# EXPLICIT PREDICTIVE CONTROL LAWS - On the Geometry of Feasible Domains and the Presence of Nonlinearities

### Sorin Olaru, Didier Dumur, Simona Dobre

#### 2007

#### Abstract

This paper proposes a geometrical analysis of the polyhedral feasible domains for the predictive control laws under constraints. The fact that the system dynamics influence the topology of such polyhedral domains is well known from the studies dedicated to the feasibility of the control laws. Formally the system state acts as a vector of parameters for the optimization problem to be solved on-line and its influence can be fully described by the use of parameterized polyhedra and their dual constraints/generators representation. Problems like the constraints redundancy or the construction of the associated explicit control laws at least for linear or quadratic cost functions can thus receive fully geometrical solutions. Convex nonlinear constraints can be approximated using a description based on the parameterized vertices. In the case of nonconvex regions the explicit solutions can be obtain by constructing Voronoi partitions based on a collection of points distributed over the borders of the feasible domain.

#### References

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#### Paper Citation

#### in Harvard Style

Olaru S., Dumur D. and Dobre S. (2007). **EXPLICIT PREDICTIVE CONTROL LAWS - On the Geometry of Feasible Domains and the Presence of Nonlinearities** . In *Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,* ISBN 978-972-8865-84-9, pages 70-77. DOI: 10.5220/0001633200700077

#### in Bibtex Style

@conference{icinco07,

author={Sorin Olaru and Didier Dumur and Simona Dobre},

title={EXPLICIT PREDICTIVE CONTROL LAWS - On the Geometry of Feasible Domains and the Presence of Nonlinearities},

booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},

year={2007},

pages={70-77},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001633200700077},

isbn={978-972-8865-84-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,

TI - EXPLICIT PREDICTIVE CONTROL LAWS - On the Geometry of Feasible Domains and the Presence of Nonlinearities

SN - 978-972-8865-84-9

AU - Olaru S.

AU - Dumur D.

AU - Dobre S.

PY - 2007

SP - 70

EP - 77

DO - 10.5220/0001633200700077