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Perninge, M. (2024). A note on reflected BSDEs in infinite horizon with stochastic Lipschitz coefficients. Stochastic Analysis and Applications, 42(5), 945-962
Åpne denne publikasjonen i ny fane eller vindu >>A note on reflected BSDEs in infinite horizon with stochastic Lipschitz coefficients
2024 (engelsk)Inngår i: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 42, nr 5, s. 945-962Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon RBSDEs to the setting where the driver has a stochastic Lipschitz coefficient. As an application, we consider robust optimal stopping problems for functional stochastic differential equations (FSDEs) where the driver has linear growth.

sted, utgiver, år, opplag, sider
Taylor & Francis Group, 2024
Emneord
Controller-stopper games, infinite horizon, optimal stopping, reflected BSDEs, snell envelope
HSV kategori
Forskningsprogram
Naturvetenskap, Matematik
Identifikatorer
urn:nbn:se:lnu:diva-132966 (URN)10.1080/07362994.2024.2396575 (DOI)001325654700001 ()2-s2.0-85205594504 (Scopus ID)
Forskningsfinansiär
Swedish Energy Agency, 42982-1
Tilgjengelig fra: 2024-10-12 Laget: 2024-10-12 Sist oppdatert: 2024-10-24bibliografisk kontrollert
Marcial, A. & Perninge, M. (2024). Finding a closest saddle-node bifurcation in power systems: An approach by unsupervised deep learning. Electric power systems research, 235, Article ID 110632.
Åpne denne publikasjonen i ny fane eller vindu >>Finding a closest saddle-node bifurcation in power systems: An approach by unsupervised deep learning
2024 (engelsk)Inngår i: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 235, artikkel-id 110632Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We propose a neural network using an unsupervised learning strategy for direct computation of closest saddle- node bifurcations, eliminating the need for labeled training data. Our method not only estimates the worst-case load increase scenarios but also significantly reduces the computational complexity traditionally associated with this task during inference time. Simulation results validate the effectiveness and real-time applicability of our approach, demonstrating its potential as a robust tool for modern power system analysis.

sted, utgiver, år, opplag, sider
Elsevier, 2024
Emneord
Saddle-node bifurcations, Voltage stability, Unsupervised learning, Deep learning
HSV kategori
Forskningsprogram
Fysik, Elektroteknik alt Electrical engineering
Identifikatorer
urn:nbn:se:lnu:diva-131791 (URN)10.1016/j.epsr.2024.110632 (DOI)001266918000001 ()2-s2.0-85197538486 (Scopus ID)
Tilgjengelig fra: 2024-08-15 Laget: 2024-08-15 Sist oppdatert: 2024-09-05bibliografisk kontrollert
Perninge, M. (2024). Infinite horizon impulse control of stochastic functional differential equations driven by Lévy processes. Stochastics: An International Journal of Probablitiy and Stochastic Processes, 96(3), 1241-1281
Åpne denne publikasjonen i ny fane eller vindu >>Infinite horizon impulse control of stochastic functional differential equations driven by Lévy processes
2024 (engelsk)Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 96, nr 3, s. 1241-1281Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider impulse control of stochastic functional differential equations (SFDEs) driven by Lévy processes under an additional Lp-Lipschitz condition on the coefficients. Our results, which are first derived for a general stochastic optimization problem over infinite horizon impulse controls and then applied to the case of a controlled SFDE, apply to the infinite horizon as well as the random horizon settings. The methodology employed to show existence of optimal controls is a probabilistic one based on the concept of Snell envelopes.

sted, utgiver, år, opplag, sider
Taylor & Francis Group, 2024
HSV kategori
Forskningsprogram
Matematik, Tillämpad matematik
Identifikatorer
urn:nbn:se:lnu:diva-125185 (URN)10.1080/17442508.2023.2262666 (DOI)001078314400001 ()2-s2.0-85173551056 (Scopus ID)
Forskningsfinansiär
Swedish Energy Agency, 48405-1
Tilgjengelig fra: 2023-10-17 Laget: 2023-10-17 Sist oppdatert: 2024-09-03bibliografisk kontrollert
Perninge, M. (2024). Optimal stopping of BSDEs with constrained jumps and related zero-sum games. Stochastic Processes and their Applications, 173, Article ID 104355.
Åpne denne publikasjonen i ny fane eller vindu >>Optimal stopping of BSDEs with constrained jumps and related zero-sum games
2024 (engelsk)Inngår i: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 173, artikkel-id 104355Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper, we introduce a non-linear Snell envelope which at each time represents the maximal value that can be achieved by stopping a BSDE with constrained jumps. We establish the existence of the Snell envelope by employing a penalization technique and the primary challenge we encounter is demonstrating the regularity of the limit for the scheme. Additionally, we relate the Snell envelope to a finite horizon, zero-sum stochastic differential game, where one player controls a path-dependent stochastic system by invoking impulses, while the opponent is given the opportunity to stop the game prematurely. Importantly, by developing new techniques within the realm of control randomization, we demonstrate that the value of the game exists and is precisely characterized by our non-linear Snell envelope.

