A Novel Approach for Complete Identification of Dynamic Fractional Order Systems Using Stochastic Optimization Algorithms and Fractional Calculus

TL;DR

This paper presents a new method for identifying fractional-order dynamical systems using fractional calculus and particle swarm optimization, achieving high accuracy even with noisy data.

Contribution

It introduces a novel parameter estimation scheme combining fractional calculus with PSO for complete identification of fractional systems.

Findings

High accuracy in parameter estimation with noisy data

Effective use of fractional calculus for system equations

Robustness of the method under data corruption

Abstract

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The said simultaneous equations are generated and updated using particle swarm optimization (PSO) technique, the fitness function being the sum of squared deviations from the actual set of observations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a very high degree of accuracy even for erroneous data.