Conditional length strategy based iterative learning control for locally lipschitz nonlinear systems with an adaptive observer.

This paper provides an adaptive iterative learning framework for locally Lipschitz nonlinear systems. A reference model based adaptive observer is constructed to estimate unknown states. A conditional length strategy is proposed to ensure the boundedness of system and observer outputs at each iteration. Meanwhile, the projection mechanism and the bounded-input bounded-state property are introduced to sequentially demonstrate the boundedness of observer states, controller, and system states, rendering the locally Lipschitz nonlinearity to a global one. Convergence of tracking error across the full length is elaborated by a composite energy function and a contradiction. Two simulation examples are presented to validate the proposed approach.