SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1312-1340, January 2021.
A linear control system with quadratic cost functional over infinite time horizon is considered without assuming a controllability/stabilizability condition and the global integrability condition for the nonhomogeneous term of the state equation and the weight functions in the linear terms in the running cost rate function. Classical approaches do not apply for such problems. Existence and nonexistence of overtaking optimal controls in various cases are established. Some concrete examples are presented. These results show that the overtaking optimality approach can be used to solve some of the above-mentioned problems and at the same time, the limitation of this approach is also revealed.

中文翻译：

---

无限地平线线性二次超车最优控制问题

SIAM控制与优化杂志，第59卷，第2期，第1312-1340页，2021年1月
，在没有假设非均质性的可控制性/稳定性条件和全局可积性条件的情况下，考虑了具有无限时间范围内二次成本函数的线性控制系统。状态方程的项和运行成本率函数中线性项的权重函数。经典方法不适用于此类问题。建立了在各种情况下超越最优控制的存在和不存在。给出了一些具体的例子。这些结果表明，超车最优方法可用于解决上述一些问题，同时也揭示了这种方法的局限性。