Disturbance Attenuation Regulator I-A: Signal Bound Finite Horizon Solution

[2601.10867] Disturbance Attenuation Regulator I-A: Signal Bound Finite Horizon Solution Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2601.10867 (eess) [Submitted on 15 Jan 2026 ( v1 ), last revised 24 Aug 2026 (this version, v3)] Title: Disturbance Attenuation Regulator I-A: Signal Bound Finite Horizon Solution Authors: Davide Mannini , James B. Rawlings View PDF HTML (experimental) Abstract: This paper develops a generalized finite horizon recursive solution to the discrete time signal bound disturbance attenuation regulator (SiDAR) for state feedback control. This problem addresses linear dynamical systems subject to signal bound disturbances, i.e., disturbance sequences whose squared signal two-norm is bounded by a fixed budget. The term generalized indicates that the results accommodate arbitrary initial states. By combining game theory and dynamic programming, we derive a recursive solution for the optimal state feedback policy valid for arbitrary initial states. The optimal policy is nonlinear in the state and requires solving a tractable convex scalar optimization for the Lagrange multiplier at each stage; the control is then explicit. For fixed disturbance budget $\alpha$, the state space partitions into two distinct regions: $\mathcal{X}_L(\alpha)$, where the optimal control policy is linear and coincides with the standard linear $H_{\infty}$ state feedback control, and $\mathcal{X}_{NL}(\alpha)$, where the optimal control policy is nonlinear. We establish monotonicity and boundedness of the associated Riccati recursions and characterize the geometry of the solution regions. A numerical example illustrates the theoretical properties. This work provides a complete feedback solution to the finite horizon SiDAR for arbitrary initial states. Companion papers address the steady-state problem and convergence properties for the signal bound case, and the stage bound disturbance attenuation regulator (StDAR). Subjects: Systems and Control (eess.SY) Cite as: arXiv:2601.10867 [eess.SY] (or arXiv:2601.10867v3 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2601.10867 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Davide Mannini [ view email ] [v1] Thu, 15 Jan 2026 21:34:58 UTC (506 KB) [v2] Thu, 21 May 2026 17:18:25 UTC (663 KB) [v3] Mon, 24 Aug 2026 18:02:17 UTC (664 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2026-01 Change to browse by: cs cs.SY eess References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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