Control and Nonlinearity

By Jean-Michel Coron. 2007

1,169 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/29a7d065bdebc961eac2e6d1054ab52529b9017d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

EXISTENCE OF CLASSICAL SOLUTIONS AND FEEDBACK STABILIZATION FOR THE FLOW IN GAS NETWORKS (2011, methodology): “In order to take this fact into account, we have generalized the construction given in [7] to the case of non-constant equilibria.”
RECENT RESULTS ON THE CONTROLLABILITY OF LINEAR COUPLED PARABOLIC PROBLEMS: A SURVEY (2011, background): “For a proof, see for instance [37] and [20] (Theorem 2.”
Analysis of a conservation law modeling a highly re-entrant manufacturing system (2009, result): “ systems. For the controllability of linear hyperbolic systems, see, in particular, the important survey [22]. The attainable sets of nonlinear conservation laws are studied in [1,15,18,20,21], while [14] provides a comprehensive survey of controllability that also includes nonlinear conservation la”
Local controllability of 1D linear and nonlinear Schr (2010, neutral): “The controllability of (17) is linked to the rank of the Lie algebra spanned by H0 and H1 (see for instance [5] by Albertini and D’Alessandro, [7] by Altafini, [26] by Brockett, see also [3] by Agrachev and Sachkov, [32] by Coron for a more general discussion).”
On Some non Asymptotic Bounds for the Euler Scheme (2010, background): “R Theorem 1.11 Chapter 1 in Coron [Cor07].”
Control of the Continuity Equation with a Non Local Flow (2009, background): “d to ρo. We emphasize that all this is obtained within the framework of non smooth solutions, diﬀerently from many results in the current literature that are devoted to diﬀerentiability [21], control [18, 19] or optimal control [15] for conservation laws, but limited to smooth solutions. Furthermore”
A unified controllability/observability theory for some stochastic and deterministic partial differential equations (2010, background): “After [29], important works in this field can be found in [1, 4, 8, 11, 13, 17, 21, 25, 26, 43, 46, 55, 56].”
Characterization by observability inequalities of controllability and stabilization properties (2018, neutral): “The function V (y) = 〈y, C−1 λ y〉 is a Lyapunov function (as noticed in [5]), and the feedback Kλ yields exponential stability with rate −λ.”
Null-controllability of hypoelliptic quadratic differential equations (2016, positive): “By using the Hilbert Uniqueness Method [15] (Theorem 2.44), the result of null-controllability given by Theorem 1.4 is therefore equivalent to the following observability estimate: Theorem 1.5.”
New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence (2016, background): “For a proof see, for instance, [37], [15], [36] or [21].”
Control Principles of Complex Networks (2015, background): “Yet, as we discuss next, studying the controllability properties of its linearization around an equilibrium point or along a trajectory can often offer an efficient test of local nonlinear controllability (Coron, 2009).”