Piecewise Linear Approximation and PID Control Optimization for Nonlinear Systems

[2501.00820] Piecewise Linear Approximation and PID Control Optimization for Nonlinear Systems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2501.00820 (math) [Submitted on 1 Jan 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: Piecewise Linear Approximation and PID Control Optimization for Nonlinear Systems Authors: Robert Vrabel View a PDF of the paper titled Piecewise Linear Approximation and PID Control Optimization for Nonlinear Systems, by Robert Vrabel View PDF HTML (experimental) Abstract: This paper investigates the control of nonlinear systems using a piecewise linear approximation framework. The proposed approach combines a PID controller with locally linearized models obtained by partitioning the nonlinear function into subregions over a compact domain. This approximation yields an analytically tractable representation of the system dynamics, enabling the application of transfer-based and frequency-domain analysis tools that are not directly applicable to nonlinear systems. As the number of linear segments increases, the approximated system progressively approaches the behavior of the original nonlinear system, allowing for a meaningful frequency-domain interpretation of the dynamics. The PID controller parameters are optimized using the Particle Swarm Optimization method with performance criteria based on ITAE (Integral of Time-weighted Absolute Error) and ISO (Integral of Squared Overshoot). Numerical simulations confirm the effectiveness of the proposed method, demonstrating that controller parameters obtained from the piecewise linear model ensure stable and accurate control when applied to the original nonlinear system, while maintaining a balance between computational effort and approximation accuracy. Subjects: Optimization and Control (math.OC) MSC classes: 93C10 (Primary) 93C15, 68T20 (Secondary) Cite as: arXiv:2501.00820 [math.OC] (or arXiv:2501.00820v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2501.00820 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Robert Vrabel [ view email ] [v1] Wed, 1 Jan 2025 12:46:03 UTC (285 KB) [v2] Sat, 11 Apr 2026 16:59:14 UTC (199 KB) Full-text links: Access Paper: View a PDF of the paper titled Piecewise Linear Approximation and PID Control Optimization for Nonlinear Systems, by Robert Vrabel View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-01 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Weakly chained matrices, policy iteration, and impulse control#984767
• Approximate nonlinear optimal control methodologies#263733
• Extended mean-field control under constraints: The generalized Fritz-John conditions and Lagrangian method#160821
• Convergence Analysis of Newton Methods for Nonlinear Optimal Control Problems#1078188
• Feedback linearization, stability and control of piecewise affine systems exploiting canonical and conventional representations#499376