Work

Sliding Mode Control of Switched Hamiltonian Systems: A Geometric Algebra Approach

Year: 2025

Type: article

Abstract: In this article, a Geometric Algebra (GA) and Geometric Calculus (GC) based exposition is carried out dealing with the formal characterization of sliding regimes for general Single-Input-Single-Output (SISO) nonlinear switched controlled Hamiltonian systems. Necessary and sufficient conditions for the local existence of a sliding regime on a given vector manifold are presented. Feedback controller design strategies for achieving local sliding regimes on a given smooth vector manifold—defined in the phase space of the system—are also derived using the GA-GC framework. One such controller design method, which is mathematically justified, is based on the invariance property of the leaves of the foliation induced by the sliding surface coordinate function level sets. The idealized average smooth sliding motions are shown to arise from an extrinsic projection operator whose geometric properties are exploited for characterizing robustness with respect to unknown exogenous perturbation vector fields. An application example is provided from the power electronics area.

Source: Advances in Applied Clifford Algebras

DOI: 10.1007/s00006-025-01380-z

Authors: H. Sira-Ramírez, B. C. Gómez-León, M. A. Aguilar-Orduña

Institutions: Instituto Politécnico Nacional, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional

Language: English

Topic: Control and Stability of Dynamical Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Instituto Politécnico Nacional, Consejo Nacional de Ciencia y Tecnología, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional