# m-Order Time Optimal Control Synthesis Function of Discrete System

## TL;DR

This paper introduces an m-order time optimal control synthesis function for discrete systems using generating functions, detailing its derivation, control strategies, and validating their effectiveness through simulations.

## Contribution

It presents a novel m-order synthesis function for discrete systems, extending the 2nd-order case with a generating function approach and new control methods.

## Key findings

- Effective signal extraction and predictive compensation methods
- Immunity and effectiveness verified by numerical simulation
- Extension of 2nd-order synthesis to m-order using generating functions

## Abstract

In this paper, first of all, we introduce the basic concepts of generating function in combinatorics and some combinatorial identities. In order to facilitate the understanding of m-order time optimal control synthesis function of discrete system (referred as m-order synthesis function), secondly, we introduce the derivation process and control ideas of 2nd-order synthesis function, and then deduce in detail the m-order synthesis function by means of generating function. By use of the m-order tracking-form synthesis function with filter factor, the methods of signal extraction and its predictive compensation are presented in this paper, and their immunity and effectiveness are verified by numerical simulation.

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Source: https://tomesphere.com/paper/1905.08096