Summary: This paper presents a suboptimal error-tracking iterative learning control (ILC) scheme to solve the trajectory-tracking problem for a class of nonparametric systems with uncertain input gains in the presence of arbitrary initial states. The ILC controller is developed by integrating ILC with suboptimal control. Firstly, a desired error trajectory is constructed according to the given method, and then Sontag formula is employed for the control design of nominal system, while robust control and learning control are synthetically applied to deal with nonparametric uncertainties. While the closed-loop system operates, as iteration number increases, the controller can render system error to perfectly follow its desired error trajectory over the entire time interval, by which, the system state can precisely track its reference signal in the pre-specified part of above-mentioned interval. Numerical simulations demonstrate that our suboptimal error-track ILC scheme improves convergence performance in comparison with conventional solutions.