Two Classes Of Uncertain Systems Containing Nonlinear Term Of The Output Tracking Control

Output tracking control, as a class of special trajectory tracking control prob-lem, discussing how to track the output of expected model, exists widely in the engineering practical control, and has been an important subject in tracking control problem. In recent years, the problem has been paid much more attention by many experts in control fields. Meanwhile, many good results have been obtained. In this paper we will research the problem about the output tracking control for two kinds of uncertain systems with nonlinear terms from different angles. The main conclusions in this paper are as follows:(1) Asymptotic output tracking control problem for a class of uncertain time-delay systems with nonlinear terms is discussed in this paper. Firstly, the design method of sliding control law for a class of uncertain time-delay systems with non-linear terms is proposed by variable structure control theory, guaranteeing the tra-jectories of the tracking control system to arrive at the slide surface in finite time interval and be kept here thereafter. Secondly, the sufficient condition for asymp-totic stability of the error system composed by tracking control system and the given reference model and sliding mode dynamic is obtained via linear matrix inequality (LMI). We realize the purpose that the output of tracking control system asymp-totically track the output of given reference model. Finally, a simulation example is presented to verify the validity of the proposed method.(2) Finite-time output tracking control problem for a class of uncertain systems with nonlinear terms is investigated in this paper. Firstly, the adaptive law of unknown disturbance parameter p in the uncertain system with nonlinear term is given by the idea of adaptive control, and the estimate of the unknown disturbance parameter p is obtained. Secondly, using the p, the sliding control law for the auxiliary system is proposed by variable structure control theory, guaranteeing the trajectories of the auxiliary system to arrive at the switching surface in finite time interval and be kept here thereafter. Finally, the sufficient condition for finite-time stability of the auxiliary system via the Lyapunov stability theorem is presented, making the output of the tracking control system follow the output of given reference model in finite time. A simulation example is presented to verify the validity of the proposed method.