Optimal control for a new class of singularly perturbed linear systems

Singularly perturbed linear control systems have been traditionally studied with one-vector input that controls both the slow and fast state variables. Motivated by examples of real physical systems, in this paper we extend the study to corresponding two-vector input systems. We have identified several classes of real physical singularly perturbed systems that can be more efficiently controlled using two-vector inputs. In such systems, one vector input is used to control the slow state space variables and the other vector input is used to control the fast state variables. This control structure offers more flexibility controlling given systems and appears to be more effective. We study the linear-quadratic regulator (LQR) problem for this new class of singularly perturbed systems and develop a numerical algorithm based on fixed-point iterations to obtain its solution. The latter is obtained in terms of reduced-order sub-problems which avoid possible numerical stiffness issues and are computationally advantageous for large scale systems.