非线性系统双模鲁棒预测控制: 不变集切换方法

提出了一种基于不变集切换的非线性系统鲁棒预测控制算法.采用分段蕴含方法将非线性系统动态用一组线性变参数(LPV)系统动态包裹;计算出非线性系统的平衡面,对于每个LPV蕴含模型,针对相应的平衡点构造多面体不变集,得到覆盖非线性系统平衡面的一组相互重叠的不变集;在线根据系统当前状态所处的不变集和LPV区间切换控制律,最终保证闭环系统的稳定性.与传统的非线性预测控制相比,这种方法在构造不变集和确定控制律的计算都是离线进行,而在线只需根据当前状态切换控制律即可,从而避免了求解复杂的非凸非线性规划,在很大程度上降低了在线计算量.

Dual-Mode Robust Predictive Control for Nonlinear Systems: aSwitching Method Between Polyhedral Invariant Sets

A Robust predictive control algorithm for a class of nonlinear systems subject to input and state constraints is proposed based on invariant set switch.The trajectories of the nonlinear system are embedded within those of a bank of Linear Parameter Varying uncertain systems via a so called Piece-Wise Embedding scheme at first. Then, the equilibrium surface of the nonlinear system is obtained by caculation, and for each LPV embedding model a polyhedral invariant set corresponding to the equilibrium point is constructed. Then finite invariant sets overlapped each other are obtained. These invariant sets cover the equilibrium surface such that the closed-loop stability of the nonlinear system can be guaranteed by switching the control laws according to the current state. Compared with the traditional nonlinear predictive control, this algorithm is computationally efficient because most of the problems are solved offline, so that the online computational burden can be greatly reduced.