Design of iterative learning control schemes for systems with zero Markov parameters

This paper gives new results on the design of iterative learning control laws in the repetitive process setting for error convergence and regulation of the transient dynamics. Such control laws are applied to systems that repeat the same operation, known as trials, over a finite duration. The underlying approach is to specify a reference trajectory and using the recorded data from the previous trials to update the control input signal such that the sequence of trial outputs converge to this specified trajectory. For linear time-invariant dynamics, successful design requires that the first Markov parameter is non-zero, i.e., the system transfer-function is proper. The new design in this paper allows direct treatment of strictly proper dynamics by use of anticipative action based on previous trial data and the resulting design computations are linear matrix inequality based. A simulation case study based on robotic manipulator dynamics, whose model was developed from experimentally measured data, is used to demonstrate the feasibility and effectiveness of the new design procedure.