Optimal iterative learning control design for continuous-time systems with nonidentical trial lengths using alternating projections between multiple sets.

Iterative learning control (ILC) applies to systems that repeat the same finite duration task repeatedly. Each repetition is usually termed as a trial, and the associated duration is called the trial length. Once a trial is completed, all information is available for use in updating the control input for the subsequent trial. The vast majority of the currently available designs demand a strictly identical trial length. This paper gives a new result on the design and analysis for continuous-time linear dynamics based on a modified alternating projection method, where the trial lengths may be nonidentical. This result employs multiple sets to represent the actual varying trial length dynamics and is developed by reformulating the problem to one that minimizes the defined distance in a Hilbert space setting. Compared to the standard alternating projections using two sets, the theory of alternating projections between multiple sets is employed to obtain deterministic convergence result for the nonidentical trial length problem. A numerical case study is also given to illustrate the application of the new design.