Optimal trajectory tracking controller design: Model based to model free methods

This paper presents a new adaptive optimal control which is based on a particular hybrid systems called piecewise linear continuous systems. This referred proposed controller which is based on a L₂ norm prescribed to minimize a tracking error and a time-delay estimation technique is developed from model based and finally can be applied to systems without knowing internal dynamics. Thus this proposed Method has adaptive and optimal characters with a very simple Proportional-Derivative (PD) controller structure. It realizes the trajectory tracking of multi-inputs multi-outputs linear continuous systems under systems output feedback. Finally, to validate the proposed method performance, two illustrative examples which contains a knowing dynamic systems and a real-time based unknown motion control example are presented.