In this paper, discrete‐time adaptive control of linearly parameterized fully actuated Port‐controlled Hamiltonian systems with parameter uncertainties in energy function is considered. A discrete‐time adaptive interconnection and damping assignment passivity‐based control (IDA‐PBC) method, utilizing the immersion and invariance (I&I) approach, for the considered uncertain Hamiltonian system, is presented. A discrete‐time parameter estimator based on the immersion and invariance approach is derived to obtain an automatic tuning mechanism for the IDA‐PBC controller. The stability analysis for the estimator and the closed‐loop system is done using the Lyapunov theory. The proposed method is applied to two fully actuated physical systems and its performance is tested by simulations. Simulation results show that the proposed I&I‐based adaptive IDA‐PBC controller successfully preserves the performance of the IDA‐PBC controller designed with true parameters under a large amount of uncertainty.

中文翻译：

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通过I＆I方法对线性参数化离散时间端口控制的哈密顿系统进行基于自适应互连和阻尼分配的无源控制

在本文中，考虑了在能量函数中具有参数不确定性的线性参数化全驱动端口控制哈密顿系统的离散时间自适应控制。针对所考虑的不确定哈密顿系统，提出了一种采用沉浸和不变性（I＆I）方法的离散时间自适应互连和阻尼分配基于无源性的控制（IDA-PBC）方法。推导了基于沉浸和不变性方法的离散时间参数估计器，以获得IDA-PBC控制器的自动调整机制。估计器和闭环系统的稳定性分析是使用李雅普诺夫理论进行的。所提方法适用于两个完全驱动物理系统及其性能通过仿真进行测试。仿真结果表明，所提出的基于I＆I的自适应IDA-PBC控制器在很大的不确定性下成功地保留了采用真实参数设计的IDA-PBC控制器的性能。