sted, utgiver, år, opplag, sider
Elsevier, 2024
HSV kategori
Forskningsprogram
Matematik, Tillämpad matematik
Identifikatorer
urn:nbn:se:lnu:diva-129789 (URN)10.1016/j.spa.2024.104355 (DOI)001230030900001 ()2-s2.0-85190241469 (Scopus ID)
Forskningsfinansiär
Swedish Energy Agency, P2020-90032
Tilgjengelig fra: 2024-05-31 Laget: 2024-05-31 Sist oppdatert: 2024-06-03bibliografisk kontrollert
Marcial, A. & Perninge, M. (2023). An Unsupervised Neural Network Approach for Solving the Optimal Power Flow Problem. In: Gini G., Nijmeijer H., Filev D. (Ed.), Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO: . Paper presented at 20th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2023, Rome, 13-15 November 2023 (pp. 214-220). SciTePress, 1
Åpne denne publikasjonen i ny fane eller vindu >>An Unsupervised Neural Network Approach for Solving the Optimal Power Flow Problem
2023 (engelsk)Inngår i: Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO / [ed] Gini G., Nijmeijer H., Filev D., SciTePress, 2023, Vol. 1, s. 214-220Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

Optimal Power Flow is a central tool for power system operation and planning. Given the substantial rise in intermittent power and shorter time windows in electricity markets, there’s a need for fast and efficient solutions to the Optimal Power Flow problem. With this in consideration, this paper propose an unsupervised deep learning approach to approximate the optimal solution of Optimal Power Flow problems. Once trained, deep learning models benefit from being several orders of magnitude faster during inference compared to conventional non-linear solvers.

sted, utgiver, år, opplag, sider
SciTePress, 2023
Serie
Proceedings of the International Conference on Informatics in Control, Automation and Robotics, ISSN 2184-2809
HSV kategori
Forskningsprogram
Fysik, Elektroteknik alt Electrical engineering
Identifikatorer
urn:nbn:se:lnu:diva-129963 (URN)10.5220/0012187400003543 (DOI)2-s2.0-85181567286 (Scopus ID)
Konferanse
20th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2023, Rome, 13-15 November 2023
Tilgjengelig fra: 2024-06-05 Laget: 2024-06-05 Sist oppdatert: 2024-06-28bibliografisk kontrollert
Jönsson, J. & Perninge, M. (2023). Finite Horizon Impulse control of Stochastic Functional Differential Equations. SIAM Journal of Control and Optimization, 61(2), 924-948
Åpne denne publikasjonen i ny fane eller vindu >>Finite Horizon Impulse control of Stochastic Functional Differential Equations
2023 (engelsk)Inngår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 61, nr 2, s. 924-948Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this work we show that one can solve a finite horizon non-Markovian impulse control problem with control dependent dynamics. This dynamic satisfies certain functional Lipschitz conditions and is path dependent in such a way that the resulting trajectory becomes a flow.

sted, utgiver, år, opplag, sider
SIAM Publications, 2023
Emneord
dynamic programming, Snell envelope, stopping times, backward SDEs, stochastic delay equations, impulse control
HSV kategori
Forskningsprogram
Fysik, Vågor, signaler och system
Identifikatorer
urn:nbn:se:lnu:diva-121995 (URN)10.1137/20M1350303 (DOI)000995819400019 ()2-s2.0-85159768517 (Scopus ID)
Forskningsfinansiär
Swedish Energy Agency, 42982-1
Tilgjengelig fra: 2023-06-21 Laget: 2023-06-21 Sist oppdatert: 2023-08-18bibliografisk kontrollert
Perninge, M. (2023). Non-Markovian Impulse Control Under Nonlinear Expectation. Applied mathematics and optimization, 88(3), Article ID 72.
Åpne denne publikasjonen i ny fane eller vindu >>Non-Markovian Impulse Control Under Nonlinear Expectation
2023 (engelsk)Inngår i: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 88, nr 3, artikkel-id 72Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper and lower value functions satisfy a dynamic programming principle (DPP). We first prove the dynamic programming principle (DPP) for a truncated version of the upper value function in a straightforward manner. Relying on a uniform convergence argument then enables us to show the DPP for the general setting. Following this, we use an approximation based on a combination of truncation and discretization to show that the upper and lower value functions coincide, thus establishing that the game has a value and that the DPP holds for the lower value function as well. Finally, we show that the DPP admits a unique solution and give conditions under which a saddle point for the game exists. As an example, we consider a stochastic differential game (SDG) of impulse versus classical control of path-dependent stochastic differential equations (SDEs).

