An Active Control Design for a Class of Parametrically Excited Systems Based on the Gradient Algorithm

This paper introduces a new control design for a dynamic system subject to stationary or nonstationary parametric excitations. In this new design, the system dynamics is transformed into one with a null system matrix using the variation of parameters method. A stabilizing state feedback control can then be immediately obtained by following the gradient algorithm that is originally developed for the parameter identification purpose. Such a design has the advantage that the control requires only past and present information of the time-varying parametric excitations while previous control designs usually require prediction of future information of the excitations. The closed-loop system stability is guaranteed if the open-loop state response does not diverge too fast. The control design approach can also be applied to the observer design in case where there is only partial observation of the system state.