Math. Model. Nat. Phenom.
Volume 14, Number 3, 2019
Fractional order mathematical models in physical sciences
|Number of page(s)||19|
|Published online||30 April 2019|
Local generalization of transversality conditions for optimal control problem★
Department of Mathematics, University of Balikesir,
* Corresponding author: firstname.lastname@example.org
Accepted: 19 February 2019
In this paper, we introduce the transversality conditions of optimal control problems formulated with the conformable derivative. Since the optimal control theory is based on variational calculus, the transversality conditions for variational calculus problems are first investigated and then supported by some illustrative examples. Utilizing from these formulations, the transversality conditions for optimal control problems are attained by using the Hamiltonian formalism and Lagrange multiplier technique. To illustrate the obtained results, the dynamical system on which optimal control problem constructed is taken as a diffusion process modeled in terms of the conformable derivative. The optimal control law is achieved by analytically solving the time dependent conformable differential equations occurring from the eigenfunction expansions of the state and the control functions. All figures are plotted using MATLAB.
Mathematics Subject Classification: 34H05 / 49K20
Key words: Fractional order / conformable derivative / conformable calculus of variations / conformable optimal control / transversality conditions
© EDP Sciences, 2019
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