Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

Fiori, Simone

doi:10.3390/sym13112092

Cited by 19 publications

(11 citation statements)

References 69 publications

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“…3) supports simpler definitions of control of non-linear systems whose states belong to 269 curved manifolds [26].…”

mentioning

confidence: 80%

Antifragile Control Systems: The Case of An Anti-Symmetric Network Model of the Tumor–Immune–Drug Interactions

Axenie¹,

Kurz²,

Saveriano³

2022

Preprint

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A therapy’s outcome is determined by a tumor’s response to treatment which, in turn, depends on multiple factors such as the severity of the disease and the strength of patient’s immune response. Gold standard cancer therapies are in most cases fragile when sought to break the ties to either tumor kill ratio or patient toxicity. Lately, research has shown that cancer therapy can be at most robust when handling adaptive drug resistance and immune escape patterns developed by evolving tumors. This is due to the stochastic and volatile nature of the interactions, at the tumor environment level, tissue vasculature, and immune landscape, induced by drugs. Herein, we explore the path towards antifragile therapy control, that generates treatment schemes that are not fragile but go beyond robustness. More precisely, we describe a first instantiation of a control-theoretic method to make therapy schemes cope with the systemic variability in the tumor–immune–drug interactions and gain more tumor kill with less patient toxicity. Considering the anti-symmetric interactions within a model of the tumor–immune–drug network, we introduce the antifragile control framework that demonstrates promising results in simulation. We evaluate our control strategy against state-of-the-art therapy schemes on various experiments and discuss the insights we gained on the potential that antifragile control could have in treatment design in clinical settings.

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“…3) supports simpler definitions of control of non-linear systems whose states belong to 269 curved manifolds [26].…”

mentioning

confidence: 80%

Antifragile Control Systems: The Case of An Anti-Symmetric Network Model of the Tumor–Immune–Drug Interactions

Axenie¹,

Kurz²,

Saveriano³

2022

Preprint

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“…This rotation matrix is defined to be the one that describes the orientation of the spacecraft-fixed reference frame F C with respect to the station-fixed reference frame F S . In the present context, the mathematical space SOp3q is regarded as a Lie group with tangent bundle TSOp3q and Lie algebra sop3q (see, e.g., [31,32]).…”

Section: Physical Model and Equations Of Motionmentioning

confidence: 99%

Modeling, Simulation and Control of a Spacecraft: Automated Rendezvous under Positional Constraints

Fiori,

Rachiglia,

Sabatini

et al. 2024

Aerospace

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The aim of this research paper is to propose a framework to model, simulate and control the motion of a small spacecraft in the proximity of a space station. In particular, rendezvous in the presence of physical obstacles is tackled by a virtual potential theory within a modern manifold calculus setting and simulated numerically. The roto-translational motion of a spacecraft as well as the control fields are entirely formulated through a coordinate-free Lie group-type formalism. Likewise, the proposed control strategies are expressed in a coordinate-free setting through structured control fields. Several numerical simulations guide the reader through an evaluation of the most convenient control strategy among those devised in the present work.

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“…Such novel regulation scheme will be referred to as M-PID regulation. Control of systems on state manifolds is a relatively new research branch in non-linear control theory which is gaining increasing interest in applied sciences and in engineering, especially in the field of mechanical systems regulation [2,3,13,22,30].…”

mentioning

confidence: 99%

“…Classical numerical methods, such as the Euler method or those in the Runge-Kutta class, will fail if applied directly, as they are intrinsically designed to work on flat spaces and are not suitable to keep up with the non-flat structure of curved manifold-type state spaces. These numerical methods may, however, be extended so as to cope with curved state manifolds by means of numerical calculus on manifold [10,11,13].…”

mentioning

confidence: 99%

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Synchronization of dynamical systems on Riemannian manifolds by an extended PID-type control theory: Numerical evaluation

Fiori

Cervigni

Ippoliti

et al. 2022

DCDS-B

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<p style='text-indent:20px;'>The present document outlines a non-linear control theory, based on the PID regulation scheme, to synchronize two second-order dynamical systems insisting on a Riemannian manifold. The devised extended PID scheme, referred to as M-PID, includes an unconventional component, termed 'canceling component', whose purpose is to cancel the natural dynamics of a system and to replace it with a desired dynamics. In addition, this document presents numerical recipes to implement such systems, as well as the devised control scheme, on a computing platform and a large number of numerical simulation results focused on the synchronization of Duffing-like non-linear oscillators on the unit sphere. Detailed numerical evaluations show that the canceling contribution of the M-PID control scheme is not critical to the synchronization of two oscillators, however, it possesses the beneficial effect of speeding up their synchronization. Simulation results obtained in non-ideal conditions, namely in the presence of additive disturbances and delays, reveal that the devised synchronization scheme is robust against high-frequency additive disturbances as well as against observation delays.</p>

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Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

Cited by 19 publications

References 69 publications

Antifragile Control Systems: The Case of An Anti-Symmetric Network Model of the Tumor–Immune–Drug Interactions

Antifragile Control Systems: The Case of An Anti-Symmetric Network Model of the Tumor–Immune–Drug Interactions

Modeling, Simulation and Control of a Spacecraft: Automated Rendezvous under Positional Constraints

Synchronization of dynamical systems on Riemannian manifolds by an extended PID-type control theory: Numerical evaluation

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