Control of time-varying systems based on forward Riccati formulation in hybrid functions domain

Abstract

In this paper, the time-varying system control is resolved with the aid of forward Riccati formulation and hybrid functions. The applied Riccati equations need neither advanced knowledge of the system dynamics nor the assumption of the future information of system matrices. Herein, the state space equation of LTV system is rewritten in the Hybrid functions (HF) domain where results a set of linear discrete equations instead of having a complex Forward-in-time Propagating Riccati Equation (FPRE). The HF evolve from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF) that can estimate any functions based on the summation of two series. The feasibility of the proposed method is investigated by various numerical control cases. Numerical results demonstrated that the proposed method is usable in both periodic and non-periodic systems with less control effort and significant damping time.