Rachid Malti’s research while affiliated with French National Centre for Scientific Research and other places

The ICFDA 2025 Conference on Fractional Differentiation and its Applications is a specialized conference on fractional-order calculus and its applications. It is a generalization of the integer-order ones. The fractional-order differentiation of arbitrary orders takes into account the memory effect of most systems. The order of the derivatives may also be variable, distributed or complex. Recently, fractional-order calculus became a more accurate tool to describe systems in various fields in mathematics, biology, chemistry, medicine, mechanics, electricity, control theory, economics, and signal and image processing. The ICFDA 2025 Conference will be held In Algiers, Algeria. The conference will be in face-to-face meetings.

The International Energy Agency (IEA) 2023 report highlights that global energy losses have persisted over the years, with 32% of the energy supply lost in 2022 alone. To mitigate this, this research adopts optimisation to enhance the efficiency of district heating networks (DHNs), a key global energy supply technology. Given the dynamic nature of DHNs and the challenges in predicting disturbances, a dynamic real-time optimisation (DRTO) approach is proposed. However, this research does not implement DRTO; instead, it develops a fast grey-box linear parameter varying (LPV) model for future integration into the DRTO algorithm. A high-fidelity physical model replicating theoretical time delays in pipes serves as a reference for model validation. For a single pipe, the grey-box model achieved a 91.5% fit with an R2 value of 0.993 and operated 5 times faster than the reference model. At the DHN scale, it captured 98.64% of the reference model’s dynamics, corresponding to an R2 value of 0.9997, while operating 52 times faster. Low-fidelity physical models (LFPMs) were also developed and validated, proving to be more precise and faster than the grey-box models. This research recommends performing dynamic optimisation with both models to determine which better identifies local minima.

The paper addresses structural properties of distributed order controllers. A Distributed Order PID (DOPID) controller is a control structure in which a continuum of “differintegral” actions of orders between -1 and 1 are integrated together, and where relative contributions of different orders is determined by a weighting function. This stands in sharp contrast to conventional proportional-integral-derivative controllers, or even fractional order PID (FPID) controller and multi-term FPID, in which discrete actions appear only and a finite set of real parameters, controller gains, are sufficient to specify contributions of each action. The paper presents an in-depth analysis of the DOPID controller, emphasizing its theoretical properties and distinctions with integer and fractional order PID. It is shown that DOPID can be considered a generalization of these controllers only if the weighting function is a sequence of Dirac pulses. Some structural deficiencies of DOPID in case of a wide class of weighting functions have been emphasized. A modified DOPID structure — which we refer to as the DOPID of the Second Kind — is proposed and analyzed as well. Among other things, it has been shown that such modified DOPID controller provides better generalization to discrete order controllers (PID and FPID). This work is an extended and supplemented version of the paper presented at ICFDA 2024 at Bordeaux University, July 2024 (see [27]).

In this paper, the problem of identifying Multiple-Input-Single-Output (MISO) systems with fractional models from noisy input-output available data is studied. The proposed idea is to use Higher-Order-Statistics (HOS), like fourth-order cumulants (foc), instead of noisy measurements. Thus, a fractional fourth-order cumulants based-simplified and refined instrumental variable algorithm (frac-foc-sriv) is first developed. Assuming that all differentiation orders are known a priori, it consists in estimating the linear coefficients of all Single-Input-Single-Output (SISO) sub-models composing the MISO model. Then, the frac-foc-sriv algorithm is combined with a nonlinear optimization technique to estimate all the parameters: coefficients and orders. The performances of the developed algorithms are analyzed using numerical examples. Thanks to fourth-order cumulants, which are insensitive to Gaussian noise, and the iterative strategy of the instrumental variable algorithm, the parameters estimation is consistent.