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- Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
- Proceedings of the 48h IEEE Conference on…
- 2009

This conference paper is a summary of the article “Dirichlet problems for some Hamilton-Jacobi equations with inequality constraints”, J.-P. Aubin, A. Bayen, P. Saint-Pierre, SIAM Journal on Control… (More)

- Patrick Saint-Pierre
- 2001 European Control Conference (ECC)
- 2001

This paper deals with hybrid dynamical systems with state constrains and target. We investigate the subset of initial positions from which there exists at least one run forever remaining in the… (More)

- Meeko M. K. Oishi, Ian A Mitchell, C. Tomlin, Patrick Saint-Pierre
- Proceedings of the 45th IEEE Conference on…
- 2006

We consider feedback linearizable systems subject to bounded control input and nonlinear state constraints. In a single computation, we synthesize 1) parameterized nonlinear controllers based on… (More)

- Alexandre M. Bayen, Christian G. Claudel, Patrick Saint-Pierre
- 2007 46th IEEE Conference on Decision and Control
- 2007

This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs), based on a Lax-Hopf… (More)

- Pierre Cardaliaguet, Marc Quincampoix, Patrick Saint-Pierre
- SIAM J. Control and Optimization
- 2000

We prove the existence of a value for pursuit games with state constraints. We also prove that this value is lower semicontinuous.

- Lars Grüne, Patrick Saint-Pierre
- Systems & Control Letters
- 2006

We apply set valued analysis techniques in order to characterize the input–to–state dynamical stability (ISDS) property, a variant of the well known input–to–state stability (ISS) property. Using a… (More)

- J.-P. Aubin, A. Bayen, Patrick Saint-Pierre
- Proceedings of the 2005, American Control…
- 2005

This paper presents a new approach which links the solution to the Burgers tracking problem to the concept of capture basin used in viability theory. This link enables the proof of the existence and… (More)

- Patrick Saint-Pierre
- HSCC
- 2002

We investigate, for constrained controlled systems with impulse, the subset of initial positions contained in a set K from which starts at least one run viable in K the hybrid viability kernel… (More)

This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) [3], based on a Lax-Hopf… (More)

- Noël Bonneuil, Patrick Saint-Pierre
- Applied Mathematics and Computation
- 2005

The perpetuation of three-trophic level ecosystems where the three species exhibit unpredictable time-varying survival strategies is described by a specific set, the viability kernel, gathering all… (More)