Under terminal constraints, the set of states such that a model-predictive control strategy is feasible, and thus stable, is equivalent to the viable-reachable set of the controlled system. We prove that viscosity and storage function approaches to viability theory are equivalent to each other. Based on these results we propose inner and outer bounds of the feasible set by storage functions, which for polynomial systems can be computed using sum-of-squares programmes. Numerical, discrete-time and continuous-time examples are given for lateral car dynamics and the forced Van der Pol oscillator, respectively.

中文翻译：

---

具有终端约束的模型预测控制中的生存力、粘度和存储函数

在终端约束下，模型预测控制策略可行且稳定的状态集等价于受控系统的可行可达集。我们证明了生存力理论的粘度和储存函数方法彼此等效。基于这些结果，我们通过存储函数提出了可行集的内界和外界，对于多项式系统，可以使用平方和程序来计算。分别给出了横向汽车动力学和强制范德波尔振荡器的数值、离散时间和连续时间示例。