Adaptive Neural Network Iterative Learning Control For Nonlinear Time-delay Systems

The presence of time delay has a significant effect on system performance andindeed destroys the stability of the systems. Therefore, the study for time-delay systemshas important practical interest. During developing Lyapunov's second method, twomain methods—Lyapunov-Krasovskii functionals method and Lyapunov-Razumikhinfunctions method—are used for the study of time-delay systems. For two classes of nonlinear time-delay systems, based on Lyapunov-Krasovskiifunctionals method, three memoryless adaptive tracking control approaches arepresented in this paper. Firstly, for parametric strict feedback nonlinear systems withdelay in the output and parametric output-feedback nonlinear time-delay systems,time-delay filters are introduced to estimate the states of the systems. Two memorylessadaptive tracking control approaches are presented by using backstepping anddomination techniques. The global asymptotical tracking of given trajectories isachieved and the boundedness of all signals of the resulted closed-loop system is alsoguaranteed. Secondly, for two classes of unknown nonlinear time-delay systems, tworobust memoryless adaptive NN control design approach are proposed. Unknowntime-delay functions are approximated by NNs. When the states are unavailable,time-delay filters are designed to estimate the states of the systems. Backsteppingtechnique is used to design adaptive laws and control laws. Domination technique isused to deal with time-delay terms. Adaptive bounding technique is used to deal withunknown boundedness of approximation errors. The arbitrary output tracking accuracyis achieved by tuning the design parameters. Thirdly, based on the results in chapter 3,two design approaches of adaptive iterative learning control (AILC) are proposed fortwo classes of parametric nonlinear time-delay systems. The unknown parameters areestimated in the time domain. The global uniformly exactly tracking of the trajectory onthe specified time interval is achieved and the boundedness of all signals of theclosed-loop system is ensured. Compared with the traditional ILC, the requirement onthe nonlinear time-delay functions is relaxed. Several important problems such as therate of convergence, the initial value and non-uniform objective tracking are alsostudied. The feasibility of the proposed algorithms is illustrated by some simulationexamples.