A Formulation and Numerical Scheme for Fractional Optimal Control Problems

By Om Prakash Agrawal. 2008

196 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/151b5ee51d95fb5476f9c38842111ff3936b9f1a

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Citations in the corpus

A new Wavelet Method for Variable‐Order Fractional Optimal Control Problems (2018, background): “The authors in [28,29] have investigated the necessary conditions for optimization of FOCPs.”
An approximate method for solving fractional optimal control problems by hybrid functions (2018, methodology): “The necessary conditions of optimality for FOCPs result in a Hamiltonian system of equations involving both right and left fractional differential operators (Agrawal, 2004; Agrawal and Baleanu, 2007; Agrawal, 2008a,b).”
An efficient approximate method for solving delay fractional optimal control problems (2016, methodology): “Agrawal [1] achieved the necessary conditions of optimization for FOCPs with the Caputo fractional derivative.”
Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost (2020, methodology): “3 The left Caputo fractional derivative of a function f ∈Cn[a,∞) of order α is defined in as follows [7]:”
Existence of a weak solution for fractional Euler-Lagrange equations (2012, background): “-Liouville. We refer to [1, 6, 29] for more details. Let us note that a direct consequence of this work is the emergence of many studies concerning a class of fractional optimal control problems, see [2, 3, 14, 15, 20] and references therein. However, fractional diﬀerential equations are in general ”
A numerical solution for fractional optimal control problems via Bernoulli polynomials (2016, methodology): “The Caputo fractional derivative allows us to incorporate the traditional initial conditions in a straightforward manner (Agrawal, 2008b).”
Non standard finite difference method for solving variable order fractional optimal control problems (2017, methodology): “Linear time variant problems This problem was studied using different techniques in Agrawal and Baleanu (2008), Lotfi et al. (2011), Podlubny (1999) and Tricaud and Chen (2010) for the fixed order derivatives.”
Fractional order optimal control problems with free terminal time (2013, methodology): “u is piecewise continuous. When N = 0 we obtain a classical optimal control problem; the case M = 0 with ﬁxed T has already been studied for diﬀerent types of fractional order derivatives (see, e.g., [1, 3, 4, 8, 9, 22, 23]). In [10] a special type of the proposed problem is also studied for ﬁxed T.”