The Research Of Iterative Learning Control Of Nonlinearly Parameterized Systems

Iterative learning control is one kind of control methodology effectively dealing with repeated tracking control problems or periodic disturbance rejection problems. Though traditional PID-type iterative learning control algorithms can achieve perfect tracking, they has some defects, such as globally Lipschitz continuity of nonlinear function and initial values resetting. The adaptive iterative learning control, proposed in the mid 90s of the last century, overcame some shortcomings of PID-type methods, and provided powerful tools to handle control problems of parameterized systems.By the forms of uncertain parameters in state equations or output equations, parameterized systems could be divided into linearly and nonlinearly parameterized uncertain systems. Although there are many results in linearly parameterized systems, the progress of nonlinearly parameterized systems has been seldom made. Since many of actual control problems in industry are nonlinear, the research of nonlinearly parameterized systems has of significations both in theory and reality.Based on Lyapunov stability theory, this paper proposes three new adaptive iterative learning control methodologies of nonlinearly parameterized systems. The main results are as follows. Firstly, a new adaptive iterative learning control approach is proposed for a class of nonlinearly parameterized strictly-feedback systems. By merging with parameter separation technique and Backstepping method deal with nonlinearly parameterized uncertain term and unmatched uncertain term. By constructing a differential-difference type updating law and a learning control law makes the tracking error converge to zero in terms of mean-square on the finite interval, meanwhile, by constructing composite energy function, we prove the boundedness of all closed-loop signals in a finite time interval. Secondly, a new adaptive iterative learning control approach is proposed for a class of nonlinearly parameterized systems of unknown control gain with unknown time-varying and time-invariant parameters. Through designing stabilized functions and adaptive law of time-invariant parameters by Lyapunov approach to the first n-1 equations, and re-estimating parameters to the last function, the approach effectively deals with the problem with unknown control gain. Thirdly, a adaptive iterative learning control approach is proposed for a more general class of nonlinearly parameterized systems. The approach effectively deals with the nonlinearly parameterized term with states vector, and achieves tracking problem of the system. Finally, the simulation researches are done for above three methods, which illustrate the effectiveness and feasibility of the proposed algorithms.