有限激励条件下采用组合自适应的鲁棒模型参考自适应控制
Robust Model Reference Adaptive Control with Combined Adaptation under Finite Excitation Condition
AI总结：
本文针对含未知对角控制有效性矩阵和有界非参数不确定性的多输入多输出非线性系统，提出基于修正格拉姆-施密特正交化的组合自适应鲁棒模型参考自适应控制算法，消除了收敛速率对回归器激励水平的依赖。
AI中文摘要：
在自适应控制中，参数线性形式的参数不确定性由未知参数和已知回归器信号组成。未知参数收敛到理想值要求回归器满足持续激励（PE）条件，该条件依赖未来数据，因此无法在线保证。基于记忆的参数更新律通过在可在线验证的有限激励（FE）条件下实现理想参数收敛来解决这一问题。本文针对一类具有未知对角控制有效性矩阵和有界非参数不确定性的多输入多输出非线性系统，提出一种新算法，通过修正格拉姆-施密特正交化过程构造记忆项。在有限激励条件下，构造的记忆项在参数估计误差动态中产生单位系数矩阵。该单位系数矩阵消除了对时变自适应增益的需求，能明确给出参数估计误差的最终界，且保留了记忆项下非参数不确定性界的结构。在此基础上，针对有限激励条件下的控制器增益估计，开发了组合自适应律。结果表明，闭环跟踪误差和估计误差以指数方式衰减到原点的邻域，该邻域由明确的最终界表征，其衰减速率仅取决于用户定义的增益和系统常数，与回归器激励水平无关。这消除了收敛速率对回归器激励水平的依赖，而这是现有方法（如并发学习、记忆回归器扩展和DREM）的关键局限。
英文摘要：
In adaptive control, parametric uncertainties in linear-in-parameter form consist of unknown parameters and known regressor signals. Convergence of the unknown parameters to their ideal values requires the regressor to satisfy a persistent excitation (PE) condition, which depends on future data and is therefore infeasible to guarantee online. Memory-based parameter update laws address this by enabling ideal parameter convergence under the online-verifiable finite excitation (FE) condition. In this paper, a new algorithm is proposed to construct a memory term via the Modified Gram-Schmidt orthogonalization procedure for a class of multi-input multi-output nonlinear systems with an unknown diagonal control effectiveness matrix and bounded nonparametric uncertainties. Under the finite excitation condition, the constructed memory term yields an identity coefficient matrix in the parameter estimation error dynamics. The identity coefficient matrix eliminates the need for time-varying adaptation gains, enables an explicit ultimate bound on the parameter estimation error, and preserves the structure of the nonparametric uncertainty bound under the memory term. Building on this, a combined adaptation law is developed for controller gain estimation under FE. The closed-loop tracking and estimation errors are shown to decay exponentially to a neighborhood of the origin, characterized by an explicit ultimate bound, with a decay rate that depends solely on user-defined gains and system constants, independent of the level of regressor excitation. This removes the dependence of the convergence rate on the level of regressor excitation, a key limitation of existing approaches such as concurrent learning, memory regressor extension, and DREM.
