Design and implementation of fuzzy-PD controller based on relation models: A cross-entropy optimization approach

This EPJ special topics issue is a collection of contributions about some recent developments in statistical mechanics and dynamical complexity. The various articles report results on statistical fluctuations, non equilibrium models, chaos and nonlinear interactions, complexity and its various associated measures.The long-standing endeavor of Statistical Mechanics is to establish a mathematical framework which allows to encompass different levels of description of a many-particle system: (i) the microscopic setting, stemming from the Boltzmann-Gibbs statistical ensemble theory [1, 2]; (ii) the mesoscopic scale, typically described in the framework of kinetic theory [3-5], interacting particle systems [6][7][8][9][10][11][12] or even more general stochastic processes [13,14]; (iii) the macroscopic level, which is the standard set-up in contexts such as the derivation of hydrodynamic equations, turbulence [15][16][17], Irreversible Thermodynamics [18], etc. Equilibrium phenomena have been investigated and understood much more thoroughly than non-equilibrium ones. At present, the equilibrium theory may be considered complete, for what concerns the microscopic foundations of equilibrium thermodynamics, including the theory of phase transitions and critical phenomena. On the other hand, in spite of the long-standing research activity, Nonequilibrium Statistical Mechanics is still an open field of research. One of the reasons is that nonequilibrium phenomena are so numerous, diverse and complex that attaining a unified description may still appear as an elusive ambition. In particular, away from equilibrium one cannot bypass the analysis of the microscopic dynamics even in the study of stationary states, that are the simplest beyond equilibrium.Nevertheless, relevant progresses were made in this field in the last decades, cf.[19]. We refer, for instance, to the discovery of the Fluctuation Relations for deterministic and stochastic dynamics [20][21][22]. Much effort was needed, in particular, to identify the minimal mathematical ingredients as well as the physical mechanisms lying beneath the validity of such relations [23][24][25]. Another result, whose mathematical theory was originally dug out in the sixties of the last century [26,27] and was then gradually a

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“…Several analytical and experimental results are combined together. The articles can be grouped into six categories, namely: [53][54][55][56] .…”

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confidence: 99%

“…The article [54] is about experimental observation of Fuzzy-PD Controller for a moving robot. The analysis has been investigated with a Cross-Entropy Optimization Approach.…”

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confidence: 99%

Complexity, Chaos and Fluctuations

Banerjee

Colangeli

2017

Eur. Phys. J. Spec. Top.

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“…It is also used in machine learning as a loss function for the training set of neural networks [ 14 ] or to improve the clustering of data [ 15 ]. Further, it is used in robotics for the optimisation of controllers based on fuzzy logic [ 16 , 17 ]. Regarding the social sciences, it can also be used to explain complex global behaviours [ 18 ] and can be used in swarm intelligence [ 19 ].…”

Section: Related Workmentioning

confidence: 99%

Cross-Entropy as a Metric for the Robustness of Drone Swarms

Cofta

Ledziński

Śmigiel

et al. 2020

Entropy

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Due to their growing number and increasing autonomy, drones and drone swarms are equipped with sophisticated algorithms that help them achieve mission objectives. Such algorithms vary in their quality such that their comparison requires a metric that would allow for their correct assessment. The novelty of this paper lies in analysing, defining and applying the construct of cross-entropy, known from thermodynamics and information theory, to swarms. It can be used as a synthetic measure of the robustness of algorithms that can control swarms in the case of obstacles and unforeseen problems. Based on this, robustness may be an important aspect of the overall quality. This paper presents the necessary formalisation and applies it to a few examples, based on generalised unexpected behaviour and the results of collision avoidance algorithms used to react to obstacles.

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“…The simulation results showed that the performance of fuzzy PID was better than that of the traditional LFC [6].…”

Section: Introductionmentioning

confidence: 96%

Control of Different-Axis Two-Wheeled Self-Balancing Vehicles

et al. 2020

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This paper investigates the controls of straight running and turning of a different-axis twowheeled self-balancing (DATWSB) vehicle. The inverted pendulum system (IPS) with gyroscopic effect is used to describe the uncertainty caused by the working conditions. Based on the generalized coordinate systems, the nonlinear mathematical model of the IPS is established according to Lagrange equation. The sliding mode controller (SMC) and adaptive sliding mode controller (ASMC) are respectively designed to control the system, in which the roll angle feedback is used. The simulation results of three models with/without the controllers are presented, which indicate that the ASMC can make the IPS recover upright faster in straight running, and better achieve the desired roll angle in turning compared with the SMC. Bikesim, a commercial software, is used to build a two-wheeled vehicle model with self-balancing function in combination with Matlab/Simulink. The results show that the ASMC can guarantee the anti-interference and turning abilities of the DATWSB vehicle. INDEX TERMS Different-axis two-wheeled self-balancing vehicle, gyroscopic effect, inverted pendulum, sliding mode control, adaptive sliding mode control.

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Design and implementation of fuzzy-PD controller based on relation models: A cross-entropy optimization approach

Cited by 11 publications

References 15 publications

Complexity, Chaos and Fluctuations

Complexity, Chaos and Fluctuations

Cross-Entropy as a Metric for the Robustness of Drone Swarms

Control of Different-Axis Two-Wheeled Self-Balancing Vehicles

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