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

作　　者：刘刚[1] 秦伟伟 刘洁瑜[2] 汪立新[2] 

机构地区：[1]第二炮兵工程大学空间工程系,陕西西安710025 [2]第二炮兵工程大学自动控制系,陕西西安710025

出　　处：《控制理论与应用》2014年第6期735-740,共6页Control Theory & Applications

基　　金：国家自然科学基金资助项目(61203007;61304001)

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.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 multi-step 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.

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 

分 类 号：O231[理学—运筹学与控制论]