Adaptive Iterative Learning Control For Nonlinear Systems With Time-varying Parametric Uncertainties

Adaptive iterative learning control, which can solve trajectory trackingproblem of systems with repetitive motion character or restrain periodic interference,is one of the main controlling methods of nonlinear systems with time-varyingparametric uncertainties currently. However, while there exit time-delay or unknowncontrol directions in time-varying parametric uncertain nonlinear systems, seldomresearches have been made on iterative learning control, and the results are not veryideal, especially the problem of uniform convergence of the tracking error is stillunsolved. In fact, time-delay phenomenon and unknown control directionphenomenon are very common in practical systems. Time-delay has a huge impacton the controlling performance, while unknown control direction increases thedifficulty of the design of the control algorithm greatly. Therefore, researches basedon these problems have important theoretical value and practical significance.Adaptive Iterative learning control algorithms are proposed in this paper fortime-varying parametric uncertain systems with time-delay or unknown controldirections, these studies have achieved the following significant results.1. Adaptive iterative learning control for a class of time-delay nonlinear systemwith unknown time-varying parameter. An adaptive iterative learning controlalgorithm is proposed by using parameter separation technique to deal withtime-delay problem. Generally, traditional convergence proof can only getL2convergence or pointwise convergence on the iteration interval. But in this paper,by constructing a new composite energy function and using a new analysis method,we can prove the tracking error converge to zero uniformly on the iteration intervalas the iteration number approaches to infinity.2. Repetitive learning control for a class of nonlinear system with unknowncontrol direction. Now, although few studies have been made of nonlinear systemwith time-varying uncertainties, the problem of uniform convergence hasn’t beensolved. For a class of nonlinear systems with unknown time-varying parameter andunknown control direction, an adaptive repetitive learning control law which is based on Nussbaum-type gain function and a new composite energy function is proposed inthis paper. The construction of the new composite energy function is different frombefore, which only related to the current estimate error of the parameter, it alsorelates to the previous estimate error. The algorithm can guarantee that the trackingerror convergences to zero uniformly on the repetitive interval without use ofsaturation control, which breaks the restrict of having to use saturation control inorder to get uniform convergence. On this basis, we increase unknown constanttime-delay parameter to the original system, combined with time-delay processingmethod and unknown control direction processing method, we design an adaptiverepetitive learning control law. These algorithms can all guarantee the uniformconvergence of the tracking error without using saturation control, which improvesthe existing results.3. Repetitive learning control algorithm for ship direction control. As a practicalapplication, we apply the designed algorithm to the nonlinear ship model withunknown constant and time-varying parameters, to solve the ship direction controlproblem with unknown control direction.4. All the control algorithms proposed in this paper are all simulated by Matlab.The simulation results proved the effectiveness and feasibility of the proposedalgorithm.