摘要：This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback linearization, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization problem of the model predictive controller significantly, which, however, is no longer linear in the presence of parameter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.

摘要：证明了两个定理 :定理 1揭示了三点多边形的外接圆在中点处的法矢与两个边界法矢的关系 ;定理 2揭示了四面体外接球面在中点处的法矢与三个相邻三角平面的法矢量的关系 .给出了一个判别二维多边形和三维多面体顶点法矢计算方法优劣的准则 .在此基础上 ,提出一种用于估计三维多面体顶部的法矢量的计算方法 .