Control and Optimization
Akbar Hashemi Borzabadi; Mohammad Gholami Baladezaei; Morteza Ghachpazan
Abstract
This paper explores the advantages of Sub-ODE strategy in deriving near-exact solutions for a class of linear and nonlinear optimal control problems (OCPs) that can be transformed into nonlinear partial differential equations (PDEs). Recognizing that converting an OCP into ...
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This paper explores the advantages of Sub-ODE strategy in deriving near-exact solutions for a class of linear and nonlinear optimal control problems (OCPs) that can be transformed into nonlinear partial differential equations (PDEs). Recognizing that converting an OCP into differential equations typically increases the complexity by adding constraints, we adopt the Sub-ODE method, as a direct method, thereby negating the need for such transformations to extract near exact solutions. A key advantage of this method is its ability to produce control and state functions that closely resemble the explicit forms of optimal control and state functions. We present results that demonstrate the efficacy of this method through several numerical examples, comparing its performance to various other approaches, thereby illustrating its capability to achieve near-exact solutions.
Mohammad Gholami Baladezaei; Morteza Gachpazan; Akbar Hashemi Borzabadi
Abstract
In this paper, the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems. In the given approach, first state and control functions have been parameterized as a power series, ...
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In this paper, the benefits of 1/G'-expansion technique are utilized to create a direct scheme for extracting approximate solutions for a class of optimal control problems. In the given approach, first state and control functions have been parameterized as a power series, which is constructed according to the solutions of a Bernoulli differential equation, where the number of terms in produced power series is determined by the balance method. A proportionate replacement and solving the created optimization problem lead to suitable solutions close to the analytical ones for the main problem. Numerical experiments are given to evaluate the quality of the proposed method.
