High Performance Computing of SDRE models with Discrete Kalman Filtering for Robust H∞-Controls
Abstract
State-dependent Riccati equation (SDRE) control requires repeated online solution of continuous-time algebraic Riccati equations (CAREs). A projected-channel H∞ formulation preserves the physical actuator and sensor dimensions of under-actuated, partially observed systems. We derive a computable sufficient attenuation bound for positive-semidefinite stabilizing Riccati solutions and construct an update that enforces their spectral-radius coupling condition. A discrete Kalman recursion supplies the scheduling state estimates. The two CAREs arising in controller synthesis are solved by a structure-preserving doubling algorithm (SDA) or a warm-started Newton--Kleinman iteration equipped with a doubling Lyapunov solver. Numerical studies use a twelve-state F-16 model with complete aerodynamic forces, moments, and trim, together with quadrotor spiral tracking. With instantaneous command updates, all three CARE backends give essentially the same closed-loop response. In the tracking simulations, measured computation times determine when new control inputs are applied, and the previous inputs are held during computation. SDA and Newton reduce airspeed and pitch errors in all six paired aircraft tracking runs. In the faster quadrotor task with limited computational resources, SDA and Newton complete all paired runs, while runs using MATLAB \texttt{icare} terminate early.
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BibTeX
@misc{cai2026high,
title = {{High Performance Computing of SDRE models with Discrete Kalman Filtering for Robust $H_\infty$-Controls}},
author = {Yunfeng Cai and Tiexiang Li and Wen-Wei Lin and Junxin Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36840},
eprint = {2609.36840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36840},
}
RIS
TY - UNPB
TI - High Performance Computing of SDRE models with Discrete Kalman Filtering for Robust H_∞-Controls
AU - Yunfeng Cai
AU - Tiexiang Li
AU - Wen-Wei Lin
AU - Junxin Zhang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36840
UR - https://arxiv.org/abs/2609.36840
AB - State-dependent Riccati equation (SDRE) control requires repeated online solution of continuous-time algebraic Riccati equations (CAREs). A projected-channel H_∞ formulation preserves the physical actuator and sensor dimensions of under-actuated, partially observed systems. We derive a computable sufficient attenuation bound for positive-semidefinite stabilizing Riccati solutions and construct an update that enforces their spectral-radius coupling condition. A discrete Kalman recursion supplies the scheduling state estimates. The two CAREs arising in controller synthesis are solved by a structure-preserving doubling algorithm (SDA) or a warm-started Newton--Kleinman iteration equipped with a doubling Lyapunov solver. Numerical studies use a twelve-state F-16 model with complete aerodynamic forces, moments, and trim, together with quadrotor spiral tracking. With instantaneous command updates, all three CARE backends give essentially the same closed-loop response. In the tracking simulations, measured computation times determine when new control inputs are applied, and the previous inputs are held during computation. SDA and Newton reduce airspeed and pitch errors in all six paired aircraft tracking runs. In the faster quadrotor task with limited computational resources, SDA and Newton complete all paired runs, while runs using MATLAB \texttt{icare} terminate early.
ER -