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1

Normality of the maximum principle for nonconvex constrained Bolza problems

Piernicola Bettiol, Hélène Frankowska

Journal:

Journal of Differential Equations

Year:

2007

Language:

english

File:

PDF, 164 KB

english, 2007

2

On ergodic problem for Hamilton-Jacobi-Isaacs equations

Bettiol, Piernicola

Journal:

ESAIM Control Optimisation and Calculus of Variations

Year:

2005

Language:

english

File:

PDF, 278 KB

english, 2005

3

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || A Geometric Approach to the Optimal Control of Nonholonomic Mechanical Systems

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 543 KB

english, 2015

4

Existence and Characterization of the Values of Two Player Differential Games with State Constraints

Bettiol, Piernicola, Quincampoix, Marc, Vinter, Richard B.

Journal:

Applied Mathematics & Optimization

Year:

2019

Language:

english

File:

PDF, 470 KB

english, 2019

5

A new variational inequality in the calculus of variations and Lipschitz regularity of minimizers

Bettiol, Piernicola, Mariconda, Carlo

Journal:

Journal of Differential Equations

Year:

2019

Language:

english

File:

PDF, 1.50 MB

english, 2019

6

A Du Bois-Reymond Convex Inclusion for Nonautonomous Problems of the Calculus of Variations and Regularity of Minimizers

Bettiol, Piernicola, Mariconda, Carlo

Journal:

Applied Mathematics & Optimization

Year:

2019

File:

PDF, 479 KB

2019

7

Hölder continuity of minimizers for the state constrained Boza problem

Piernicola Bettiol, Hélène Frankowska

Journal:

Year:

2007

Language:

english

File:

PDF, 98 KB

english, 2007

8

Zero-sum state constrained differential games: existence of value for Bolza problem

Piernicola Bettiol, Pierre Cardaliaguet, Marc Quincampoix

Journal:

International Journal of Game Theory

Year:

2006

Language:

english

File:

PDF, 370 KB

english, 2006

9

Hölder Continuity of Adjoint States and Optimal Controls for State Constrained Problems

Piernicola Bettiol, Hélène Frankowska

Journal:

Applied Mathematics & Optimization

Year:

2008

Language:

english

File:

PDF, 503 KB

english, 2008

10

Some properties of generating functions obtained by Amann-Conley-Zehnder reduction

Piernicola Bettiol

Journal:

Journal of Mathematical Sciences

Year:

2007

Language:

english

File:

PDF, 204 KB

english, 2007

11

Regularity of Solution Maps of Differential Inclusions Under State Constraints

Piernicola Bettiol, Hélène Frankowska

Journal:

Set-Valued and Variational Analysis

Year:

2007

Language:

english

File:

PDF, 394 KB

english, 2007

12

estimates on trajectories confined to a closed subset

Piernicola Bettiol, Hélène Frankowska, Richard B. Vinter

Journal:

Journal of Differential Equations

Year:

2012

Language:

english

File:

PDF, 267 KB

english, 2012

13

Sensitivity Interpretations of the Costate Variable for Optimal Control Problems with State Constraints

Bettiol, Piernicola, Vinter, Richard B.

Journal:

SIAM Journal on Control and Optimization

Year:

2010

Language:

english

File:

PDF, 275 KB

english, 2010

14

On Trajectories Satisfying a State Constraint: $W^{1,1}$ Estimates and Counterexamples

Bettiol, Piernicola, Bressan, Alberto, Vinter, Richard

Journal:

SIAM Journal on Control and Optimization

Year:

2010

Language:

english

File:

PDF, 229 KB

english, 2010

15

Estimates for Trajectories Confined to a Cone in $\mathbb{R}^{\lowercase{n}}$

Bettiol, Piernicola, Bressan, Alberto, Vinter, Richard B.

Journal:

SIAM Journal on Control and Optimization

Year:

2011

Language:

english

File:

PDF, 266 KB

english, 2011

16

Stratified Necessary Conditions for Differential Inclusions with State Constraints

Bettiol, Piernicola, Boccia, Andrea, Vinter, Richard B.

Journal:

SIAM Journal on Control and Optimization

Year:

2013

Language:

english

File:

PDF, 225 KB

english, 2013

17

Linear estimates for trajectories of state-constrained differential inclusions and normality conditions in optimal control

Bettiol, Piernicola, Facchi, Giancarlo

Journal:

Journal of Mathematical Analysis and Applications

Year:

2014

Language:

english

File:

PDF, 378 KB

english, 2014

18

Trajectories Satisfying a State Constraint: Improved Estimates and New Non-Degeneracy Conditions

Bettiol, Piernicola, Vinter, Richard

Journal:

IEEE Transactions on Automatic Control

Year:

2011

Language:

english

File:

PDF, 213 KB

english, 2011

19

[IEEE 2010 49th IEEE Conference on Decision and Control (CDC) - Atlanta, GA, USA (2010.12.15-2010.12.17)] 49th IEEE Conference on Decision and Control (CDC) - On the solution map of control systems with multiple state constraints

Bettiol, Piernicola, Frankowska, Helene

Year:

