On weighted time optimal control for linear hybrid automata using quantifier elimination

Yan Pang, Michael P. Spathopoulos

Research output: Contribution to conferencePaper

Abstract

This paper considers the optimal control problem for linear hybrid automata. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier Elimination (QE) techniques are employed in order to derive quantifier free inequalities that are linear. The optimal cost is obtained using linear programming. The optimal switching times and optimal continuous control inputs are computed and used in order to derive the optimal hybrid controller. Our results areapplied to an air traffic management example.

Conference

ConferenceProceedings of the 7th IFAC International Workshop on Discrete Event Systems
CityReims, France
Period22/09/0424/09/04

Fingerprint

Constrained optimization
Linear programming
Controllers
Air
Costs

Keywords

  • hybrid automata
  • quantifier elimination
  • time optimal control

Cite this

Pang, Y., & Spathopoulos, M. P. (2004). On weighted time optimal control for linear hybrid automata using quantifier elimination. Paper presented at Proceedings of the 7th IFAC International Workshop on Discrete Event Systems, Reims, France, .
Pang, Yan ; Spathopoulos, Michael P. / On weighted time optimal control for linear hybrid automata using quantifier elimination. Paper presented at Proceedings of the 7th IFAC International Workshop on Discrete Event Systems, Reims, France, .6 p.
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title = "On weighted time optimal control for linear hybrid automata using quantifier elimination",
abstract = "This paper considers the optimal control problem for linear hybrid automata. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier Elimination (QE) techniques are employed in order to derive quantifier free inequalities that are linear. The optimal cost is obtained using linear programming. The optimal switching times and optimal continuous control inputs are computed and used in order to derive the optimal hybrid controller. Our results areapplied to an air traffic management example.",
keywords = "hybrid automata, quantifier elimination, time optimal control",
author = "Yan Pang and Spathopoulos, {Michael P.}",
year = "2004",
month = "9",
language = "English",
note = "Proceedings of the 7th IFAC International Workshop on Discrete Event Systems ; Conference date: 22-09-2004 Through 24-09-2004",

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Pang, Y & Spathopoulos, MP 2004, 'On weighted time optimal control for linear hybrid automata using quantifier elimination' Paper presented at Proceedings of the 7th IFAC International Workshop on Discrete Event Systems, Reims, France, 22/09/04 - 24/09/04, .

On weighted time optimal control for linear hybrid automata using quantifier elimination. / Pang, Yan; Spathopoulos, Michael P.

2004. Paper presented at Proceedings of the 7th IFAC International Workshop on Discrete Event Systems, Reims, France, .

Research output: Contribution to conferencePaper

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T1 - On weighted time optimal control for linear hybrid automata using quantifier elimination

AU - Pang, Yan

AU - Spathopoulos, Michael P.

PY - 2004/9

Y1 - 2004/9

N2 - This paper considers the optimal control problem for linear hybrid automata. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier Elimination (QE) techniques are employed in order to derive quantifier free inequalities that are linear. The optimal cost is obtained using linear programming. The optimal switching times and optimal continuous control inputs are computed and used in order to derive the optimal hybrid controller. Our results areapplied to an air traffic management example.

AB - This paper considers the optimal control problem for linear hybrid automata. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier Elimination (QE) techniques are employed in order to derive quantifier free inequalities that are linear. The optimal cost is obtained using linear programming. The optimal switching times and optimal continuous control inputs are computed and used in order to derive the optimal hybrid controller. Our results areapplied to an air traffic management example.

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KW - quantifier elimination

KW - time optimal control

M3 - Paper

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Pang Y, Spathopoulos MP. On weighted time optimal control for linear hybrid automata using quantifier elimination. 2004. Paper presented at Proceedings of the 7th IFAC International Workshop on Discrete Event Systems, Reims, France, .