Optimizing semilinear representations for State-dependent Riccati Equation-based feedback control

TL;DR

This paper introduces an optimized method for nonlinear feedback stabilization using semilinear representations of SDREs, aiming to closely approximate the optimal control law from the HJB equation.

Contribution

It proposes a novel approach to construct and optimize semilinear representations for SDREs to improve feedback control accuracy.

Findings

Enhanced stability of closed-loop systems

Near-optimal control performance achieved

Effective approximation of HJB-based feedback

Abstract

An optimized variant of the State Dependent Riccati Equations (SDREs) approach for nonlinear optimal feedback stabilization is presented. The proposed method is based on the construction of equivalent semilinear representations associated to the dynamics and their affine combination. The optimal combination is chosen to minimize the discrepancy between the SDRE control and the optimal feedback law stemming from the solution of the corresponding Hamilton Jacobi Bellman (HJB) equation. Numerical experiments assess effectiveness of the method in terms of stability of the closed-loop with near-to-optimal performance.