Additive-State-Decomposition Dynamic Inversion Stabilized Control for a Class of Uncertain MIMO Systems

TL;DR

This paper introduces a novel additive-state-decomposition dynamic inversion control method for stabilizing uncertain MIMO systems, effectively handling nonparametric time-varying uncertainties and validated through simulations and real quadrotor experiments.

Contribution

It proposes a new control approach combining additive state decomposition and dynamic inversion to stabilize uncertain MIMO systems with large uncertainties.

Findings

Successfully stabilizes uncertain MIMO systems in simulations.

Effectively stabilizes a quadrotor with uncertain inertia moments.

Ensures closed-loop stability under nonparametric uncertainties.

Abstract

This paper presents a new control, namely additive-state-decomposition dynamic inversion stabilized control, that is used to stabilize a class of multi-input multi-output (MIMO) systems subject to nonparametric time-varying uncertainties with respect to both state and input. By additive state decomposition and a new definition of output, the considered uncertain system is transformed into a minimum-phase uncertainty-free system with relative degree one, in which all uncertainties are lumped into a new disturbance at the output. Subsequently, dynamic inversion control is applied to reject the lumped disturbance. Performance analysis of the resulting closed-loop dynamics shows that the stability can be ensured. Finally, to demonstrate its effectiveness, the proposed control is applied to two existing problems by numerical simulation. Furthermore, in order to show its practicability, the proposed control is also performed on a real quadrotor to stabilize its attitude when its inertia moment matrix is subject to a large uncertainty.