The effects of redundant control inputs in finite-time optimal control

This paper is concerned with the effects of redundant control inputs on the quadratic optimal performance index in finite-time optimal control. Actually, the effects of redundant control input on quadratic performance index is equal to study the effects of the redundant control input on the solution of Riccati differential equation (RDE). Hence, some sufficient conditions are presented to strictly decrease the solution of RDE with the column of input matrix increased. Especially, a necessary and sufficient condition is derived to strictly decrease the solution of the homogeneous RDE after control input extensions. Moreover, one sufficient condition is obtained, which guarantees that the minimum control energy index strictly decreases with input extension. It is shown that redundant control inputs can improve the system performance based on these results. Some examples are taken to illustrate the effectiveness of related problems.