Abstract
Lie groups and control theory are closely related as various engineering problems have been modelled as a control problem on Lie groups. Lie groups play a vital role in studying various concepts of control theory. Keeping in view the contribution of Lie groups in the study of controllability and optimal control, a control system is designed on the Symplectic Lie group \(SP(2, {\mathbb{R}})\). A brief study of optimal control by minimizing the cost function is done. The stability of the system dynamics is thoroughly analysed. And finally, two unconventional numerical integrators, Kahan and Lie–Trotter, have been applied on the system dynamics to study some related properties.
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