Workshop: modern trends in controlled stochastic processes: theory and applications

Lead Research Organisation: University of Liverpool
Department Name: Mathematical Sciences

Abstract

After preliminary contacts, we have more than 25 overseas participants and 5 prospective British participants from outside Liverpool. If we add 5 members of staff and research students at the Department of Mathematical Sciences (University of Liverpool) we obtain the initial list which will be slightly extended at a later date up to 40 participants. According to the title, there will be a good balance between purely mathematical issues like construction of the controlled models, their properties, approximations etc, and practical applications based on the developed theory, like congestion management in Internet, risk management in economics and insurance, inventory control, optimal interventions in epidemics, etc. At the moment, we have the draft schedule of the workshop, described in the Case for Support. The participants will be allowed to give 20-25-minutes long official presentations. Besides they will have plenty of time to communicate informally, to create and develop research links. As can be seen from the Case for Support, the workshop will involve many world leading scientists, along with talented young researchers and PhD students.

Planned Impact

The participants of the workshop and other academic researchers in the theory and applications of (controlled) Random Processes will be the main beneficiaries of the workshop, because personal contacts will result in new views on modern important problems, new theorems, high quality joint papers. Since the participants are interested in applications to Finance, Queues, Reliability, Teletraffic, Biology, Medicine etc, the prospective joint research will be useful for applied mathematicians, engineers and other specialists working in the corresponding areas. The prospective participants collaborate with France Telecom, Alcatel-Lucent, Shell, Russian Inst. of Control Sciences, THALES, DCNS, Airbus Defence and Space, US EPA, Huawei, Nokia, Northrop Grumman, US Department of Energy, IBM, and so on, meaning that British, European, Asian and American industry will also be the beneficiary of the workshop. In a nutshell, practical applications of the developed theory, discussed on the current workshop, will help to solve many real-life problems like congestion management in Internet, power control in wireless networks, water management, portfolio optimisation, risk management, optimal interventions in epidemics, and so on. Several scientific results presented and discussed at the workshop, will be incorporated into lectures/tutorials at the Universities of Liverpool, Bordeaux, Nice, Sao Paolo, Kanagawa, New York, Moscow, Karlsruhe etc, so that undergraduate students can also be the beneficiaries. Information about the workshop will be distributed to the academic community by e-mail, using the personal links of the participants; we also plan to provide the links on our personal webpages. All the participants will share the results of the workshop with their colleagues at their universities and research institutes. The results of collaboration will be, as usual, presented at regular international meetings and published in high quality journals. The extended reports will be published as a scientific monograph at River Publishers by the end of 2020, or at the beginning of 2021.

Publications

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Piunovskiy A (2022) Duality in optimal impulse control in Journal of Mathematical Analysis and Applications

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Piunovskiy A (2023) Turnpikes in finite Markov decision processes and random walk in ?????? ???????????? ? ?? ??????????

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Piunovskiy A (2021) Aggregated occupation measures and linear programming approach to constrained impulse control problems in Journal of Mathematical Analysis and Applications

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Piunovskiy A (2024) Extreme Occupation Measures in Markov Decision Processes with an Absorbing State in SIAM Journal on Control and Optimization

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Piunovskiy A (2021) Linear programming approach to optimal impulse control problems with functional constraints in Journal of Mathematical Analysis and Applications

 
Description This grant supported one-week workshop in Liverpool with participants from about 15 different countries including UK, USA, Japan, China, France, Germany etc. Due to covid-19 pandemic the meetings were online via zoom, but four people managed to arrive in Liverpool in person. There were 26 presentations. This workshop was an excellent opportunity for world leading researchers to discuss the current state of the stochastic control theory and applications (to Queueing Theory, Financial Mathematics, internet traffic, pollution, medicine, fishery, inventory and so on). The feedback from the participants was very positive. A number of extended presentations were published in the form of the monograph "Modern trends in controlled stochastic processes,Vol.III" (Springer) ISBN 978-3-030-76927-7. After this workshop, several participants established strong research links, started new joint projects funded by their national research foundations and prepared joint papers. Note, there was a number of very young researchers at the beginning of their career. Their talks were in the last day of the workshop following the vote for the best young researcher's presentation.
Exploitation Route New projects following this workshop, new publications of the participants, incorporation of the new ideas discussed during the workhop in the lectures for undergraduates and postgraduate students, new projects for PhD students.
Sectors Digital/Communication/Information Technologies (including Software),Environment,Financial Services, and Management Consultancy,Healthcare,Government, Democracy and Justice,Pharmaceuticals and Medical Biotechnology

URL https://www.amazon.co.uk/MOXIC-Abstract-Rectangular-Children-Anti-Slip/dp/3030769275/ref=sr_1_6?dchild=1&keywords=piunovskiy&qid=1635605771&s=books&sr=1-6
 
