<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

H∞ and guaranteed cost control of discrete linear repetitive processes

AbstractRepetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. In general, they cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here first we give major new results on the design of control laws using an H∞ setting and including the possibility of uncertainty in the process model. Then we give the first ever results on guaranteed cost control, i.e. including a performance criterion in the design. The designs in both cases can be computed using linear matrix inequalities. These results are for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control

Sparse Iterative Learning Control with Application to a Wafer Stage: Achieving Performance, Resource Efficiency, and Task Flexibility

Trial-varying disturbances are a key concern in Iterative Learning Control (ILC) and may lead to inefficient and expensive implementations and severe performance deterioration. The aim of this paper is to develop a general framework for optimization-based ILC that allows for enforcing additional structure, including sparsity. The proposed method enforces sparsity in a generalized setting through convex relaxations using $\ell_1$ norms. The proposed ILC framework is applied to the optimization of sampling sequences for resource efficient implementation, trial-varying disturbance attenuation, and basis function selection. The framework has a large potential in control applications such as mechatronics, as is confirmed through an application on a wafer stage.Comment: 12 pages, 14 figure