arXiv subjects

Guang-Ren Duan

Publications and source records attributed to Guang-Ren Duan.

4 recordsLinked to original sources

arXiv2026

Determination of the output injection of invertible linear systems for guaranteeing a regular relative degree

For an invertible linear time-invariant system, the Morse normal form reveals that there exist an output injection and an output transformation such that the resulting system possesses a regular relative degree. Based on this fact, this paper develops a method to determine all admissible output injections and output transformations that achieve this property. In contrast to the recursive and implicit computation methods in the existing literature, the proposed determination method for the output injections is explicit and easy to use, since the solutions are obtained by solving linear matrix equations. A rigorous proof of the proposed method is provided, and an illustrative example is presented to demonstrate the applicability of the approach.

math.DS↗

arXiv2026

Observer-Based Active Fault/Disturbance Compensation Control for Fully Actuated Systems

This paper is concerned with fault/disturbance compensation control for fully actuated systems. In particular, we explore observer-based control, incorporating an active compensation mechanism. First, we propose a novel observer with enhanced design flexibility for the fully actuated system model, enabling simultaneous estimation of system states and exogenous unknown signals, such as faults or disturbances. Then, a nonlinear controller is developed with an active fault or disturbance compensation term, leveraging the fully actuated system approach. The asymptotic stability of both the state estimation error and the closed-loop control system is systematically established. Finally, the feasibility and merits of the proposed method are validated through comparative simulations and experiments.

eess.SY↗

arXiv2025

A Unidirectionally Connected FAS Approach for 6-DOF Quadrotor Control

This paper proposes a unidirectionally connected fully actuated system (UC-FAS) approach for the sub-stabilization and tracking control of 6-DOF quadrotors, tackling limitations both in state-space and FAS framework to some extent. The framework systematically converts underactuated quadrotor dynamics into a UC-FAS model, unifying the existing different FAS transformation ways. By eliminating estimation of the high-order derivatives of control inputs, a drawback of current methods, the UC-FAS model simplifies controller design and enables direct eigenstructure assignment for closed-loop dynamics. Simulations demonstrate precise 6-DOF tracking performance. This work bridges theoretical FAS approach advancements with practical implementation needs, offering a standardized paradigm for nonlinear quadrotor control.

eess.SY↗

arXiv2012

Toward Solution of Matrix Equation X=Af(X)B+C

This paper studies the solvability, existence of unique solution, closed-form solution and numerical solution of matrix equation $X=Af(X) B+C$ with $f(X) =X^{\mathrm{T}},$ $f(X) =\bar{X}$ and $f(X) =X^{\mathrm{H}},$ where $X$ is the unknown. It is proven that the solvability of these equations is equivalent to the solvability of some auxiliary standard Stein equations in the form of $W=\mathcal{A}W\mathcal{B}+\mathcal{C}$ where the dimensions of the coefficient matrices $\mathcal{A},\mathcal{B}$ and $\mathcal{C}$ are the same as those of the original equation. Closed-form solutions of equation $X=Af(X) B+C$ can then be obtained by utilizing standard results on the standard Stein equation. On the other hand, some generalized Stein iterations and accelerated Stein iterations are proposed to obtain numerical solutions of equation equation $X=Af(X) B+C$. Necessary and sufficient conditions are established to guarantee the convergence of the iterations.

math.NA↗