scholarly journals Optimal control of system governed by nonlinear volterra integral and fractional derivative equations

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Leila Moradi ◽  
Dajana Conte ◽  
Eslam Farsimadan ◽  
Francesco Palmieri ◽  
Beatrice Paternoster
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Optimal Solution ◽  
Control Problems ◽  
Operational Matrices ◽  
Optimal Solutions ◽  
Discrete Problems ◽  
The Galerkin Method ◽  
Chelyshkov Polynomials

AbstractThis work presents a novel formulation for the numerical solution of optimal control problems related to nonlinear Volterra fractional integral equations systems. A spectral approach is implemented based on the new polynomials known as Chelyshkov polynomials. First, the properties of these polynomials are studied to solve the aforementioned problems. The operational matrices and the Galerkin method are used to discretize the continuous optimal control problems. Thereafter, some necessary conditions are defined according to which the optimal solutions of discrete problems converge to the optimal solution of the continuous ones. The applicability of the proposed approach has been illustrated through several examples. In addition, a comparison is made with other methods for showing the accuracy of the proposed one, resulting also in an improved efficiency.

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.

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