论文标题
使用高阶调谐器对一类非线性系统的离散时间自适应控制
Discrete-Time Adaptive Control of a Class of Nonlinear Systems Using High-Order Tuners
论文作者
论文摘要
本文涉及一类具有所有状态的离散时间非线性系统的自适应控制。最近，在识别问题的背景下，开发了一种高阶调谐器算法，以最小化凸损失函数，并具有随时间变化的回归变量。根据Nesterov的算法，显示高阶调谐器可以保证当回归器随时间而变化时，可以保证有界参数估计，并在回归器恒定时导致跟踪误差的加速收敛性。在本文中，我们将高级调谐器应用于特定类别的离散时间非线性动力学系统的自适应控制。首先，我们表明，对于此类的植物，可以将潜在的动态误差模型因果转换为代数误差模型。其次，我们表明，使用此代数错误模型，可以将高阶调谐器应用于可证明稳定参考轨迹周围的动态系统类别。
This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying regressors in the context of an identification problem. Based on Nesterov's algorithm, the high-order tuner was shown to guarantee bounded parameter estimation when regressors vary with time, and to lead to accelerated convergence of the tracking error when regressors are constant. In this paper, we apply the high-order tuner to the adaptive control of a particular class of discrete-time nonlinear dynamical systems. First, we show that for plants of this class, the underlying dynamical error model can be causally converted to an algebraic error model. Second, we show that using this algebraic error model, the high-order tuner can be applied to provably stabilize the class of dynamical systems around a reference trajectory.
