### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Number of pages | 39 |

Publication status | Published - 1987 |

### Publication series

Name | Memorandum COSOR |
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Volume | 8717 |

ISSN (Print) | 0926-4493 |

### Fingerprint

### Cite this

*Continuity properties of the cheap control problem without stability*. (Memorandum COSOR; Vol. 8717). Eindhoven: Technische Universiteit Eindhoven.

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*Continuity properties of the cheap control problem without stability*. Memorandum COSOR, vol. 8717, Technische Universiteit Eindhoven, Eindhoven.

**Continuity properties of the cheap control problem without stability.** / Geerts, A.H.W.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Continuity properties of the cheap control problem without stability

AU - Geerts, A.H.W.

PY - 1987

Y1 - 1987

N2 - An open problem concerning the convergence of the optimal cost for the cheap control problem without stability is solved. It turns out that the definition of a new type of linear-quadratic optimal control problems is necessary. This new problem requires the infimization of the cost functional under the constraint that the state trajectory modulo a certain subspace vanishes as time goes to infinity. The associated optimal cost turns out to be the limit of the optimal cost for the cheap control problem without stability. Moreover, for left invertible systems, the optimal control, state and output for the perturbed problem tend to the optimal control, state and output for the new problem. Also a characterization of the optimal cost for the latter problem is given in terms of the dissipation inequality.

AB - An open problem concerning the convergence of the optimal cost for the cheap control problem without stability is solved. It turns out that the definition of a new type of linear-quadratic optimal control problems is necessary. This new problem requires the infimization of the cost functional under the constraint that the state trajectory modulo a certain subspace vanishes as time goes to infinity. The associated optimal cost turns out to be the limit of the optimal cost for the cheap control problem without stability. Moreover, for left invertible systems, the optimal control, state and output for the perturbed problem tend to the optimal control, state and output for the new problem. Also a characterization of the optimal cost for the latter problem is given in terms of the dissipation inequality.

M3 - Report

T3 - Memorandum COSOR

BT - Continuity properties of the cheap control problem without stability

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -