Formal Methods in Manufacturing

12	Model Predictive Control of Manufacturing Systems with Max-Plus Algebra Ton J.J. van den Boom and Bart De Schutter

CONTENTS

12.1 Introduction

12.1.1 Model Predictive Control For Time-Driven Systems

12.1.2 Max-Plus Algebra And Max-Plus-Linear Systems

12.1.2.1 Max-Plus Algebra

12.1.2.2 Max-Plus-Linear Systems

12.1.2.3 Max-Plus-Scaling Functions and Max-Plus-Nonnegative-Scaling Functions

12.2 Model Predictive Control For Max-Plus-Linear Systems

12.2.1 Evolution Of The System

12.2.2 Cost Criterion

12.2.2.1 Tracking Error or Output Cost Criterion J_out

12.2.2.2 Input Cost Criterion J_in

12.2.3 Constraints

12.2.4 Evolution of The Input Beyond The Control Horizon

12.2.5 Standard Mpc Problem For Mpl Systems

12.2.6 Algorithms to Solve The Mpl–Mpc ...