Abstract: The Steepest Descent Method (SDM) is, appealingly, a straightforward gradient search technique, but not very effective in most applications, hence not recommended as a plug-and-play optimization procedure for several reasons. The SDM will often zigzag toward an optimum, requiring more steps of relatively little improvement toward the optimum. A significant disadvantage of the SDM for optimization problems is the number of iterations required to locate an extremum accurately. The search for a better, efficient, and robust technique, peculiar not to solving optimization problems alone but to solving optimal control problems, led to the Improved Steepest Descent Method (ISDM). The Improved Steepest Descent Method (ISDM) would solve nonlinear two-point boundary-value problems to determine the optimal controls and trajectories of Continuous-Time Linear Quadratic Regulator Problems (CLQRP). The method was employed to solve some CLQRP. The numerical results obtained from the ISDM show improvement over the classical SDM which is favourable compared with existing results.
Keywords: Optimal Control, Improved Steepest Descent Method, Continuous-Time Quadratic Linear Regulator Problem.
Title: On Application of Improved Steepest Descent Method (ISDM) Algorithm to Determine the Optimal Control and Trajectories of Continuous-Time Linear Quadratic Regulator Problems (CLQRP)
Author: Adebayo Kayode James, Alabi Taiye John, Adisa Isaac Olabisi, Ademoroti Albert Olalekan, Dele-Rotimi Adejoke Olumide
International Journal of Interdisciplinary Research and Innovations
ISSN 2348-1218 (print), ISSN 2348-1226 (online)
Vol. 13, Issue 3, July 2025 - September 2025
Page No: 88-96
Research Publish Journals
Website: www.researchpublish.com
Published Date: 21-July-2025
