Article Dans Une Revue Communications in Nonlinear Science and Numerical Simulation Année : 2023

Numerical interpretation of controllability coefficients in nonlinear dynamics

Luis Aguirre
Felipe Freitas
  • Fonction : Auteur

Résumé

As its dual, observability, the controllability of controllable systems actuated in different ways can be quantified by coefficients which can be computed either by a numerical approach or a symbolic one. If the interpretation of observability coefficients is rather straightforward, this is not the case for controllability. This paper, after proposing slight but important adjustments to the computation of numerical controllability coefficients puts forward a numerical framework that can be used to provide some clue as how to interpret the role played by numerical and symbolical controllability coefficients. Using four different chaotic systems, it is showed how controllability may depend on the derivative to which the control law is applied and how this may be related to the corresponding coefficients. In practice could help to decide where to place actuators. The developed framework has two backbones: the power needed to achieve control and the rate of success of the control, the latter is not considered in the surveyed literature. Our results show that numerical and symbolic coefficients quantify different aspects of the problem and confirm how controllability is difficult to interpret in practice without any consideration for observability.

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Dates et versions

hal-05060921 , version 1 (08-05-2025)

Identifiants

Citer

Luis Aguirre, Felipe Freitas, Christophe Letellier. Numerical interpretation of controllability coefficients in nonlinear dynamics. Communications in Nonlinear Science and Numerical Simulation, 2023, 116, pp.106875. ⟨10.1016/j.cnsns.2022.106875⟩. ⟨hal-05060921⟩
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