### Abstract

In this paper, we address the problem of designing probabilistic robust controllers for discrete-time systems whose objective is to reach and remain in a given target set with high probability. More precisely, given probability distributions for the initial state, uncertain parameters and disturbances, we develop algorithms for designing a control law that i) maximizes the probability of reaching the target set in N steps and ii) makes the target set robustly positively invariant. As defined the problem is nonconvex. To solve this problem, a sequence of convex relaxations is provided, whose optimal value is shown to converge to solution of the original problem. In other words, we provide a sequence of semidefinite programs of increasing dimension and complexity which can arbitrarily approximate the solution of the probabilistic robust control design problem addressed in this paper. Two numerical examples are presented to illustrate preliminary results on the numerical performance of the proposed approach.

Original language | English (US) |
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Title of host publication | 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1892-1897 |

Number of pages | 6 |

ISBN (Print) | 9781467357173 |

DOIs | |

State | Published - Jan 1 2013 |

Event | 52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: Dec 10 2013 → Dec 13 2013 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0191-2216 |

### Other

Other | 52nd IEEE Conference on Decision and Control, CDC 2013 |
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Country | Italy |

City | Florence |

Period | 12/10/13 → 12/13/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013*(pp. 1892-1897). [6760158] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760158

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*2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013.*, 6760158, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 1892-1897, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6760158

**Convex relaxations of a probabilistically robust control design problem.** / Jasour, A. M.; Lagoa, Constantino Manuel.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Convex relaxations of a probabilistically robust control design problem

AU - Jasour, A. M.

AU - Lagoa, Constantino Manuel

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this paper, we address the problem of designing probabilistic robust controllers for discrete-time systems whose objective is to reach and remain in a given target set with high probability. More precisely, given probability distributions for the initial state, uncertain parameters and disturbances, we develop algorithms for designing a control law that i) maximizes the probability of reaching the target set in N steps and ii) makes the target set robustly positively invariant. As defined the problem is nonconvex. To solve this problem, a sequence of convex relaxations is provided, whose optimal value is shown to converge to solution of the original problem. In other words, we provide a sequence of semidefinite programs of increasing dimension and complexity which can arbitrarily approximate the solution of the probabilistic robust control design problem addressed in this paper. Two numerical examples are presented to illustrate preliminary results on the numerical performance of the proposed approach.

AB - In this paper, we address the problem of designing probabilistic robust controllers for discrete-time systems whose objective is to reach and remain in a given target set with high probability. More precisely, given probability distributions for the initial state, uncertain parameters and disturbances, we develop algorithms for designing a control law that i) maximizes the probability of reaching the target set in N steps and ii) makes the target set robustly positively invariant. As defined the problem is nonconvex. To solve this problem, a sequence of convex relaxations is provided, whose optimal value is shown to converge to solution of the original problem. In other words, we provide a sequence of semidefinite programs of increasing dimension and complexity which can arbitrarily approximate the solution of the probabilistic robust control design problem addressed in this paper. Two numerical examples are presented to illustrate preliminary results on the numerical performance of the proposed approach.

UR - http://www.scopus.com/inward/record.url?scp=84902338298&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902338298&partnerID=8YFLogxK

U2 - 10.1109/CDC.2013.6760158

DO - 10.1109/CDC.2013.6760158

M3 - Conference contribution

AN - SCOPUS:84902338298

SN - 9781467357173

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1892

EP - 1897

BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013

PB - Institute of Electrical and Electronics Engineers Inc.

ER -