On the Existence of Optimal Solutions for Optimal Control Problems Involving the Caputo Fractional Derivatives with Nonsingular Kernels

2018 ◽  
Author(s):  
Rafal Kamocki ◽  
Kamil Pajek
Keyword(s):  
Optimal Control ◽  
Fractional Derivatives ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Optimal Solutions ◽  
Caputo Fractional Derivatives ◽  
Existence Of Optimal Solutions

Solving multiobjective optimal control problems using an improved scalarization method

2020 ◽  
Vol 37 (4) ◽  
pp. 1524-1547
Author(s):  
Gholam Hosein Askarirobati ◽  
Akbar Hashemi Borzabadi ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Uniform Distribution ◽  
Optimal Control Problems ◽  
Pareto Frontier ◽  
Optimal Solution ◽  
Control Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multiobjective Optimal Control

Abstract Detecting the Pareto optimal points on the Pareto frontier is one of the most important topics in multiobjective optimal control problems (MOCPs). This paper presents a scalarization technique to construct an approximate Pareto frontier of MOCPs, using an improved normal boundary intersection (NBI) scalarization strategy. For this purpose, MOCP is first discretized and then using a grid of weights, a sequence of single objective optimal control problems is solved to achieve a uniform distribution of Pareto optimal solutions on the Pareto frontier. The aim is to achieve a more even distribution of Pareto optimal solutions on the Pareto frontier and improve the efficiency of the algorithm. It is shown that in contrast to the NBI method, where Pareto optimality of solutions is not guaranteed, the obtained optimal solution of the scalarized problem is a Pareto optimal solution of the MOCP. Finally, the ability of the proposed method is evaluated and compared with other approaches using several practical MOCPs. The numerical results indicate that the proposed method is more efficient and provides more uniform distribution of solutions on the Pareto frontier than the other methods, such a weighted sum, normalized normal constraint and NBI.

Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation

2021 ◽  
pp. 107754632110514
Author(s):  
Asiyeh Ebrahimzadeh ◽  
Raheleh Khanduzi ◽  
Samaneh P A Beik ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Focal Point ◽  
Control Problems ◽  
Operational Matrices ◽  
State Variables ◽  
Caputo Fractional Derivatives ◽  
Fractional Optimal Control ◽  
Whale Optimization ◽  
Fractional Optimal Control Problems

Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann–Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.

Numerical Method for Solving Fractional Optimal Control Problems

2009 ◽  
Author(s):  
Raj Kumar Biswas ◽  
Siddhartha Sen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Control Problems ◽  
Caputo Fractional Derivatives ◽  
Fractional Optimal Control ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Fractional Optimal Control Problems ◽  
The Right

A numerical technique for the solution of a class of fractional optimal control problems has been proposed in this paper. The technique can used for problems defined both in terms of Riemann-Liouville and Caputo fractional derivatives. In this technique a Reflection Operator is used to convert the right Riemann-Liouville derivative into an equivalent left Riemann-Liouville derivative, and then the two point boundary value problem is solved numerically. The proposed method is straightforward and it uses an available numerical technique to solve fractional differential equations resulting from the formulation. Examples considered here show that the numerical results obtained using this and other techniques agree very well.

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