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Summary This paper presents a control technique for output tracking of reference signals in continuous‐time dynamical systems. The technique is comprised of the following three elements: (i) a fluid‐flow version of the Newton–Raphson method for solving algebraic equations, (ii) a system‐output prediction which has to track the future reference signal, and (iii) a speedup of the control action for enhancing the tracker's accuracy and, in some cases, stabilizing the closed‐loop system. The technique can be suitable for linear and nonlinear systems, implementable by simple algorithms, and can track reference points as well as time‐dependent reference signals. Though inherently local, the tracking controller is proven to have a global convergence for a class of linear systems. The derived theoretical results of the paper include convergence of the tracking controller and error analysis, and are supported by illustrative simulation and laboratory experiments.
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This content will become publicly available on December 26, 2025
Control of a Noncooperative Positive Nonlinear System by Augmented Positive Linear System Regulation
Positive systems, which are systems whose states are always non-negative, can have both positive linear and positive nonlinear approximations that are valid dynamical models in a prescribed domain. When a linearization of a nonlinear system in a domain near an operating point is equivalent to another linear system representation, a reference-tracking controller for that linear system should also achieve reference-tracking control of the nonlinear system in that domain. Here, we show that only if a linearized positive nonlinear system (PNS) is a positive system (i.e., the PNS is cooperative) will a reference-tracking controller for an equivalent positive linear system realization achieve similar results on the nonlinear system. For an example noncooperative PNS of human blood coagulation, where a published reference-tracking controller assumed a positive linear plant, we develop feedforward and feedback controllers that augment the prior controller to overcome noncooperativity and similarly control the positive nonlinear model.
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- Award ID(s):
- 2339335
- PAR ID:
- 10581021
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Control Systems Letters
- Volume:
- 8
- ISSN:
- 2475-1456
- Page Range / eLocation ID:
- 3303-3308
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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