The note considers optimal and model predictive controls for linear systems with strictly convex quadratic stage and terminal cost functions, and under closed polyhedral stage constraints, finitely many open spherical exclusion stage constraints, and closed polyhedral terminal constraints. The computational complexity of exact nonconvex optimal and model predictive controls is alleviated through the local convexification of the nonconvex exclusion constraints, which is obtained via safe polyhedral tubes. The safe polyhedral tubes are constructed via simple algebraic operations and are of paramount importance for the design of locally convexified optimal and model predictive controls via strictly convex quadratic programming.

该说明考虑了具有严格凸二次阶段和终端成本函数的线性系统的最优和模型预测控制，以及在封闭多面体阶段约束、有限多个开球排除阶段约束和封闭多面体终端约束下。精确非凸优化和模型预测控制的计算复杂性通过非凸排除约束的局部凸化得到缓解，非凸排除约束是通过安全多面体管获得的。安全多面体管是通过简单的代数运算构建的，对于通过严格凸二次规划设计局部凸优化和模型预测控制至关重要。