A hybrid parametrization approach for a class of nonlinear optimal control problems

Abstract

In this paper, a suitable hybrid iterative scheme for solving a class of non-linear optimal control problems (NOCPs) is proposed. The technique is based upon homotopy analysis and parametrization methods. Actually an appropriate parametrization of control is applied and state variables are computed using homotopy analysis method (HAM). Then performance index is transformed by replacing new control and state variables. The results obtained from the given method are compared with the results which are obtained using the spectral homotopy analysis method (SHAM), homotopy perturbation method (HPM), optimal homotopy perturbation method (OHPM), modified variational iteration method (MVIM) and differential transformations. The existence and uniqueness of the solution are presented. The comparison and ability of the given approach is illustrated via two examples.

Fitness Dependent Optimizer Based Computational Technique for Solving Optimal Control Problems of Nonlinear Dynamical Systems

“…The authors ultimately yielded more effective approximate numerical results than conventional techniques. M. Alipour et al [7] tailored a hybrid scheme using a combination of the Homotopy Analysis Method (HAM) and discretization techniques. The authors applied this technique to various NOCPs, comparing the obtained approximate solution with the traditional methods and verifying the applicability of the proposed hybrid approach.…”

Perturbed‐analytic direct transcription for optimal control (PADOC)

“…In a recent publication, 33 an analytic transcription method has been presented (presumably as the first appearing attempt in the literature for direct trajectory optimization). The method has been built on the homotopy analysis method (HAM), which is known as a powerful analytic nonlinear solver for about two decades (interested readers are referred to some original references such as References 34‐37).…”

“…In this respect, authors have treated different nonlinearities with different linear operators through the HAM on a case‐by‐case basis (see e.g., References 34,36,38). Therefore, the method proposed in Reference 33 will fail as it confronts strongly‐nonlinear system dynamics. As a consequence, PADOC stands as the first robust analytic transcription method in the literature.…”

Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

“…In addition, control theory of dynamical systems with impulse [7,35,47,74] or time delay [39,48,109,110] have been studied in the last decates. Some other excellent results for such systems are obtained on stability [13,33,42,43,44,61,70,105,106,126,127] and stabilization [8,34,36,46,52,82,112,113], optimal control [1,4,11,17,27,30], etc. As an important component of technology and mathematical control theory, controllability has already gained considerable attention.…”