bibliography for weak solutions of ODE's
up vote
1
down vote
favorite
Could someone recommend to me some bibliography about weak solutions of ODE's and solutions of ODE's that are not Lipschitz or discontinuous??
calculus differential-equations nonlinear-system
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
add a comment |
up vote
1
down vote
favorite
Could someone recommend to me some bibliography about weak solutions of ODE's and solutions of ODE's that are not Lipschitz or discontinuous??
calculus differential-equations nonlinear-system
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Could someone recommend to me some bibliography about weak solutions of ODE's and solutions of ODE's that are not Lipschitz or discontinuous??
calculus differential-equations nonlinear-system
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
Could someone recommend to me some bibliography about weak solutions of ODE's and solutions of ODE's that are not Lipschitz or discontinuous??
calculus differential-equations nonlinear-system
calculus differential-equations nonlinear-system
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
edited Nov 21 at 16:26
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
asked Oct 22 '14 at 11:07
Rafael Rojas
327213
327213
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
accepted
Discontinuous ODE may be called "ODE with discontinuous right hand side" or "Filippov's systems". They where studied in the 70's or 80's by A. F. Filippov who published a book on them titled "Differential Equations with Discontinuous Righthand Sides". Such topic was exploited by V. Utkin to develop the so-called Sliding Mode Control. In such a control technique, the discontinuity of the control action provide robustness to the control system. There is lot of literature about that.
As literature about discontinuous ODEs I can recommend "Discontinuous Systems by Orlov, Y." and the first two chapters of the book by Filippov.
An interesting approach my be found in "Hybrid Dynamical Systems" by Goebel R., Sanfelice, R. G. & Teel, A. R.. There, such kind of discontinuous differential equations are treated as hybrid systems, where a discrete part interacts with a continuous part. This approach based in hybrid systems is very popular.
Regarding numerical solutions to such systems, I strongly recommend the paper "Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach by Dieci, L. & Lopez, L."
answered Nov 21 at 20:12
Rafael Rojas
327213
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Discontinuous ODE may be called "ODE with discontinuous right hand side" or "Filippov's systems". They where studied in the 70's or 80's by A. F. Filippov who published a book on them titled "Differential Equations with Discontinuous Righthand Sides". Such topic was exploited by V. Utkin to develop the so-called Sliding Mode Control. In such a control technique, the discontinuity of the control action provide robustness to the control system. There is lot of literature about that.
As literature about discontinuous ODEs I can recommend "Discontinuous Systems by Orlov, Y." and the first two chapters of the book by Filippov.
An interesting approach my be found in "Hybrid Dynamical Systems" by Goebel R., Sanfelice, R. G. & Teel, A. R.. There, such kind of discontinuous differential equations are treated as hybrid systems, where a discrete part interacts with a continuous part. This approach based in hybrid systems is very popular.
Regarding numerical solutions to such systems, I strongly recommend the paper "Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach by Dieci, L. & Lopez, L."
answered Nov 21 at 20:12
Rafael Rojas
327213
add a comment |
up vote
0
down vote
accepted
Discontinuous ODE may be called "ODE with discontinuous right hand side" or "Filippov's systems". They where studied in the 70's or 80's by A. F. Filippov who published a book on them titled "Differential Equations with Discontinuous Righthand Sides". Such topic was exploited by V. Utkin to develop the so-called Sliding Mode Control. In such a control technique, the discontinuity of the control action provide robustness to the control system. There is lot of literature about that.
As literature about discontinuous ODEs I can recommend "Discontinuous Systems by Orlov, Y." and the first two chapters of the book by Filippov.
An interesting approach my be found in "Hybrid Dynamical Systems" by Goebel R., Sanfelice, R. G. & Teel, A. R.. There, such kind of discontinuous differential equations are treated as hybrid systems, where a discrete part interacts with a continuous part. This approach based in hybrid systems is very popular.
Regarding numerical solutions to such systems, I strongly recommend the paper "Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach by Dieci, L. & Lopez, L."
answered Nov 21 at 20:12
Rafael Rojas
327213
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Discontinuous ODE may be called "ODE with discontinuous right hand side" or "Filippov's systems". They where studied in the 70's or 80's by A. F. Filippov who published a book on them titled "Differential Equations with Discontinuous Righthand Sides". Such topic was exploited by V. Utkin to develop the so-called Sliding Mode Control. In such a control technique, the discontinuity of the control action provide robustness to the control system. There is lot of literature about that.
As literature about discontinuous ODEs I can recommend "Discontinuous Systems by Orlov, Y." and the first two chapters of the book by Filippov.
An interesting approach my be found in "Hybrid Dynamical Systems" by Goebel R., Sanfelice, R. G. & Teel, A. R.. There, such kind of discontinuous differential equations are treated as hybrid systems, where a discrete part interacts with a continuous part. This approach based in hybrid systems is very popular.
Regarding numerical solutions to such systems, I strongly recommend the paper "Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach by Dieci, L. & Lopez, L."
answered Nov 21 at 20:12
Rafael Rojas
327213
Discontinuous ODE may be called "ODE with discontinuous right hand side" or "Filippov's systems". They where studied in the 70's or 80's by A. F. Filippov who published a book on them titled "Differential Equations with Discontinuous Righthand Sides". Such topic was exploited by V. Utkin to develop the so-called Sliding Mode Control. In such a control technique, the discontinuity of the control action provide robustness to the control system. There is lot of literature about that.
As literature about discontinuous ODEs I can recommend "Discontinuous Systems by Orlov, Y." and the first two chapters of the book by Filippov.
An interesting approach my be found in "Hybrid Dynamical Systems" by Goebel R., Sanfelice, R. G. & Teel, A. R.. There, such kind of discontinuous differential equations are treated as hybrid systems, where a discrete part interacts with a continuous part. This approach based in hybrid systems is very popular.
Regarding numerical solutions to such systems, I strongly recommend the paper "Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach by Dieci, L. & Lopez, L."
answered Nov 21 at 20:12
Rafael Rojas
327213
edited Nov 22 at 15:33
answered Nov 21 at 20:12
Rafael Rojas
327213
answered Nov 21 at 20:12
Rafael Rojas
327213
answered Nov 21 at 20:12
Rafael Rojas
327213
327213
add a comment |
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f985670%2fbibliography-for-weak-solutions-of-odes%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
