Applied Analysis of the Navier-Stokes Equations, p.220 ,
, of Cambridge Texts in Applied Mathematics, vol.12, 1995.
Design of control policies for spatially inhomogeneous robot swarms with application to commercial pollination, Proceedings of ICRA, pp.378-385, 2011. ,
Constrained autonomous satellite docking via differential flatness and model predictive control, 2016 IEEE 55th Conference on Decision and Control (CDC), pp.3306-3311, 2016. ,
, Bootstrap current optimization in Tokamaks using sum-of-squares polynomials, pp.4359-4365, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01053418
On the analysis of systems described by classes of partial differential equations, in: Decision and Control, 45th IEEE Conference, pp.747-752, 2006. ,
Dissipation inequalities for 235 the analysis of a class of PDEs, Automatica, vol.66, pp.163-171, 2016. ,
A nonlinear hybrid life support system: Dynamic modeling, control design, and safety verification, Control Systems Technology, vol.15, issue.6, pp.1003-1017, 2007. ,
Certificate for safe emergency shutdown of wind turbines, American Control Conference (ACC), pp.3667-3672, 2013. ,
Safety verification and reachability analysis for hybrid systems, Annual Reviews in Control, vol.33, issue.1, pp.25-245, 2009. ,
Ellipsoidal techniques for reachability analysis: internal approximation, Systems & Control Letters, vol.41, issue.3, pp.201-211, 2000. ,
Computational techniques for the verification of hybrid systems, Proceedings of the IEEE, vol.91, issue.7, pp.986-250, 2003. ,
Barrier certificates for nonlinear model validation, Automatica, vol.42, issue.1, pp.117-126, 2006. ,
A framework for worst-case and stochastic safety verification using barrier certificates, Automatic Control, IEEE Transac-255 tions on, vol.52, issue.8, pp.1415-1428, 2007. ,
Methods for safety verification of time-delay systems, Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on, pp.4348-4353, 2005. ,
Finite-time regional verification of stochastic non-linear 260 systems, The International Journal of Robotics Research, vol.31, issue.7, pp.901-923, 2012. ,
On the existence of compositional barrier certificates, 51st IEEE Annual Conference on Decision and Control (CDC), pp.4580-4585, 2012. ,
On the necessity of barrier certificates, Proceedings of 265 the 16th IFAC World Congress, pp.742-742, 2005. ,
Converse barrier certificate theorems, IEEE Transactions on Automatic Control, vol.61, issue.5, pp.1356-1361, 2016. ,
Stabilization with relaxed controls, Nonlinear Analysis: Theory, Methods & Applications, vol.7, pp.1163-1173, 1983. ,
A universal construction of Artsteins theorem on nonlinear stabilization, Syst. Control Lett, vol.13, issue.2, pp.117-123, 1989. ,
, Constructive safety using control barrier functions, pp.473-478, 2007.
Control barrier function based quadratic 275 programs with application to adaptive cruise control, 53rd IEEE Conference on Decision and Control, pp.6271-6278, 2014. ,
Stabilization with guaranteed safety using control Lyapunov-Barrier Function, Automatica, vol.66, pp.39-47, 2016. ,
Stability analysis for a class 280 of partial differential equations via semidefinite programming, IEEE Transactions on Automatic Control, vol.61, issue.6, pp.1649-1654, 2016. ,
A convex approach to hydrodynamic analysis, 54th IEEE Conference on Decision and Control (CDC), pp.7262-7267, 2015. ,
Barrier functionals for output functional estimation of PDEs, 2015 American Control Conference (ACC), pp.2594-2599, 2015. ,
Bounds on linear PDEs via semidefinite optimization, Mathematical Programming, vol.108, issue.1, pp.135-158, 2006. ,
Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations, IFAC Proceedings Volumes, vol.44, pp.10887-10892, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00462301
An optimal poincare inequality for convex do-295 mains, Archive for Rational Mechanics and Analysis, vol.5, issue.1, pp.286-292, 1960. ,
A survey of the S-lemma, SIAM Review, vol.49, issue.3, pp.371-418, 2007. ,
A tutorial on sum of squares techniques for systems analysis, Proceedings of the 2005, vol.300, pp.2686-2700, 2005. ,
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization, 2000. ,
, Moments, Positive Polynomials and Their Applications, 2009.
Convex solutions to integral inequalities in two-dimensional domains, 54th IEEE Conference on Decision and Control (CDC), pp.7268-7273, 2015. ,
Introducing INTSOSTOOLS: A SOS-310 TOOLS plug-in for integral inequalities, pp.1231-1236, 2015. ,
, SOSTOOLS: Sum of squares optimization toolbox for MATLAB V3, p.0, 2013.
Using SeDuMi 1.02, a MATLAB toolbox for optimization over sym-315 metric cones, 1998. ,
, Options, futures and other derivatives, 2015.
, The Mathematics of Financial Derivatives, 1995.
Construction of an optimal background profile for the 320 ,
, Kuramoto-Sivashinsky equation using semidefinite programming, Physics Letters A, vol.379, issue.1, pp.23-32, 2015.
On global stabilization of Burgers equation by boundary control, Systems & Control Letters, vol.37, issue.3, pp.123-141, 1999. ,
Global stabilization of a Korteweg-De 325 ,
, Vries equation with saturating distributed control, SIAM Journal on Control and Optimization, vol.55, issue.3, pp.1452-1480, 2017.
An optimization-based method for bounding state functionals of nonlinear stochastic systems, 2016 55th IEEE Conference on Decision and Control (CDC), 2016. ,
, An Introduction to Infinite-Dimensional Linear Systems Theory, vol.21, 1995.
Well-Posed Linear Systems, 2005. ,
Dissipative operators in a banach space, Pacific J. Math, vol.335, issue.2, pp.679-698, 1961. ,
, Translations of Mathematical Monographs, 2005.