2010

Language:

english

File:

PDF, 307 KB

english, 2010

20

(L∞+

Piernicola Bettiol,Franco Rampazzo

Journal:

Nonlinear Differential Equations and Applications NoDEA

Year:

2013

Language:

english

File:

PDF, 354 KB

english, 2013

21

[IEEE 2012 IEEE 51st Annual Conference on Decision and Control (CDC) - Maui, HI, USA (2012.12.10-2012.12.13)] 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) - Stratified necessary conditions for unbounded differential inclusions with state constraints

Bettiol, Piernicola, Boccia, Andrea, Vinter, Richard

Year:

2012

Language:

english

File:

PDF, 272 KB

english, 2012

22

[IEEE 2013 IEEE 52nd Annual Conference on Decision and Control (CDC) - Firenze (2013.12.10-2013.12.13)] 52nd IEEE Conference on Decision and Control - Sensitivity interpretations of the co-state trajectory for opimal control problems with state constraints

Bettiol, Piernicola, Frankowska, Helene, Vinter, Richard

Year:

2013

Language:

english

File:

PDF, 297 KB

english, 2013

23

[IEEE 2008 47th IEEE Conference on Decision and Control - Cancun, Mexico (2008.12.9-2008.12.11)] 2008 47th IEEE Conference on Decision and Control - Sensitivity relations for optimal control problems with state constraints

Bettiol, Piernicola, Vinter, Richard

Year:

2008

Language:

english

File:

PDF, 198 KB

english, 2008

24

[IEEE 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC) - Shanghai, China (2009.12.15-2009.12.18)] Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference - Existence of feasible approximating trajectories for differential inclusions with obstacles as state constraints

Bettiol, Piernicola, Vinter, Richard

Year:

2009

Language:

english

File:

PDF, 940 KB

english, 2009

25

[IEEE 2010 49th IEEE Conference on Decision and Control (CDC) - Atlanta, GA, USA (2010.12.15-2010.12.17)] 49th IEEE Conference on Decision and Control (CDC) - Existence of feasible approximating trajectories satisfying multiple state constraints

Bettiol, Piernicola, Vinter, Richard

Year:

2010

Language:

english

File:

PDF, 201 KB

english, 2010

26

Improved Sensitivity Relations in State Constrained Optimal Control

Bettiol, Piernicola, Frankowska, Hélène, Vinter, Richard B.

Journal:

Applied Mathematics & Optimization

Year:

2015

Language:

english

File:

PDF, 284 KB

english, 2015

27

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || Optimal Control of Cancer Treatments: Mathematical Models for the Tumor Microenvironment

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 615 KB

english, 2015

28

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || ω-Limit Sets for Differential Inclusions

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 177 KB

english, 2015

29

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || Weak Solutions for First Order Mean Field Games with Local Coupling

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 569 KB

english, 2015

30

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || Second-Order Necessary Optimality Conditions for the Mayer Problem Subject to a General Control Constraint

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 477 KB

english, 2015

31

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || Lunar Perturbation of the Metric Associated to the Averaged Orbital Transfer

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 1.01 MB

english, 2015

32

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || Generalized Lax-Hopf Formulas for Cournot Maps and Hamilton-Jacobi-McKendrick Equations

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 573 KB

english, 2015

33

[Springer INdAM Series] Analysis and Geometry in Control Theory and its Applications Volume 11 || Conjugate Times and Regularity of the Minimum Time Function with Differential Inclusions

Bettiol, Piernicola, Cannarsa, Piermarco, Colombo, Giovanni, Motta, Monica, Rampazzo, Franco

Year:

2015

Language:

english

File:

PDF, 339 KB

english, 2015

34

The Hamilton Jacobi Equation For Optimal Control Problems with Discontinuous Time Dependence

Bettiol, Piernicola, Vinter, Richard B.

Journal:

SIAM Journal on Control and Optimization

Year:

2017

Language:

english

File:

PDF, 282 KB

english, 2017

35

$$L^{\infty }$$ L ∞ estimates on trajectories confined to a closed subset, for control systems with bounded time variation

Bettiol, Piernicola, Vinter, Richard B.

Journal:

Mathematical Programming

Year:

2016

Language:

english

File:

PDF, 569 KB

english, 2016

36

On a new necessary condition in the Calculus of Variations for Lagrangians that are highly discontinuous in the state and velocity

Bettiol, Piernicola, Mariconda, Carlo

Journal:

Rendiconti Lincei - Matematica e Applicazioni

Year:

2019

Language:

english

File:

PDF, 160 KB

english, 2019

37

A new variational inequality in the calculus of variations and Lipschitz regularity of minimizers

Bettiol, Piernicola, Mariconda, Carlo

Journal:

Journal of Differential Equations

Year:

2019

File:

PDF, 1.50 MB

2019

38

Regularity and necessary conditions for a Bolza optimal control problem

Bettiol, Piernicola, Mariconda, Carlo

Journal:

Journal of Mathematical Analysis and Applications

Year:

2020

File:

PDF, 423 KB

2020