Nonholonomic dynamic linearisation based adaptive PID-type ILC for nonlinear systems with iteration-varying uncertainties

In this work, three nonholonomic dynamic linearisation based adaptive P-, PD-, and PID-type iterative learning control schemes are proposed for nonlinear plants with nonrepetitive uncertainties including the different initial states and the iteration varying desired trajectories. We first linearise a non-affined nonlinear system into a linearly affined data model by developing a nonholonomic dynamic linearisation in iteration domain without assuming that the difference between the control inputs in two consecutive iterations be nonzero. On this basis, three adaptive P-type, PD-type, PID-type ILC methods are proposed, respectively. Moreover, both a projection-based parameter updating law to estimate unknown gradients and an iteration-difference observer to estimate nonlinear uncertainties are developed together. The proposed approaches not only have data-driven property like the traditional PID-type ILC, but also can deal with nonrepetitive uncertainties in initial states, desired trajectories, disturbances and so on, like the traditional adaptive ILC. The effectiveness and applicability of the three methods are confirmed by rigorous derivation and simulations.