Description Joint research with Prof. F.Dufour, INRIA, Bordeaux-France 
Organisation The National Institute for Research in Computer Science and Control (INRIA)
Department Bordeaux
Country France 
Sector Public 
PI Contribution No contribution from my university.
Collaborator Contribution INRIA supported my multiple research visits to Bordeaux and visits of Prof.F.Dufour to Liverpool in 2009-2019.
Impact Multiple joint articles with prof. F.Dufour on stochastic optimal control, sometimes involving also other researchers (e.g., O.Costa-Brazil, M.Horiguchi-Japan). For example: Impulsive control for continuous-time Markov decision processes: a linear programming approach (F.Dufour and A.Piunovskiy - co-authors) // Appl. Math. Optim., 2016, V.74, N.1, p.129-161. Constrained and unconstrained optimal discounted control of piecewise deterministic Markov processes (O.Costa, F.Dufour and A.Piunovskiy - co-authors) // SIAM J. Control Optim, 2016, V.54, N.3, p.1444-1474. Optimal impulsive control of piecewise deterministic Markov processes (F.Dufour, M.Horiguchi and A.Piunovskiy - co-authors) // Stochastics, 2016, V.88, N.7, p.1073-1098. On the equivalence of the integral and differential Bellman equations in impulse control problems (F.Dufour, A.Piunovskiy and A.Plakhov - co-authors) // Int. J. of Control, 2020. DOI: 10.1080/00207179.2020.1786766 At the end of 2021, together with Dr.Y.Zhang and Prof.F.Dufour, we started working on the new monograph on the optimal impulsive control.
Start Year 2009
 
Description Optimal Impulsive Control 
Organisation Inria Bordeaux - Sud-Ouest Research Centre
Country France 
Sector Public 
PI Contribution We started a joint project in 2016 supported by the Royal Society. That project was successfully accomplished. After several visits Liverpool-Aveiro-Liverpool, a number of articles were published (see outputs). In 2019 Prof.F.Dufour joined this collaboration. After my visit to INRIA supported by the host organization, the article in Intern.J.Control was published (see outputs). After the workshop in 2021 supported by EPSRC we agreed to prepare a monograph on optimal impulsive control: F.Dufour, A.Piunovskiy and Y.Zhang are the co-authors.
Collaborator Contribution We started a joint project in 2016 supported by the Royal Society. That project was successfully accomplished. Prof.F.Dufour (INRIA) organized my visit to Bordeaux and agreed to participate in preparation of the monograph "Optimal Impulsive Control".
Impact Optimal impulse control of dynamical systems (A.Piunovskiy, A.Plakhov, D.Torres and Y.Zhang - co-authors) // SIAM J. Control Optim, 2019, V.57, N.4, pp.2720-2752. Optimal impulse control of a SIR epidemic (A.Piunovskiy, A.Plakhov and M.Tumanov - co-authors) // Optim. Control Appl. Meth., 2020, V.41, N.2, pp.448-468. On the equivalence of the integral and differential Bellman equations in impulse control problems (A.Piunovskiy, F.Dufour and A.Plakhov - co-authors) // Int. J. of Control, 2020. DOI: 10.1080/00207179.2020.1786766
Start Year 2016
 
Description Optimal Impulsive Control 
Organisation University of Aveiro
Department Department of Mathematics
Country Portugal 
Sector Academic/University 
PI Contribution We started a joint project in 2016 supported by the Royal Society. That project was successfully accomplished. After several visits Liverpool-Aveiro-Liverpool, a number of articles were published (see outputs). In 2019 Prof.F.Dufour joined this collaboration. After my visit to INRIA supported by the host organization, the article in Intern.J.Control was published (see outputs). After the workshop in 2021 supported by EPSRC we agreed to prepare a monograph on optimal impulsive control: F.Dufour, A.Piunovskiy and Y.Zhang are the co-authors.
Collaborator Contribution We started a joint project in 2016 supported by the Royal Society. That project was successfully accomplished. Prof.F.Dufour (INRIA) organized my visit to Bordeaux and agreed to participate in preparation of the monograph "Optimal Impulsive Control".
Impact Optimal impulse control of dynamical systems (A.Piunovskiy, A.Plakhov, D.Torres and Y.Zhang - co-authors) // SIAM J. Control Optim, 2019, V.57, N.4, pp.2720-2752. Optimal impulse control of a SIR epidemic (A.Piunovskiy, A.Plakhov and M.Tumanov - co-authors) // Optim. Control Appl. Meth., 2020, V.41, N.2, pp.448-468. On the equivalence of the integral and differential Bellman equations in impulse control problems (A.Piunovskiy, F.Dufour and A.Plakhov - co-authors) // Int. J. of Control, 2020. DOI: 10.1080/00207179.2020.1786766
Start Year 2016