A General Formulation and Solution Scheme for Fractional Optimal Control Problems

By Om Prakash Agrawal. 2004

829 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/5a6a25011713fd8cb8306c94eff1b124f087d4a9

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Citations in the corpus

A numerical solution for fractional optimal control problems via Bernoulli polynomials (2016, methodology): “The necessary conditions of optimality for FOCPs with Riemann–Liouville fractional derivatives, as outlined by Agrawal (2004) and Agrawal and Baleanu (2004), results in a Hamiltonian system of equations.”
An efficient approximate method for solving delay fractional optimal control problems (2016, methodology): “A general formulation and a solution scheme for FOCPs were first introduced in [2], where fractional derivatives were introduced in the Riemann–Liouville sense, and FOCP formulation was expressed using the fractional variational principle and the Lagrange multiplier technique.”
Fractional order optimal control problems with free terminal time (2013, neutral): “, [1, 3, 4, 8, 9, 23, 24]).”
A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems (2007, methodology): “…(4), the necessary equations for the optimal control are given as t D 1 H x (11) H u 0 (12) and 0 D t x H (13) Following the approach presented in Agrawal (2004), we also require that 1 0 (14) Equations (11)–(14) represent the necessary conditions in terms of a Hamiltonian for the optimal…”
Non standard finite difference method for solving variable order fractional optimal control problems (2017, methodology): “…that our numerical results for problem 2 achieve better agreement with other techniques of solutions used for the constant order derivatives as in Agrawal (1989, 2002, 2004), Agrawal and Baleanu (2008), Baleanu et al. (2009), Biswas and Sen (2009), Jafari and Trajadodi (2014, Khadr and Hendy…”
RETRACTED: Optimal control of fractional order singular system (2019, methodology): “E In this regard, Agrawal 31 presented a variational virtual work-based approximate numerical scheme for solving necessary conditions of FOCPs.”
Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices (2013, background): “Consider the following time invariant problem (Agrawal, 2004; Lotfi et al., 2011) Minimize J ¼ 1 2 Z 1 0 x2ðtÞ þ u2ðtÞdt , subject to the system dynamics D xðtÞ ¼ xðtÞ þ uðtÞ, with initial condition xð0Þ ¼ 1: For this problem we have the exact solution in the case of ¼ 1 as follows xðtÞ ¼ coshð…”
Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem (2007, background): “This is different from [2, 14, 15] where the necessary conditions only involve the same type of derivatives (Riemann-Liouville) as those in the definition of the fractional optimal control problem.”
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 hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems (2017, background): “For instance, Agrawal (2004) proposed general formulations and numerical schemes to solve FOCPs in the Riemann–Liouville and Caputo senses.”
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, methodology): “…to (16), the necessary equations for the optimal control are given as 0D t x ¼ @H @l , tD 1l ¼ @H @x , @H @u ¼ 0 ð17Þ following the approach presented in Agrawal (2004), we also require that lð1Þ ¼ 0 ð18Þ Equations (17) represent the necessary conditions in terms of a Hamiltonian for the FOCPs…”
Fractional optimal control problems: a pseudo-state-space approach (2011, methodology): “Agrawal (2004) developed a formulation of the FOCP and used a variational virtual-workbased formulation to develop a numerical scheme in which the solution is approximated over the entire domain using some approximating functions.”