A new approach for the nonlinear fractional optimal control problems with external persistent disturbances

DOI10.1016/j.jfranklin.2018.03.012zbMath1390.49016OpenAlexW2796278304WikidataQ130035843 ScholiaQ130035843MaRDI QIDQ1648025

Amin Jajarmi, Mojtaba Hajipour, Ehsan Mohammadzadeh, Dumitru Baleanu

Publication date: 27 June 2018

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2018.03.012

zbMATH Keywords

nonlinear fractional optimal control problemsGrünwald-Letnikov fractional derivativeexternal persistent disturbances

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Perturbations in control/observation systems (93C73) Optimality conditions for problems involving ordinary differential equations (49K15) Fractional ordinary differential equations (34A08)

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Cites Work

• Unnamed Item
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• Nonlinear dynamics for local fractional Burgers' equation arising in fractal flow
• Free final time fractional optimal control problems
• An extension of estimation of domain of attraction for fractional order linear system subject to saturation control
• Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload
• Entropy analysis of integer and fractional dynamical systems
• The Grünwald-Letnikov method for fractional differential equations
• A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations
• A discrete method to solve fractional optimal control problems
• Fractional conservation laws in optimal control theory
• Optimal control of nonlinear time-delay systems with persistent disturbances
• Fractals and fractional calculus in continuum mechanics
• Nonlinear systems. Analysis, stability, and control
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Internal model based tracking and disturbance rejection for stable well-posed systems
• Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
• Disturbance rejection for fractional-order time-delay systems
• Conditional optimization problems: fractional order case
• Statements on chaos control designs, including a fractional order dynamical system, applied to a ``MEMS comb-drive actuator
• Homotopy perturbation technique
• Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method
• A general formulation and solution scheme for fractional optimal control problems
• Active disturbance rejection control for nonlinear fractional-order systems
• Modelling heat transfer in heterogeneous media using fractional calculus
• On the optimal control for fractional multi-strain TB model
• Fractional optimal control problems: a pseudo-state-space approach
• A Central Difference Numerical Scheme for Fractional Optimal Control Problems
• Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances
• A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
• An iterative approach for solving fractional optimal control problems
• Nonlinear Model Predictive Control: An Introductory Review
• Solving fractional optimal control problems within a Chebyshev–Legendre operational technique
• Fractional Optimal Control Problems with Several State and Control Variables
• Fractional Calculus With Applications in Mechanics