Matrix-Scheduling of QSR-Dissipative Systems

TL;DR

This paper introduces a matrix-based gain-scheduling approach for QSR-dissipative systems, enabling more flexible control design and extending existing results to broader system classes, demonstrated through robotic control simulations.

Contribution

It generalizes gain-scheduling using matrices instead of scalar signals, allowing for enhanced control design flexibility and broader applicability to QSR-dissipative systems.

Findings

Matrix scheduling offers greater design freedom.

Extended gain-scheduling results to broader system classes.

Simulation shows improved performance with matrix scheduling.

Abstract

This paper considers gain-scheduling of QSR-dissipative subsystems using scheduling matrices. The corresponding QSR-dissipative properties of the overall matrix-gain-scheduled system, which depends on the QSR properties of the subsystems scheduled, are explicitly derived. The use of scheduling matrices is a generalization of the scalar scheduling signals used in the literature, and allows for greater design freedom when scheduling systems, such as in the case of gain-scheduled control. Furthermore, this work extends the existing gain-scheduling results to a broader class of QSR-dissipative systems. The matrix-scheduling of important special cases, such as passive, input strictly passive, output strictly passive, finite L2 gain, very strictly passive, and conic systems are presented. The proposed gain-scheduling architecture is used in the context of controlling a planar three-link robot subject to model uncertainty. A novel control synthesis technique is used to design QSR-dissipative subcontrollers that are gain-scheduled using scheduling matrices. Numerical simulation results highlight the greater design freedom of scheduling matrices, leading to improved performance.