Transcale LQ tracking control for a class of discrete systems based on wavelet packet decomposition

This paper studies the problem of transcale LQ tracking control for a class of discrete systems. Based on the wavelet packet decomposition (WPD), the conventional LQ optimal tracking control is transformed into a suboptimal transcale LQ tracking control problem such that the control law of the initial scale reflects the control laws of the lowest-scale decomposition layer, these control laws can guarantee the performance indexes of the models of the lowest scale are minimized in the meaning of the LQ optimal tracking control. It is shown how a design philosophy based on 1) optimal control, 2) parallel processing, 3) WPD leads to an effectively control algorithm. One example is given to demonstrate the theoretical results.