Fractional Behaviours Modelling with Volterra Equations: Application to a Lithium-Ion Cell and Comparison with a Fractional Model

Abstract

This paper proposes to model fractional behaviors using Volterra equations. As fractional differentiation-based models that are commonly used to model such behaviors exhibit several drawbacks and are particular cases of Volterra equations (in the kernel definition), it appears legitimate in a modeling approach to work directly with Volterra equations. In this paper, a numerical method is thus developed to identify the kernel associated to a Volterra equation that describes the input–output behavior of a system. This method is used to model a lithium-ion cell using real data. The resulting model is compared to a fractional differentiation-based model with the same number of tunable parameters.

State estimation problem for fractional-order neural networks using event-triggered state observers

“…The solution to the convex optimization problem minimizes the attenuation levels and thus reduces the error in estimating the state vector of the FONNs. An effective algorithm (see, Algorithm 1) has been obtained for designing discrete-time event-triggered nonlinear fractional-order state observer equations (10) and (11).…”

“…Therefore, fractional calculus is extensively applicable in many areas, such as electrical circuits, 3 Lu systems, 4 quantum mechanics, 5 economic systems, 6 neural networks, 7 positive systems, 8 multiagent systems, 9 adsorption and desorption processes with power-law kinetics, 10 and lithium-ion cell. 11 As we all know, the information on the state vectors of dynamical systems is essential for monitoring, stabilizing, [12][13][14] fault diagnosis, fault detection, and isolation. 15 Nevertheless, in many control processes, the information on the state vectors of the systems is often unavailable due to technical or economic reasons.…”

“…1. For the first time, a novel method based on a DETM (see, equation ( 6)) and a nonlinear fractional-order state observer (see, equations (10) and (11)) is derived to estimate the state vector of FONNs subject to external disturbances. The novelty of our work compared with existing works [25][26][27][28][29][30] is fourfold.…”

“…Therefore, fractional calculus is extensively applicable in many areas, such as electrical circuits, 3 Lu systems, 4 quantum mechanics, 5 economic systems, 6 neural networks, 7 positive systems, 8 multiagent systems, 9 adsorption and desorption processes with power-law kinetics, 10 and lithium-ion cell. 11…”