This research was conducted independently of any similar results produced earlier. After submission of the note to the journal Complexity, a reviewer pointed out that the possibility of interpretation of chaotic systems as optimally controlled systems or as optimal games has been known since the mid-80’s in the Economic Sciences, see e.g.

Because the approach and formalism applied here is slightly different than those in previous publications, and because the presented examples are, to the best of our knowledge, new, this note deserves publication as an internal report.

ABSTRACT

An interpretation of some chaotic systems as the result of optimal decisions is presented. First, a generalised discrete-time two-person game is introduced that may be solved by Dynamic Programming. Then, a specific game of this type is formulated whose optimal solution transforms an originally linear discrete-time system into a well-known discrete-time chaotic system. Finally, a particular continuous-time optimal control problem is formulated whose optimal feedback solution transforms an originally linear continuous-time system into a well-known continuous-time chaotic system.

TABLE OF CONTENTS

PREFACE

ABSTRACT

1. INTRODUCTION

2. A GENERALIZED TWO-PERSON GAME

3. CHAOS AS AN OPTIMAL GAME

4. CHAOS AS AN OPTIMALLY CONTROLLED SYSTEM

REFERENCES