Quadratic Optimization of Initial State for Dynamic Controller in Linear Systems

This study presents an optimization-based controller state initialization method for improving the initial transient response. Uncertainties in the uncontrolled periods around transition events or a large change in the reference may result in unexpected growth of initial tracking error. The proposed method mainly aims to regulate out the initial error at the instance of feedback control initiation with a small amount of control effort and a short settling time. The proposed method minimizes a cost function given by a weighted sum of infinite-horizon square integrals, provided that the other controller parameters are fixed a priori to yield closed-loop stability. The performance-oriented initial controller state optimization is desirable for efficient and rapid initial error convergence in systems such as missiles where agility is of major concern. This study suggests performance-related optimization as an alternative for controller state setting besides zero filling or solving for bump-less transfer in switching systems. The concept and the effectiveness of the proposed method is demonstrated by numerical simulation considering the three-loop missile acceleration autopilot as an example application.