Functional Fractional Calculus for System Identification and Controls

Authors:
Shantanu Das
Affiliations:
-
Venue:
Functional Fractional Calculus for System Identification and Controls
Year:
2007

Citing 0
Cited 22

Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems

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Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order

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Order and pole locator estimation in fractional order systems using bode diagram

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A fractional state space realization method with block pulse basis

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Solution of extraordinary differential equations with physical reasoning by obtaining modal reaction series

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Some results of the degenerate fractional differential system with delay

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Dynamical analysis of fractional-order modified logistic model

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Analytical solution of the linear fractional system of commensurate order

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Design of linear phase FIR filters using fractional derivative constraints

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A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices

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Formal analysis of fractional order systems in HOL

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The controllability of fractional control systems with control delay

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Relative controllability of fractional dynamical systems with distributed delays in control

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Relative controllability of fractional dynamical systems with multiple delays in control

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A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives

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Designs of two-dimensional linear phase FIR filters using fractional derivative constraints

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Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation

Automation and Remote Control
Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: Modeling and hardware implementation

Automation and Remote Control
Fractional differential equations and related exact mechanical models

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Fractional-order control of a micrometric linear axis

Journal of Control Science and Engineering
Designs of fractional derivative constrained 1-D and 2-D FIR filters in the complex domain

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Stable multi-domain spectral penalty methods for fractional partial differential equations

Journal of Computational Physics

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Abstract

When a new extraordinary and outstanding theory is stated, it has to face criticism and skepticism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its applications to real life problems. It is extraordinary because it does not deal with ordinary differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls.