Robust Output Controllability Analysis and Control Design for Incomplete Boolean Networks with Disturbance Inputs

Lei Deng,Ying Li,Peiyong Zhu,Shihua Fu

doi:10.1155/2018/2940105

Abstract

This paper addresses the problems of robust-output-controllability and robust optimal output control for incomplete Boolean control networks with disturbance inputs. First, by resorting to the semi-tensor product technique, the system is expressed as an algebraic form, based on which several necessary and sufficient conditions for the robust output controllability are presented. Second, the Mayer-type robust optimal output control issue is studied and an algorithm is established to find a control scheme which can minimize the cost functional regardless of the effect of disturbance inputs. Finally, a numerical example is given to demonstrate the effectiveness of the obtained new results.

Highlights

Boolean network (BN) was firstly introduced by Kauffman for modelling genetic regulatory networks (GRNs) [1]
This paper addresses the problems of robust-output-controllability and robust optimal output control for incomplete Boolean control networks with disturbance inputs
To the best of authors’ knowledge, there is no result available for robust output controllability and robust optimal output control of incomplete Boolean control networks (BCNs) with disturbance inputs, which motivates the study of this research

Summary

Introduction

Boolean network (BN) was firstly introduced by Kauffman for modelling genetic regulatory networks (GRNs) [1]. Two interesting problems with biological significance are robust-output-controllability and robust optimal output control for BCNs with disturbance inputs, which deserve investigation for theoretical developments as well as for practical applications. In [33], authors modeled a networked evolutionary game with bankruptcy mechanism as an LCS whose certain controlstates should be forbidden These cases show that the investigation of incomplete BCNs is of practical significance. To the best of authors’ knowledge, there is no result available for robust output controllability and robust optimal output control of incomplete BCNs with disturbance inputs, which motivates the study of this research.

Preliminaries

Main Results

An Illustrative Example

Conclusions