American Institute of Mathematical Sciences

Advanced
  • Previous Article
    On the 2-D Riemann problem for the compressible Euler equations I. Interaction of shocks and rarefaction waves
  • DCDS Home
  • This Issue
  • Next Article
    On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data
October  1995, 1(4): 547-553. doi: 10.3934/dcds.1995.1.547

Extended wellposedness of optimal control problems

T. Zolezzi 1,

1. 

Dipartimento di Matematica, Universita' di Genova, via L.B. Alberti 4, 16132 Genova, Italy

Received  July 1995 Published  August 1995

A concept of wellposedness is applied to control problems monitored by ordinary differential equations. This concept does not impose uniqueness of the optimal control, and requires strong convergence of every asymptotically minimizing sequence corresponding to small perturbations of the initial state. Sufficient conditions for such a form of wellposedness are obtained via Tikhonov wellposedness of the pointwise maximization of the Hamiltonian function.
Keywords: wellposed optimization problems, nonuniqueness, optimal control..
Mathematics Subject Classification: 49K40, 49J1.
Citation: T. Zolezzi. Extended wellposedness of optimal control problems. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 547-553. doi: 10.3934/dcds.1995.1.547
[1]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399
[2]

Maria Assunta Pozio, Fabio Punzo, Alberto Tesei. Uniqueness and nonuniqueness of solutions to parabolic problems with singular coefficients. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 891-916. doi: 10.3934/dcds.2011.30.891
[3]

Enkhbat Rentsen, J. Zhou, K. L. Teo. A global optimization approach to fractional optimal control. Journal of Industrial & Management Optimization, 2016, 12 (1) : 73-82. doi: 10.3934/jimo.2016.12.73
[4]

Bavo Langerock. Optimal control problems with variable endpoints. Conference Publications, 2003, 2003 (Special) : 507-516. doi: 10.3934/proc.2003.2003.507
[5]

Alberto Bressan, Yunho Hong. Optimal control problems on stratified domains. Networks & Heterogeneous Media, 2007, 2 (2) : 313-331. doi: 10.3934/nhm.2007.2.313
[6]

M'hamed Kesri. Structural stability of optimal control problems. Communications on Pure & Applied Analysis, 2005, 4 (4) : 743-756. doi: 10.3934/cpaa.2005.4.743
[7]

Piermarco Cannarsa, Hélène Frankowska, Elsa M. Marchini. On Bolza optimal control problems with constraints. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 629-653. doi: 10.3934/dcdsb.2009.11.629
[8]

M. Delgado-Téllez, Alberto Ibort. On the geometry and topology of singular optimal control problems and their solutions. Conference Publications, 2003, 2003 (Special) : 223-233. doi: 10.3934/proc.2003.2003.223
[9]

Giuseppe Buttazzo, Lorenzo Freddi. Optimal control problems with weakly converging input operators. Discrete & Continuous Dynamical Systems - A, 1995, 1 (3) : 401-420. doi: 10.3934/dcds.1995.1.401
[10]

Piermarco Cannarsa, Cristina Pignotti, Carlo Sinestrari. Semiconcavity for optimal control problems with exit time. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 975-997. doi: 10.3934/dcds.2000.6.975
[11]

Heinz Schättler, Urszula Ledzewicz. Lyapunov-Schmidt reduction for optimal control problems. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2201-2223. doi: 10.3934/dcdsb.2012.17.2201
[12]

Stephen Campbell, Peter Kunkel. Solving higher index DAE optimal control problems. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 447-472. doi: 10.3934/naco.2016020
[13]

Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241
[14]

Piermarco Cannarsa, Carlo Sinestrari. On a class of nonlinear time optimal control problems. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 285-300. doi: 10.3934/dcds.1995.1.285
[15]

John T. Betts, Stephen L. Campbell, Claire Digirolamo. Initial guess sensitivity in computational optimal control problems. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 39-41. doi: 10.3934/naco.2019031
[16]

Bin Li, Kok Lay Teo, Cheng-Chew Lim, Guang Ren Duan. An optimal PID controller design for nonlinear constrained optimal control problems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1101-1117. doi: 10.3934/dcdsb.2011.16.1101
[17]

Ying Zhang, Changjun Yu, Yingtao Xu, Yanqin Bai. Minimizing almost smooth control variation in nonlinear optimal control problems. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2019023
[18]

Benedetto Piccoli. Optimal syntheses for state constrained problems with application to optimization of cancer therapies. Mathematical Control & Related Fields, 2012, 2 (4) : 383-398. doi: 10.3934/mcrf.2012.2.383
[19]

Anthony M. Bloch, Peter E. Crouch, Nikolaj Nordkvist. Continuous and discrete embedded optimal control problems and their application to the analysis of Clebsch optimal control problems and mechanical systems. Journal of Geometric Mechanics, 2013, 5 (1) : 1-38. doi: 10.3934/jgm.2013.5.1
[20]

Jianxiong Ye, An Li. Necessary optimality conditions for nonautonomous optimal control problems and its applications to bilevel optimal control. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1399-1419. doi: 10.3934/jimo.2018101

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (49)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences