Repetitive control design based on forwarding for nonlinear minimum-phase systems

Abstract

We propose a new design for a repetitive control scheme for nonlinear minimum-phase systems with arbitrary relative degree and globally Lipschitz nonlinearities. We represent the delay of the repetitive control scheme as a transport equation and we propose a new forwarding-based (partial) state-feedback design that uses not only the boundary information of the delay, but the entire state of the transport equation representing the delay. Through a rigorous mathematical analysis, we show that, from a theoretical point of view, asymptotic convergence of the desired regulated output can be achieved with the proposed control design.

Incremental Stabilization of Cascade Nonlinear Systems and Harmonic Regulation: A Forwarding-Based Design

“…Remark 3. Note that the Assumption 4 extends (for the global case) the assumption in [24, Theorem 1] on the zero-dynamics to have a (locally) exponentially attractive steady-state when y = 0 (see also [34,Assumption 2], [27]).…”

“…In the considered framework, we allow the external signals (r, d) to span the whole R ne × R nu and we look for a global result in the domain of attraction. The existing results have been developed only for the class of nonlinear systems having a globally defined normal form and possessing a minimum phase property [24], [34]. On the other hand, for systems working in the "original" coordinates the existing results are only local in the amplitude of the external signals ( [23], [29]), that is, with the external signal's amplitude being sufficiently small.…”

Artificial neural network–based modelling of pacemaker and its pace tracking using discrete wavelet transform–based finite dimension repetitive controller

“…To continuously monitor the pacing of an implanted pacemaker, in this paper, a modified architecture of FDRC is presented which is depicted in Figure 5. The FDRC includes the factor of 1 1 − e − sL , which corresponds to the sub-harmonic and harmonics of the period L (Astolfi et al, 2021). As a result, the controller can track any periodic signal or can be used to minimize/eliminate any disturbance having the same period.…”

Repetitive Control for Lur’e-Type Systems: Application to Mechanical Ventilation

“…In the existing literature, several studies have considered output tracking problems for continuous-time nonlinear systems. For instance, in [1], [8], [19], and [3], the problem of output tracking for nonlinear systems that can be written in the canonical normal form is considered. In [22], incremental passivity concepts are used for the design of global regulators, and in [25], output regulation of Lur'e-type systems using convergent system properties is considered.…”

“…Although significant progress on output regulation for nonlinear systems has been made, an intuitive RC scheme for nonlinear Lur'e-type systems with a formal stability guarantee is not yet available. To achieve this, a finite-dimensional realization of the exact RC scheme in [9] and [1] is used. The reason to consider a finite-dimensional realization is the difficulty to analyze the interconnection of an infinitedimensional system, i.e., the internal model, with nonlinear plant dynamics with nonlinear outputs.…”