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In this paper, we study the constraints of control inputs, which is important to system performance, but rarely noticed. To deal with the constraints in practical situations, a new approach is proposed based on using diffeomorphism, which is the first introduced. Based on this transformation, the control input can be regarded as a function of an auxiliary variable. As a result, the value of control input is limited to a prescribed bound by choosing the proper bounded function. That is, it provides a new aspect to deal with the inequality control input constraints. The range of the input bounds is related to the uncertainties and can be designed according to the actual situation. This novel control is proven to guarantee uniform boundedness and uniform ultimate boundedness. In the simulation, we show this control renders a superior performance at a lower control cost, comparing with the LQR control.

Nonlinear uncertain systems with nonlinear control channel and unilateral input constraints