Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
In this paper, iterative learning control (ILC) of a class of non-affine-in-input processes is considered in Hilbert space, where the plant operators are quite general in the sense that they could be static or dynamic, differentiable or non-differentiable, continuous-time or discrete-time, and so forth. The control problem is first transformed to a problem of solving global implicit function to ensure the uniqueness of desired control input. Then, two contraction mapping-based ILC schemes are proposed in terms of the continuous differentiability of process model, where the learning convergence condition is derived through rigorous analysis. The proposed ILC schemes make full use of the process repetition, deal with system uncertainties easily, and are effective to infinite-dimensional or distributed parameter systems. In the end, the learning controller is applied to the boundary output control of a class of anaerobic digestion process for wastewater treatment. The control efficacy is verified by simulation. ITERATIVE LEARNING CONTROL OF NON-AFFINE-IN-INPUT PROCESSES 41 a stretched string system on a transporter. In [11], the similar ILC scheme is combined with PD controller to compensate for the unknown periodic motion on the right end for a class of axially moving material systems. Although the process models are nonlinear in [10,11], they are mainly designed for the stability maintenance of mechanical processes. Moreover, quasi-Newton-type and Broyden-type ILC laws are considered in [12] and [13], respectively, by formulating the problem in Hilbert space. Although Zhang et al. [14] have applied the quasi-Newton ILC in [12] to carrying robot system successfully, a common deficiency in [12,13] is that the uniqueness of desired control input is not specified, and thus the contraction of input error cannot be guaranteed as they stated. In the ILC of infinite-dimensional systems, such a uniqueness is obviously not trivial and would be crucial when constructing contraction mapping to drive learning convergence.In this paper, similar to [12,13], a class of non-affine-in-input processes that are formulated in Hilbert spaces is considered. Because of the uncertainties associated with the plant operator and the concerned repetitive control environment, the controller is designed under the framework of ILC. In detail, to address the uniqueness of desired control input, the control problem is first transformed to a problem of solving global implicit function. Recall that the problem of implicit function is to solve for the implicitly defined functions u D g.x/ from a functional equation f .x, u/ D 0. Although many versions of implicit function theorem have been devoted to infinite-dimensional settings (e.g., see [15,16]), all need the existence of such a point .x 0 , u 0 / that f .x 0 , u 0 / D 0 and are only applicable locally. The difficulty is overcome by exploiting properties of surjective mappings and applying fixed point theorems in Hilbert space. Then, the uniqueness of desired control input is derived by using th...
In this paper, iterative learning control (ILC) of a class of non-affine-in-input processes is considered in Hilbert space, where the plant operators are quite general in the sense that they could be static or dynamic, differentiable or non-differentiable, continuous-time or discrete-time, and so forth. The control problem is first transformed to a problem of solving global implicit function to ensure the uniqueness of desired control input. Then, two contraction mapping-based ILC schemes are proposed in terms of the continuous differentiability of process model, where the learning convergence condition is derived through rigorous analysis. The proposed ILC schemes make full use of the process repetition, deal with system uncertainties easily, and are effective to infinite-dimensional or distributed parameter systems. In the end, the learning controller is applied to the boundary output control of a class of anaerobic digestion process for wastewater treatment. The control efficacy is verified by simulation. ITERATIVE LEARNING CONTROL OF NON-AFFINE-IN-INPUT PROCESSES 41 a stretched string system on a transporter. In [11], the similar ILC scheme is combined with PD controller to compensate for the unknown periodic motion on the right end for a class of axially moving material systems. Although the process models are nonlinear in [10,11], they are mainly designed for the stability maintenance of mechanical processes. Moreover, quasi-Newton-type and Broyden-type ILC laws are considered in [12] and [13], respectively, by formulating the problem in Hilbert space. Although Zhang et al. [14] have applied the quasi-Newton ILC in [12] to carrying robot system successfully, a common deficiency in [12,13] is that the uniqueness of desired control input is not specified, and thus the contraction of input error cannot be guaranteed as they stated. In the ILC of infinite-dimensional systems, such a uniqueness is obviously not trivial and would be crucial when constructing contraction mapping to drive learning convergence.In this paper, similar to [12,13], a class of non-affine-in-input processes that are formulated in Hilbert spaces is considered. Because of the uncertainties associated with the plant operator and the concerned repetitive control environment, the controller is designed under the framework of ILC. In detail, to address the uniqueness of desired control input, the control problem is first transformed to a problem of solving global implicit function. Recall that the problem of implicit function is to solve for the implicitly defined functions u D g.x/ from a functional equation f .x, u/ D 0. Although many versions of implicit function theorem have been devoted to infinite-dimensional settings (e.g., see [15,16]), all need the existence of such a point .x 0 , u 0 / that f .x 0 , u 0 / D 0 and are only applicable locally. The difficulty is overcome by exploiting properties of surjective mappings and applying fixed point theorems in Hilbert space. Then, the uniqueness of desired control input is derived by using th...
Abstract. In this article, we investigate deformation problems of Q-curvature on closed Riemannian manifolds. One of the most crucial notions we use is the Q-singular space, which was introduced by Chang-Gursky-Yang during 1990's. Inspired by the early work of Fischer-Marsden, we derived several results about geometry related to Q-curvature. It includes classifications for nonnegative Einstein Q-singular spaces, linearized stability of non-Q-singular spaces and a local rigidity result for flat manifolds with nonnegative Qcurvature. As for global results, we showed that any smooth function can be realized as a Q-curvature on generic Q-flat manifolds, while on the contrary a locally conformally flat metric on n-tori with nonnegative Q-curvature has to be flat. In particular, there is no metric with nonnegative Q-curvature on 4-tori unless it is flat.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.