论文标题
在大型干扰下保证具有强大稳定性的模型预测控制框架
A model predictive control framework with robust stability guarantees under large disturbances
论文作者
论文摘要
为了解决模型预测控制（MPC）中的可行性问题，大多数实现通过使用松弛变量并为成本增加罚款而放宽状态限制。我们提出了一种替代策略：通过罚款放松初始状态约束。与最先进的软限制MPC公式相比，所提出的配方具有两个关键特征：（i）输入到国家的稳定性以及对大型干扰的累积约束违规行为的界限； （ii）在名义操作条件下近似最佳性能。该想法最初是通过将惩罚作为lyapunov函数设计为渐近稳定的非线性系统的开环构成的，但我们也向Lyapunov稳定系统展示了如何放松这种情况； ii）可稳定系统； iii）利用Lyapunov函数的隐式表征。在线性系统的特殊情况下，与名义设计相比，拟议的MPC公式将减少为二次程序，离线设计和在线计算复杂性仅略有增加。数值示例与最先进的软件MPC配方相比表明了好处。
To address feasibility issues in model predictive control (MPC), most implementations relax state constraints by using slack variables and adding a penalty to the cost. We propose an alternative strategy: relaxing the initial state constraint with a penalty. Compared to state-of-the-art soft constrained MPC formulations, the proposed formulation has two key features: (i) input-to-state stability and bounds on the cumulative constraint violation for large disturbances; (ii) close-to-optimal performance under nominal operating conditions. The idea is initially presented for open-loop asymptotically stable nonlinear systems by designing the penalty as a Lyapunov function, but we also show how to relax this condition to: i) Lyapunov stable systems; ii) stabilizable systems; and iii) utilizing an implicit characterization of the Lyapunov function. In the special case of linear systems, the proposed MPC formulation reduces to a quadratic program, and the offline design and online computational complexity are only marginally increased compared to a nominal design. Numerical examples demonstrate benefits compared to state-of-the-art soft-constrained MPC formulations.
