### 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 |
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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 Jan 1 |

### Keywords

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

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

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## Cite this

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

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