Deadbeat control: construction via sets

TL;DR

This paper introduces a geometric method for designing deadbeat controllers for nonlinear systems using iterative set computations, providing a constructive approach and algorithms for linear systems.

Contribution

It generalizes deadbeat control to nonlinear systems through a set-based geometric approach, offering new constructive methods and algorithms.

Findings

Provides a geometric framework for deadbeat control of nonlinear systems.

Derives explicit deadbeat feedback laws for example systems.

Introduces an algorithm for computing deadbeat gain in linear scalar-input systems.

Abstract

A geometric generalization of the discrete-time linear deadbeat control problem is studied. The proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively. For demonstration, derivations of deadbeat feedback law and tracker dynamics are provided for various example systems. Based on the method, a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given.