### Abstract

This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}^{2} + N{u(t)}^{2}], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) ≦ 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.

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

Pages (from-to) | 569-575 |

Number of pages | 7 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E79-A |

Issue number | 4 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Control theory
- Differential entropy
- Minimum entropy control
- Optimal regulator control

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Information Systems

### Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E79-A*(4), 569-575.

**A formulation by minimization of differential entropy for optimal control system.** / Goto, Masayuki; Tawara, Nobuhiko.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E79-A, no. 4, pp. 569-575.

}

TY - JOUR

T1 - A formulation by minimization of differential entropy for optimal control system

AU - Goto, Masayuki

AU - Tawara, Nobuhiko

PY - 1996

Y1 - 1996

N2 - This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}2 + N{u(t)}2], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) ≦ 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.

AB - This paper proposes a new formulation which minimizes the differential entropy for an optimal control problem. The conventional criterion of the optimal regulator control is a standard quadratic cost function E[M{x(t)}2 + N{u(t)}2], where x(t) is a state variable, u(t) is an input value, and M and N are positive weights. However, increasing the number of the variables of the system it is complex to find the solution of the optimal regulator control. Therefore, the simplicity of the solution is required. In contrast to the optimal regulator control, we propose the minimum entropy control which minimizes a differential entropy of the weighted sum of x(t) and u(t). This solution is derived on the assumptions that the linear control and x(t)u(t) ≦ 0 are satisfied. As the result, the formula of the minimum entropy control is very simple and clear. This result will be useful for the further work with multi variables of simple control formulation.

KW - Control theory

KW - Differential entropy

KW - Minimum entropy control

KW - Optimal regulator control

UR - http://www.scopus.com/inward/record.url?scp=0030121507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030121507&partnerID=8YFLogxK

M3 - Article

VL - E79-A

SP - 569

EP - 575

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 4

ER -