基于鲁棒一步集的Tub e不变集鲁棒模型预测控制

摘要

A robust MPC with Tube invariant set based on robust one-step set is proposed for a constrained discrete-time uncertain linear system with bounded unknown state disturbance. Firstly, the enlarged terminal constraint region is obtained offline by a continuum of polytopic invariant sets. In order to enlarge the region of initial state admissible set and improve the robustness of this method, robust one-step set and Tube invariant set are used for designing the robust model predictive controller. The stability and the theorem of existence of this method are also proved. This algorithm not only enlarges the region of initial state admissible set greatly, but also restrains the state disturbance effectively. And the system states could be drived into the minimal robust positively invariant set around the origin. The simulation results prove the availability of the proposed method.%针对一类干扰有界的输入和状态受约束线性离散系统，提出了一种基于鲁棒一步集的Tube 不变集鲁棒模型预测控制方法。首先采用多面体不变集离线设计方法得到基于多面体不变集序列的扩展终端约束集；然后为了扩大鲁棒模型预测控制的初始状态允许区域，并提高系统的鲁棒性，在扩展终端约束集的基础上，通过引入鲁棒一步集并借助Tube 不变集控制策略，设计了基于鲁棒一步集的鲁棒模型预测控制方法，并给出了算法的存在性和稳定性证明。该方法不仅极大地扩大了初始状态允许区域，而且对有界干扰具有有效的抑制作用，使得受扰系统收敛到以原点为中心的最小鲁棒正不变集内。最后仿真验证了算法的有效性。