A new optimal linear quadratic observer-based tracker under input constraint for the unknown system with a direct feed-through term

This paper develops a new optimal linear quadratic observer-based tracker with input constraint for the linear unknown system with a direct transmission term from input to measured output. The off-line observer/Kalman filter identification method is used to determine the linear sampled-data model with a direct feed-through term. On the basis of this model, a high-gain optimal linear quadratic analog observer-based tracker is proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and implementable observer and digital tracker from the theoretically well-designed high-gain analog observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high-gain property to fit the requirement of the input constraint, the modified linear quadratic analog tracker is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much.