运用区间算法的约束非线性系统鲁棒模型预测控制

RMPC for constrained nonlinear systems based on interval arithmetic

中文关键词  非线性模型预测控制  鲁棒一步集  区间算法  鲁棒不变集

英文关键词  nonlinear model predictive control  robust one step set  interval arithmetic  robust invariant set

中文摘要

      针对一类具有输入和状态约束的干扰有界非线性系统, 提出了基于区间分析的约束非线性鲁棒模型预测控制, 以降低计算量并扩大系统吸引域. 首先, 在集合运算的基础上, 利用区间运算和函数区间扩展, 给出了一种计 算效能更好、保守性更低的非线性系统鲁棒一步集计算方法; 其次, 构造重叠的多面体控制不变集序列并以此计算约束非线性系统的鲁棒多步集, 并通过设计基于集合的在线优化策略, 提出了基于鲁棒一步集的单步优化非线性模型预测控制, 有效降低了非线性优化的在线计算量; 最后, 仿真实例验证了算法的有效性.

英文摘要

      Based on the interval analysis, a robust nonlinear model predictive control (RNMPC) strategy with extended domain of attraction and reduced computation load is developed for a class of input-constrained and state-bounded uncertain nonlinear systems. Firstly, based on set theory, an effective and low conservatism algorithm for the robust one-step set of nonlinear systems is proposed with interval algorithm and interval extension of function in interval arithmetic. Secondly, an overlapped robust control-invariant set sequence around equilibrium points is calculated. And then, the robust multistep sets of the robust control-invariant set sequence are calculated and used to design the robust nonlinear MPC based on one-step online optimization. By employing the one-step optimization, this algorithm extends the domain of attraction. Furthermore, the optimization function is simplex and the number of variable is reduced. Therefore, this algorithm reduces the on-line computation load of nonlinear optimization. Finally, numerical simulation results validate the proposed method.