### Abstract

In this research was discuss about equation of dynamic system game with infinite time for scalar case with discount factor. Based system of dynamic game formed algebraic Riccati equation for infinite time. Furthermore, based solution from algebraic Riccati equation, formed feedback Nash for each player. Then analyzed about stability of system with substitution feedback Nash to differential equation dynamic system. Moreover, for existence solution and uniqueness solution of feedback Nash, resulting for s_{1} = 0 and s_{2} = 0 founded solution for feedback Nash and there is one feedback Nash solution which stabilize dynamic system.

Original language | English |
---|---|

Pages (from-to) | 3463-3468 |

Number of pages | 6 |

Journal | Global Journal of Pure and Applied Mathematics |

Volume | 12 |

Issue number | 4 |

Publication status | Published - 2016 |

### Fingerprint

### Keywords

- Discount
- Dynamic
- Game
- Riccati
- Scalar

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Global Journal of Pure and Applied Mathematics*,

*12*(4), 3463-3468.

**Optimal control feedback Nash in the scalar infinite non-cooperative dynamic game with discount factor.** / Andiraja, Nilwan; Yendra, Rado; Despina, Ari Pani; Rahmadeni, ; Fudholi, Ahmad.

Research output: Contribution to journal › Article

*Global Journal of Pure and Applied Mathematics*, vol. 12, no. 4, pp. 3463-3468.

}

TY - JOUR

T1 - Optimal control feedback Nash in the scalar infinite non-cooperative dynamic game with discount factor

AU - Andiraja, Nilwan

AU - Yendra, Rado

AU - Despina, Ari Pani

AU - Rahmadeni,

AU - Fudholi, Ahmad

PY - 2016

Y1 - 2016

N2 - In this research was discuss about equation of dynamic system game with infinite time for scalar case with discount factor. Based system of dynamic game formed algebraic Riccati equation for infinite time. Furthermore, based solution from algebraic Riccati equation, formed feedback Nash for each player. Then analyzed about stability of system with substitution feedback Nash to differential equation dynamic system. Moreover, for existence solution and uniqueness solution of feedback Nash, resulting for s1 = 0 and s2 = 0 founded solution for feedback Nash and there is one feedback Nash solution which stabilize dynamic system.

AB - In this research was discuss about equation of dynamic system game with infinite time for scalar case with discount factor. Based system of dynamic game formed algebraic Riccati equation for infinite time. Furthermore, based solution from algebraic Riccati equation, formed feedback Nash for each player. Then analyzed about stability of system with substitution feedback Nash to differential equation dynamic system. Moreover, for existence solution and uniqueness solution of feedback Nash, resulting for s1 = 0 and s2 = 0 founded solution for feedback Nash and there is one feedback Nash solution which stabilize dynamic system.

KW - Discount

KW - Dynamic

KW - Game

KW - Riccati

KW - Scalar

UR - http://www.scopus.com/inward/record.url?scp=84988674621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988674621&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84988674621

VL - 12

SP - 3463

EP - 3468

JO - Global Journal of Pure and Applied Mathematics

JF - Global Journal of Pure and Applied Mathematics

SN - 0973-1768

IS - 4

ER -