Hölder condition for the minimum time function of linear systems

2005 ◽  
pp. 383-392 ◽  
Author(s):  
E. Gyurkovics
Keyword(s):  
Linear Systems ◽  
Time Function ◽  
Minimum Time ◽  
Hölder Condition ◽  
Minimum Time Function

scholarly journals Minimum time function of a non-autonomous control system

2018 ◽  
Vol 51 (32) ◽  
pp. 704-707
Author(s):  
Nikolay I. Pogodaev ◽  
Vsevolod A. Voronov
Keyword(s):  
Control System ◽  
Time Function ◽  
Minimum Time ◽  
Autonomous Control ◽  
Minimum Time Function

scholarly journals On the minimum time function around the origin

2013 ◽  
Vol 3 (1) ◽  
pp. 51-82 ◽  
Author(s):  
Giovanni Colombo ◽  
◽  
Khai T. Nguyen
Keyword(s):  
Time Function ◽  
Minimum Time ◽  
Minimum Time Function

scholarly journals The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Pierpaolo Soravia
Keyword(s):  
Lyapunov Functions ◽  
Vector Fields ◽  
Hamiltonian Dynamics ◽  
Time Function ◽  
Minimum Time ◽  
Hölder Continuous ◽  
Lipschitz Continuous ◽  
Singular Manifold ◽  
Minimum Time Function ◽  
Aronsson Equation

We define and study C1-solutions of the Aronsson equation (AE), a second order quasi linear equation. We show that such super/subsolutions make the Hamiltonian monotone on the trajectories of the closed loop Hamiltonian dynamics. We give a short, general proof that C1-solutions are absolutely minimizing functions. We discuss how C1-supersolutions of (AE) become special Lyapunov functions of symmetric control systems, and allow to find continuous feedbacks driving the system to a target in finite time, except on a singular manifold. A consequence is a simple proof that the corresponding minimum time function is locally Lipschitz continuous away from the singular manifold, despite classical results showing that it should only be Hölder continuous unless appropriate conditions hold. We provide two examples for Hörmander and Grushin families of vector fields where we construct C1-solutions (even classical) explicitly.

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