Abstract
This study addressed sufficient conditions for the robust monotonic convergence of repetitive discrete-time linear parameter varying systems, with the parameter variation rate bound. The learning law under consideration is an anticipatory iterative learning control. Of particular interest in this study is that the iterations can eliminate the influence of disturbances. Based on a simple quadratic performance function, a sufficient condition for the proposed learning algorithm is presented in terms of linear matrix inequality (LMI) by imposing a polytopic structure on the Lyapunov matrix. The set of LMIs to be determined considers the bounds on the rate of variation of the scheduling parameter. The control law designs polynomial ILC by constructing a sequence of control inputs to a discrete-time R-LPV system, producing an iterative dynamic for the R-LPV system with respect to the polytopic structure for uncertain parameters. Numerical simulations were performed to demonstrate the benefits of the proposed technique.
Highlights
Repetitive linear parameter varying processes (R-LPVs) are a distinct class of 2D systems [1,2] of both system theoretic and application interest whose unique characteristic is a series of sweeps, termed “passes,” through a set of dynamics defined over a fixed finite duration known as the “pass length,” and many articles have been published [3,4]
This study addressed sufficient conditions for the robust monotonic convergence of repetitive discrete-time linear parameter varying systems, with the parameter variation rate bound
1 Introduction Repetitive linear parameter varying processes (R-LPVs) are a distinct class of 2D systems [1,2] of both system theoretic and application interest whose unique characteristic is a series of sweeps, termed “passes,” through a set of dynamics defined over a fixed finite duration known as the “pass length,” and many articles have been published [3,4]
Summary
Repetitive linear parameter varying processes (R-LPVs) are a distinct class of 2D systems [1,2] (i.e., information propagation in two independent directions) of both system theoretic and application interest whose unique characteristic is a series of sweeps, termed “passes,” through a set of dynamics defined over a fixed finite duration known as the “pass length,” and many articles have been published [3,4]. An output, called the “parameter varying pass profile,” is produced, which acts as a forcing function on, and, contributes to, the dynamics of the pass profile [5,6] Physical examples of these processes include long-wall coal-cutting and metal-rolling operations [7]. Applications have arisen, where adopting a repetitive parameter varying process setting for analysis has distinct advantages over alternatives An example of these algorithmic applications is iterative algorithms for solving nonlinear dynamic optimal stabilization problems based on the maximum principle [8], where the use of the repetitive process setting provides the basis for the development of extremely reliable and efficient iterative solution algorithms [9,10,11].
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