素单调性。我们的方法的有效性通过学术例子和 2-DOF 机器人操纵器控制问题来说明。