论文标题
在标准状态空间系统和冲动可控描述符系统中重新访问收费公路的古典系统理论
Classical System Theory Revisited for Turnpike in Standard State Space Systems and Impulse Controllable Descriptor Systems
论文作者
论文摘要
收费公路的概念将较长但有限的时间范围的最佳控制问题与稳态最佳控制联系起来。收费公路分析的一个关键要素是线性二次调节器问题和相关差分riccati方程的溶液的收敛性，因为终端时间接近无穷大。这种收敛已在1980年代的线性系统理论中进行了研究。我们扩展了经典系统理论结果，以研究标准状态空间系统和描述符系统的收费公路特性。我们介绍了在不可检索的情况下和脉冲可控描述符系统中收费公路的条件。对于后者，根据标准线性系统的理论，我们建立了解决方案与广义差异方程的存在和收敛。
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the convergence of the solution of the associated differential Riccati equation as the terminal time approaches infinity. This convergence has been investigated in linear systems theory in the 1980s. We extend classical system theoretic results for the investigation of turnpike properties of standard state space systems and descriptor systems. We present conditions for turnpike in the nondetectable case and for impulse controllable descriptor systems. For the latter, in line with the theory for standard linear systems, we establish existence and convergence of solutions to a generalized differential Riccati equation.
