针对存在有界外界扰动的有约束线性系统,本文提出了一种新的MPC控制器ABRMPC.一方面,通过引入输入幅值衰减集结策略,使得各时刻优化的变量数大大减少,简化了在线计算;另一方面,在对各步的扰动进行了考虑之后,得到新的状态约束,可保证系统实际状态始终处于原约束域内.本文重点对如何得到下一时刻的可行解进行了研究,指出了衰减系数的上界应满足的条件;而后证明了系统输入将最终趋于零,同时该控制器可使处于不变集之外的系统状态趋向于不变集,从而使系统具有鲁棒稳定性.最后通过仿真实例对文中结论进行了验证.%A new model predictive controller ABRMPC is presented for constrained linear system with bounded additive perturbation. On the one hand, by introducing input amplitude decaying aggregation strategy, the number of optimization variables at every time is greatly reduced so that the on-line computation is simplified. On the other hand, having taken into account the perturbation at each time, some new state constraints are obtained and thus the state of the real system is kept in the original constraint domain. The paper emphasizes on how to get the feasible solution at next time and gives the condition that the decaying coefficient should satisfy. When time goes to infinite, it is proved that the system input becomes zero and the controller drives the system state to approach the invariant set. It is concluded that the controlled system is robustly stable. The conclusions are finally verified through a simulation example.
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