State controllability and optimal regulator control of time-delayed systems
State controllability and optimal regulator control of time-delayed systems
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DOI：
10.1080/00207170010003469
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发表时间：
2001-01
影响因子：
2.1
通讯作者：
E. Klein;W. Ramirez
中科院分区：
文献类型：
--
作者：
E. Klein;W. Ramirez
An important recent advance in the solution of the optimal regulator control problem for time-delayed systems is extended here to multivariable systems and to systems which exhibit multiple time delays. The state equations are partitioned into discrete and continuous portions through a state transformation such that the solution of the optimal regulator problem reduces to finding a steady-state controller gain based on both a discrete and continuous Riccati matrix. The discrete Ricatti matrix is found independently of the continuous solution due to the partitioning of the state equations, and it is not necessary to solve the system of partial differential Riccati equations which arise in the traditional solution of the linear quadratic regulator (LQR) problem for time-delayed systems. In addition, through this state transformation it becomes possible to extend the standard state controllability tests to time-delayed systems. It is shown that the controllability of the transformed state space is necessary for a feasible solution to the optimal regulator problem for time-delayed systems. This is an important test to determine the practicality of various time-delayed system realizations. Numerical examples illustrate the application of the technique to systems exhibiting multiple time delays, multivariable systems and time-series models. It is shown that the classic Wood-Berry distillation model realization does not possess state controllability properties which explains why this system has been historically difficult to control using feedback techniques.
