An optimal control for a homogeneous linear dynamical systems

الملخص EN

In this article we introduce an approach to find the optimal control for homogeneous linear dynamical systems.

We introduce the linear quadratic regulator problem for the reduced order model of a dynamical system.

We apply the singular perturbation approximations techniques to the original system and obtained our reduced order system.

In this paper, our goal is to examine the solution of the problem as the positive parameter e tends to zero.

Our approach that is based on a formal asymptotic expansion of an algebraic Riccati equations associated with the Pontryagin maximum principle.

We derive an approximate expressions for the optimal feedback controls.

We compute the L2-norm beween the optimal control of the original and reduced system and compare it with the L2-norm of the solution of the Riccati equations of the original and reduced systems.

We test the results numerically and obtained a good closed-loop performance for the model reduction.