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Catedra de Matematică şi Informatică
Universitatea Tehnică "Gheorghe Asachi" Iaşi
Blvd. Carol I, nr. 11, Iaşi, 700506
Romania

Grant CNCSIS-UEFISCDI

PN-III-P1-1.1-TE-2016-0868

Project informations:

Title: Time optimal controllability for infinite dimensional systems

Project number: TE 124/2018

Project duration: 10.10.2018-9.10.2020

Summary: In the framework of this research project our aim is to study controllability problems for infinite dimensional systems. We are mainly interested in the study of the minimum time problem and minimum energy problem associated to a linear system in Banach spaces, very actual subjects in mathematical research. The setting we consider within this project is very general and covers most systems encountered in applications: distributed control systems, boundary control systems, point control systems, neutral functional differential equations. In particular we are interested in boundary control systems, for which the control operator is not bounded. We shall study regularity properties (monotonicity, continuity) for the minimum time function and the minimum energy, the connection between these two functions. We shall provide variational characterizations of the minimum norm controls to get an initial state to a given target in a given time. Also, we shall study the behavior of the cost functions when we have system perturbations.

Host institution: "Gheorghe Asachi" Technical University of Iaşi

Reasearch team members

A. I. Lazu - project leader, R. Strugariu, D. Maxim, V. Postolache

Stages and activities

2018

Stage 1. To establish new regularity results for the cost functions associated to a linear system

Activities: documentation, updating the bibliography, scientic contacts, analysis, research and establishing preliminary results

2019

Stage 2. To prove the equivalence between the minimum time problem and the minimum norm control associated to a linear system

Activities: documentation, updating the bibliography, conferences, scientic contacts, analysis, research and publication of the results

2020

Stage 3. To study variational problems for optimal control problems

Activities: documentation, updating the bibliography, conferences, scientic contacts, analysis, research and publication of the results

Results

Papers

  • S. Bilal, O. Carja, T. Donchev, A. I. Lazu, Nonlocal problem for evolution inclusions with one-sided Perron nonlinearities, REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 113 (3), 1917-1933, 2019. DOI: 10.1007/s13398-018-0589-6

  • O. Carja, A. I. Lazu, Minimum time and minimum energy for linear control systems, Systems and Control Letters 137, 2020. https://doi.org/10.1016/j.sysconle.2020.104629

  • S. Bilal, O. Carja, T. Donchev, N. Javaid, A. I. Lazu, Evolution inclusions in Banach spaces under dissipative conditions, Mathematics 2020, 8(5), 750. https://doi.org/10.3390/math8050750 .

  • M. Durea, R. Strugariu, On the sensitivity of Pareto e¢ ciency in set-valued optimization problems. J Glob Optim 78, 581-596 (2020). https://doi.org/10.1007/s10898-020-00925-9 .

  • O. Carja, A. I. Lazu, Minimum time and minimum energy for linear systems; a variational approach, Appl Math Optim (2020). https://doi.org/10.1007/s00245-020-09715-x

  • M. Durea, D. Maxim, R. Strugariu, Metric Inequality Conditions on Sets and Consequences in Optimization, J Optim Theory Appl 189, 744-771 (2021). https://doi.org/10.1007/s10957-021-01848-5

    • Scientific reports

  • Scientific report 2018

  • Scientific report 2019

  • Scientific report 2020

    • Conferences

  • RomFin2019 and FSDONA2019, June 10-15, 2019, Turku, Finland (A. I. Lazu, Nonlocal m-dissipative evolution inclusions in general Banach spaces)

  • EQUADIFF Conference, July 8-12, 2019, Leiden, Netherlands (A. I. Lazu, On the equivalence of minimum time and minimum norm control)

  • 6th International conference on Continuous Optimization (ICCOPT), August 3-8, 2019, Berlin, Germany (R. Strugariu, Stability of the directional regularity)

  • International Conference on Applied and Pure Mathematics, Octorber 31 - November 3, 2019, Iasi (A. I. Lazu, Minimum time and minimum energy for linear systems)

  • Zilele Universitatii "Al. I. Cuza" Iasi, 30 octombrie 2020 (A. I. Lazu, On the minimum norm control for linear systems).