摘要
For a stabilizable system, the extension of the control inputs has no use for stabilizability, but it is important for optimal control. In this paper, a necessary and sufficient condition is presented to strictly decrease the quadratic optimal performance index after control input extensions. A similar result is also provided for H2 optimal control problem. These results show an essential difference between single-input and multi-input control systems. Several examples are taken to illustrate related problems.
基金
Supported by the National Natural Science Foundation of China (Grant Nos. 90916003, 60674093, 60874011)
the Key Projects of Educational Ministry of China (Grant No. 107110)
