Adaptive Learning Control Of Nonlinear Systems Based On Unknown Control Direction

Iterative learning control is a kind of typical control strategy of learning control which is an important branch in the field of intelligent control. As a common tool for the repetitive systems, the aim of the iterative learning control is to achieve complete tracking of the object trajectory in a finite time interval. Improving the system control input of the current iteration cycle through the control information obtained of the previous iteration cycle is the basic idea of the iterative learning control. The tracking control problems of the nonlinear dynamic systems with uncertain parameters can be well solved by adaptive method. Adaptive iterative learning control is now developed combining the advantages of adaptive control and the iterative learning control, which can be more widely used in nonlinear systems about tracking control problems. In this pager, some nonlinear systems with unknown control direction are studied combining with the adaptive iterative learning control method. Specifically speaking, the main work of this paper includes the following aspects:Firstly, for a class of one order bilinear parameter uncertain systems with unknown control direction, an adaptive iterative learning control method is proposed. In the alignment condition, initial error allows not to be zero. In the process of the control design, the problem of unknown control direction exited in the systems is resolved by using Nussbaum gain technique. The differential and difference coupling parameter adaptive learning laws are incorporated into the control design to eliminate the influence of the unknown time-varying parameter and the unknown constant parameter in the systems. Then the stability of the systems and the convergence of the tracking error are analyzed by using Lyapunov theory.Secondly, a control scheme is designed after a further research about a class of high order bilinear parameter uncertain systems without a priori knowledge of the control direction through the adaptive iterative learning control method and the Nussbaum function. Then the boundedness of all the signals in the closed-loop systems and the matching of the system states with the reference signals are proved by a constructed Lyapunov composite energy function.Thirdly, after researching the problem about tracking control in a finite time interval for a class of one order non-parameter uncertain systems with unknown control direction and unknown time-varying delay, an adaptive iterative learning control approach is proposed which breaks the zero restriction of the initial system error. The introduction of the Nussbaum method is a good solution to the problem of unknown control direction in the systems. Nonparametric uncertainty with time-varying delay satisfying local Lipschitz condition in the systems is effectively handled by employing technique of inequality, signal replacement mechanism and the parameter adaptive method. And then the stability of the closed-loop systems is strictly proved by using Lyapunov theory.Fourthly, uniform convergence analysis of a class of high order non-parameter uncertain systems with unknown control direction and unknown time-varying delay is further studied and then a robust adaptive iterative learning control method is designed by utilizing the property of Nussbaum function and the method of part limit range. Then a Lyapunov composite energy function is given for the proof of the system states on the full track of the reference signals and the boundedness of all signals in the closed-loop systems.Finally, the feasibility and the effectiveness of the algorithms in the all systems above are verified by a simulation example.