Control of Linear Time-Varying Systems Using Forward Riccati Equation

Abstract

This paper presents a new state feedback control design for linear time-varying systems. In conventional control designs such as the LQ optimal control, the state feedback gain is calculated off-line by solving a Differential Riccati Equation (DRE) backwards with the boundary condition set at some future time. The apparent disad-vantage of using a backward DRE is that future information of the system matrices is required to find the state feedback gain at every time instant. In this paper, an inversion state transformation is applied to the system so that the DRE associated with the transformed system becomes forward in the sense that its boundary condition is set at the initial time of operation (t = t0 ). As a result, the forward DRE can be calculated on-line without using future information of the system matrices.