Numerical Discretization Schemes that Preserve Flatness

TL;DR

This paper introduces numerical discretization schemes designed to preserve the flatness property of control systems, addressing the challenge that standard discretization often destroys this structural feature.

Contribution

The authors develop new discretization methods that maintain flatness in discrete-time systems, building on the concept of discretization maps and extending previous work.

Findings

Discretization schemes that preserve flatness are constructed.

Preservation of flatness enhances control design accuracy.

The approach bridges continuous and discrete control system properties.

Abstract

Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems. Although many control systems evolve in continuous time, control implementation is performed digitally, requiring discretization. It is well known in the literature that discretization does not necessarily preserve structural properties, and it has been established that, in general, flatness is not preserved under discretization (whether exact or approximate). In this paper, inspired by our previous work [1] and based on the notion of discretization maps, we construct numerical schemes that preserve flatness.