采用鲁棒容许集对有约束的不确定系统作鲁棒模型预测控制

摘要

Based on the robust admissible set, a robust model-predictive-control(RMPC) strategy with extended domain of attraction is developed for an input-constrained and state-bounded polytopic uncertain linear system. First, the algorithm for calculating the robust admissible set of the polytopic invariant set is presented; the necessary and sufficient conditions for the existence of this robust admissible set are derived. Next, to expand the application range of Tube invariant set RMPC(Tube-RMPC) algorithm, the Tube-RMPC strategy for polytopic uncertain systems with bounded disturbances is considered. Afterwards, to extend the domain of attraction of the constrained system, we put forward the RMPC strategy with admissible set for the polytopic uncertain system with bounded disturbances. By employing the robust admissible set and Tube invariant set RMPC, this algorithm extends the domain of attraction and reduces the on-line computation load; meanwhile, the robustness of the algorithm is guaranteed by employing the minimal robust positive-invariant set. Finally, numerical simulation results validate the proposed method.%针对输入和状态受约束的干扰有界多胞不确定线性系统,提出了基于鲁棒容许集的扩大吸引域鲁棒模型预测控制(RMPC)方法.首先给出了多面体不变集的鲁棒容许集计算方法,并推导了鲁棒容许集存在的充分必要条件.其次,为了拓展Tube不变集鲁棒模型预测控制算法的适用范围,讨论了干扰有界多胞不确定线性系统的Tube不变集控制策略.之后为了扩大约束系统吸引域,提出了干扰有界多胞不确定系统的鲁棒容许集模型预测控制策略.通过采用鲁棒容许集和Tube不变集RMPC,该方法不仅扩大了吸引域,而且降低了在线计算量；同时,采用基于最小鲁棒正不变集的Tube不变集策略保证了算法的鲁棒性.最后仿真结果验证了算法的有效性.