Dual-loop iterative optimal control for the finite horizon LQR problem with unknown dynamics

Abstract

Achieving optimal performance over a finite-time horizon has gained a lot of attention in many engineering applications. Among them, the Finite Horizon Linear Quadratic Regulator (FHLQR) formulation for continuous-time linear time-varying systems has been well studied, with an optimal solution characterised by the Differential Riccati Equation (DRE). The solution of the DRE requires that the exact system dynamics are known. However, this assumption may not always hold, as the plant model might not be completely known or may change over time due to wear and tear. This paper proposes a dual-loop iterative algorithm to find the optimal solutions of the FHLQR formulation for continuous-time LTV ..