• Adebayo Kayode James
• Dele-Rotimi Adejoke Olumide
• Ayinde Samuel Olukayode
• Olaosebikan Temitayo Emmanuel
• Adisa Isaac Olabisi

This paper presents the optimal regulator for a linear system with a time delay in control input and a quadratic performance index. The duality principle is employed to obtain the dynamic that will govern the optimal regulator applied to the optimal filter for linear systems with a time delay in the observation processes. The performance of the obtained optimal regulator is then evaluated as an illustrative example against the preferred linear regulator usable for linear systems that do not have delays. To test the robustness and efficiency of the technique, several simulation graphs were plotted and tables were drawn to compare the performance of the optimal regulator.

Optimal Control Problems, Optimal Filter, Observation Process, Duality Principle, Optimal Regulator, Time Delay

"Solving Linear Systems of Optimal Control Regulator Problems with a Time Delay in the Control Input", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 6, page no.j723-j728, June-2024, Available :http://www.jetir.org/papers/JETIR2406977.pdf

"Solving Linear Systems of Optimal Control Regulator Problems with a Time Delay in the Control Input", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 6, page no. ppj723-j728, June-2024, Available at : http://www.jetir.org/papers/JETIR2406977.pdf