The effects of redundant control inputs in optimal control

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.

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