scholarly journals An Investigation on an Optimal Control Problem with a Fractional Constraint in the Riemann-Liouville Sense

2016 ◽  
Vol 7 ◽  
pp. 10-18
Author(s):  
Mehdi Nategh ◽  
Bahram Agheli
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Adomian Decomposition Method ◽  
Auxiliary Variable ◽  
Analytic Description ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Sufficient And Necessary Conditions ◽  
The Given

This work, deals with a fractional optimal control problem (in the Riemann-Liouville sense). An analytic description of an initial value appears in the constraint of the optimal control problem is presented and some sufficient and necessary conditions for the given initial value is obtained. Making use of an auxiliary variable together with the optimal control law, the given problem is converted into a system of ordinary integro-differential equations. Then using the Adomian decomposition method, an approximate solution is illustrated.

Modified Adomian decomposition method for solving fractional optimal control problems

2017 ◽  
Vol 40 (6) ◽  
pp. 2054-2061 ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems

In this study, we use the modified Adomian decomposition method to solve a class of fractional optimal control problems. The performance index of a fractional optimal control problem is considered as a function of both the state and the control variables, and the dynamical system is expressed in terms of a Caputo type fractional derivative. Some properties of fractional derivatives and integrals are used to obtain Euler–Lagrange equations for a linear tracking fractional control problem and then, the modified Adomian decomposition method is used to solve the resulting fractional differential equations. This technique rapidly provides convergent successive approximations of the exact solution to a linear tracking fractional optimal control problem. We compare the proposed technique with some numerical methods to demonstrate the accuracy and efficiency of the modified Adomian decomposition method by examining several illustrative test problems.

scholarly journals Numerical Optimal Control of HIV Transmission in Octave/MATLAB

2019 ◽  
Vol 25 (1) ◽  
pp. 1 ◽  
Author(s):  
Carlos Campos ◽  
Cristiana J. Silva ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Initial Value

We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70–75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge–Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge–Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article.

scholarly journals Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

2021 ◽  
Author(s):  
Etienne Bertin ◽  
Elliot Brendel ◽  
Bruno Hérissé ◽  
Julien Alexandre dit Sandretto ◽  
Alexandre Chapoutot
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Minimum Principle ◽  
Open Loop ◽  
Pontryagin Minimum Principle ◽  
Interval Method ◽  
Bounded Uncertainties ◽  
The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

scholarly journals Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Wichai Witayakiattilerd
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Delay Function

The existence and uniqueness of a mild solution to nonlinear fuzzy differential equation constrained by initial value were proven. Initial value constraint was then replaced by delay function constraint and the existence of a solution to this type of problem was also proven. Furthermore, the existence of a solution to optimal control problem of the latter type of equation was proven.

On the numerical scheme of a 2D optimal control problem with the hyperbolic system via Bernstein polynomial basis

2018 ◽  
Vol 41 (7) ◽  
pp. 1896-1903 ◽  
Author(s):  
Kamal Mamehrashi ◽  
Sohrab Ali Yousefi ◽  
Fahimeh Soltanian
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Bernstein Polynomial ◽  
Linear Time ◽  
Ritz Method ◽  
Approximate Solutions ◽  
Polynomial Basis ◽  
Bernstein Polynomial Basis ◽  
The Given

A numerical method for solving a 2D optimal control problem (2DOCP) governed by a linear time-varying constraint is presented in this paper. The method is based upon the Bernstein polynomial basis. The properties of Bernstein polynomial functions are presented. These properties, together with the Ritz method, are then utilized to reduce the given 2DOCP to the solution of an algebraic system of equations. By solving this system, the solution of the proposed problem is achieved. The main advantage of this scheme is that the approximate solutions satisfy all initial and boundary conditions of the problem. We extensively discuss the convergence of the method. Finally, an illustrative example is included to demonstrate the validity and applicability of the new technique.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

Sign in / Sign up

Export Citation Format

Share Document