A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems

By Om Prakash Agrawal, Dumitru Băleanu. 2007

317 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b0dee7ef13dddb55c6cfb0f203df98339dafe021

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Fractional hamilton formalism within caputo’s derivative (2006, background): “variant convolution semigroups which appear universally as attractors. During the last decade several papers, which deal with fractional variational calculus and its applications, have been published [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]. These applications”
Suboptimal control of fractional-order dynamic systems with delay argument (2018, background): “The OCP reduces to a fractional optimal control problem (FOCP) when either the performance index or the dynamic constraints or both include at least one fractional-order derivative term (Agrawal and Baleanu, 2007; Baleanu et al., 2009; Ezz–Eldien et al., 2015).”
Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics (2010, background): “or Peer Rview Recently, optimal control theory has been generalized to incorporate models of fractional order [9, 10, 11, 12] and fractional calculus is penetrating other non-”
An iterative approach for solving fractional optimal control problems (2018, unknown): “Some numerical methods for solving some types of FOCPs can be seen in Agrawal and Baleanu (2007), Agrawal (2008a, b), Baleanu et al. (2009), Agrawal et al. (2010, 2012), Tricaud and Chen (2010), Lotfi et al. (2011), Yousefi et al. (2011), Jarad et al. (2012), Akbarian and Keyanpour (2013), Alipour…”
Fractional optimal control problems: a pseudo-state-space approach (2011, methodology): “A direct numerical solution technique for solving Two Point Boundary Value Problems (TPBVPs) is proposed by Agrawal (2007).”
NECESSARY OPTIMALITY CONDITIONS FOR FRACTIONAL DIFFERENCE PROBLEMS OF THE CALCULUS OF VARIATIONS (2010, background): “The study of fractional problems of the Calculus of Variations and respective Euler-Lagrange equations is a fairly recent issue – see [1, 2, 5, 7, 8, 11, 13, 15, 16, 21] and references therein – and include only the continuous case.”
Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis (2020, background): “Existence and uniqueness of the solution of these problems are investigated by some researchers such as Agrawal and Baleanu (2007).”
On exact solutions of a class of fractional Euler–Lagrange equations (2007, background): “During the last years the fractional variational principles [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25] have developed and applied to fractional optimal control problems [26, 27].”
Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost (2020, methodology): “5 The right Riemann–Liouvelli fractional derivative of a function f ∈Cn[a,∞) of order α is defined in as follows [32]:”
A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives (2010, background): “During the last years, the fractional variational principles have been applied successfully in control theory [17–19] aswell as in physics [20–29].”
A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems (2017, background): “Many researchers have been interested in studying fractional optimal control problems and finding numerical solutions for them (for instance, see Agrawal and Baleanu, 2007; Agrawal, 2008; Tricaud and Chen, 2010; Dorville et al., 2011; Mophou, 2011; Herzallah, 2012; Sweilam et al., 2013).”