Study On Iterative Learning Control For Nonlinear Uncertain Systems

Iterative learning control(ILC) is a suitable control technique for those systems performing tasks repetitively over a finite time interval. It uses the error data to gradually update the learned value, e.g. input signal and the estimate value of unknown parameters,in each cycle. Therefore, after enough cycles, the system state can fully track its desired over the whole interval, with uncertainties independent of iterations having been compensated fully. Lyapunov-based ILC is now a hot topic in ILC system design. To extend ILC application coverage, six dimensions of investigations are carried out in this dissertation.1. Two new ILC algorithms applicable for occasions with any initial error are studied,to solve the contradiction between conventional learning algorithms, with the initial error value assumed to be zero, and the fact in actual occasions, where the initial error is nonzero. On the basis of putting forward the rectified reference signal constructing scheme and the desired error trajectory constructing scheme, reference signal initial rectification method and error-tracking method are presented respectively to deal with different tracking tasks in the controller design of parametric uncertain systems.2. This dissertation looks into state-constrained learning control algorithms to enhance the reliability and robustness for the running system. By constructing barrier Lyapunov functions functions in simple forms, a state-constrained reference signal initial rectification ILC algorithm and a state-constrained error-tracking ILC algorithm are proposed. By deploying the above two algorithms to systems with any initial error, the closed-loop system can get zero-error tracking effect over the part of operating interval, and the magnitude of the system state is enforced to the pre-specified range.3. Dead-zone nonlinearity widely exists in the implementation of control systems and impacts control performance. The dissertation constructs an adaptive learning dead-zone inverse model to estimate the dead-zone’s parameters, so as to compensate the dead-zone nonlinearity. For non-parametric uncertain systems containing a dead zone, this dissertation proposes an adaptive iterative learning control method and an error-tracking learning control method, to solve the tracking problem of zero initial-error systems and nonzero initial-error systems, respectively. On the basis of the above work, this dissertation analyzes the state-constrained problem in error-tracking control design, and gives state-constrained error-tracking control algorithm for non-parametric uncertain systems with input dead-zone nonlinearity.4. Two suboptimal learning control methods, including an iterative one and a repetitive one, are proposed for a class of nonlinear systems with both time-varying parametric and nonparametric uncertainties. Sontag formula is used for the control design of the nominal system, while the robust learning mechanism is applied to deal with both parametric and nonparametric uncertainties. A continuous controller design is carried out, in order to avoid chatter that may arise from the traditional Sontag formula. It is shown that the closed-loop system state follows the desired trajectory with the pre-specified accuracy, as iterations or repetitions increase. Numerical results demonstrate the effectiveness of the suboptimal learning control schemes.5. Consensus problems for parametric uncertain leader-following multi-agent systems are studied with the Lyapunov-based ILC approach. An error-tracking ILC algorithm is proposed, suitable for a class of parametric uncertain multi-agent systems with any initial system error. Also, a state-constrained error-tracking ILC algorithm is given for nonparametric uncertain leader-following multi-agent systems.6. Consensus problems for non-parametric uncertain leader-following multi-agent systems are studied with the Lyapunov-based ILC approach. Three cases are considered, including zero initial error, random initial error, and system state in alignment condition, with three customized ILC algorithms presented respectively. On the basis of the above work,for the sake of better reliability and safety, the state-constrained ILC algorithm and stateconstrained error-tracking ILC algorithm are put forward also for non-parametric uncertain leader-following multi-agent systems.