Adaptive Iterative Learning Control For Nonlinear Systems

In the actual project, because of nonlinear systems exist some phenomena, such as structural uncertainty, unknown parameter, delay and external interfere, which increase difficulty of study. Moreover, using conventional intelligent control is difficult to achieve the desired control objective. However, adaptive iterative learning control is a novel intelligent control and can effectively deal with a series of control problem of nonlinear systems. Thus, in this paper, according to Lyapunov stability theory, we apply adaptive iterative learning control to the studies of single nonlinear systems and complex nonlinear systems(multi-agent systems). The main work includes five aspects as follows.Firstly, for bilinear parameterized single nonlinear systems with unknown time-varying delay, an adaptive iterative learning control scheme is designed. The time-varying delay phenomenon is solved by the parameter recombination technique and the signal replacement theory. A differential-difference couple-type updating law is applied to handle the bilinear parameterized phenomenon. Then, the convergence and stability of systems are proved via constructing a Lyapunov-Krasovskii composite energy function.Secondly, for first-order bilinear parameterized leader-following multi-agent systems with unknown dynamic leader and structural uncertainty, an adaptive iterative learning control strategy is presented. The structural uncertainty term and the unknown dynamic term of leader are combined into a term, and using robust adaptive estimation technique to estimate it. Then applying a differential-difference couple-type updating law to deal with the bilinear parameterized term. And the convergence of consensus error and the boundedness of all signals of closed-loop systems are testified by constructing a Lyapunov functional.Thirdly, we generalize the above first-order leader-following multi-agent systems to second-order and design a fire-new adaptive iterative learning control strategy. Then, the Schur complement theorem and a Lyapunov functional guarantee the consensus error can converge to zero on finite time and the boundedness of all signals of closed-loop systems under.Fourthly, for first-order bilinear parameterized leader-following multi-agent systems with unknown dynamic leader and unknown external interfere, a novel adaptive iterative learning control scheme is proposed. The bilinear parameterized term is handled via importing a differential-difference couple-type updating law. Then the unknown external interfere term and the unknown dynamic term of leader are combined into a new unknown term, and employing adaptive method to estimate it. Moreover, the consensus and stability of multi-agent systems are proved via constructing a Lyapunov functional.Fifthly, this paper gives a Matlab simulation example for each algorithm, which illustrate the validity and feasibility of the algorithm.