sted, utgiver, år, opplag, sider
Springer, 2023
Emneord
Impulse control, Non-linear expectation, Risk-sensitivity, Stochastic differential games, Zero-sum games
HSV kategori
Forskningsprogram
Fysik, Elektroteknik alt Electrical engineering
Identifikatorer
urn:nbn:se:lnu:diva-124129 (URN)10.1007/s00245-023-10049-7 (DOI)001050460600004 ()2-s2.0-85168414639 (Scopus ID)
Tilgjengelig fra: 2023-09-08 Laget: 2023-09-08 Sist oppdatert: 2023-10-11bibliografisk kontrollert
Perninge, M. (2023). Probabilistic representation of viscosity solutions to quasi-variational inequalities with non-local drivers. ESAIM: Control, Optimisation and Calculus of Variations , 29, Article ID 25.
Åpne denne publikasjonen i ny fane eller vindu >>Probabilistic representation of viscosity solutions to quasi-variational inequalities with non-local drivers
2023 (engelsk)Inngår i: ESAIM: Control, Optimisation and Calculus of Variations , ISSN 1292-8119, E-ISSN 1262-3377, Vol. 29, artikkel-id 25Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider quasi-variational inequalities (QVIs) with general non-local drivers and related systems of reflected backward stochastic differential equations (BSDEs) in a Brownian filtration. We show existence and uniqueness of viscosity solutions to the QVIs by first considering the standard (local) setting and then applying a contraction argument. In addition, the contraction argument yields existence and uniqueness of solutions to the related systems of reflected BSDEs and extends the theory of probabilistic representations of PDEs in terms of BSDEs to our specific setting.

sted, utgiver, år, opplag, sider
EDP Sciences, 2023
Emneord
Backward stochastic differential equations, impulse control, partial differential equations, viscosity solutions, quasi-variational inequalities
HSV kategori
Forskningsprogram
Naturvetenskap, Matematik
Identifikatorer
urn:nbn:se:lnu:diva-120773 (URN)10.1051/cocv/2023015 (DOI)000961181800002 ()2-s2.0-85153083672 (Scopus ID)
Tilgjengelig fra: 2023-05-17 Laget: 2023-05-17 Sist oppdatert: 2023-08-24bibliografisk kontrollert
Marcial, A. & Perninge, M. (2023). Production Planning of Cascaded Hydropower Stations using Approximate Dynamic Programming. In: Ishii H., Ebihara Y., Imura J., Yamakita M. (Ed.), IFAC-PapersOnLine: 22nd IFAC World Congress, Yokohama, Japan, July 9-14, 2023. Paper presented at 22nd IFAC World Congress, Yokohama, Japan, July 9-14, 2023 (pp. 10069-10076). Elsevier, 56(2)(2)
Åpne denne publikasjonen i ny fane eller vindu >>Production Planning of Cascaded Hydropower Stations using Approximate Dynamic Programming
2023 (engelsk)Inngår i: IFAC-PapersOnLine: 22nd IFAC World Congress, Yokohama, Japan, July 9-14, 2023 / [ed] Ishii H., Ebihara Y., Imura J., Yamakita M., Elsevier, 2023, Vol. 56(2), nr 2, s. 10069-10076Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

We formulate the day-ahead bidding problem for a hydropower producer having several hydropower plants residing in a river basin. We present a novel approach inspired by Dynamic programming with approximations in value and policy space by neural networks. This allows for more accurate modeling of the problem by avoiding linear approximations of the production function and bidding. Stochastic programming is a method frequently used in literature to solve the hydropower production planning problem. Stochastic programming is used on linearized systems and under assumptions of known distributions of the involved stochastic processes. We test the proposed algorithm on a simplified system, suitable for Stochastic Programming and compare the obtained policy with the results from Stochastic Programming. The results show that the algorithm obtains a policy similar to that of Stochastic Programming.

sted, utgiver, år, opplag, sider
Elsevier, 2023
Serie
IFAC-PapersOnLine, E-ISSN 2405-8963 ; 56(2)
Emneord
Analysis and control in deregulated power systems, Approximate dynamic programming, Hydropower production planning, Neural networks
HSV kategori
Forskningsprogram
Fysik, Elektroteknik alt Electrical engineering
Identifikatorer
urn:nbn:se:lnu:diva-129978 (URN)10.1016/j.ifacol.2023.10.876 (DOI)2-s2.0-85183624066 (Scopus ID)9781713872344 (ISBN)
Konferanse
22nd IFAC World Congress, Yokohama, Japan, July 9-14, 2023
Tilgjengelig fra: 2024-06-05 Laget: 2024-06-05 Sist oppdatert: 2024-06-28bibliografisk kontrollert
Perninge, M. (2023). Zero-sum stochastic differential games of impulse versus continuous control by FBSDEs. Journal of Mathematical Analysis and Applications, 527(1), Article ID 127403.
Åpne denne publikasjonen i ny fane eller vindu >>Zero-sum stochastic differential games of impulse versus continuous control by FBSDEs
2023 (engelsk)Inngår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 527, nr 1, artikkel-id 127403Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of "backward semigroups" we first prove the dynamic programming principle (DPP) for a truncated version of the problem in a straightforward manner. Relying on a uniform convergence argument then enables us to show the DPP for the general setting. Our approach avoids technical constraints imposed in previous works dealing with the same problem and, more importantly, allows us to consider impulse costs that depend on the present value of the state process in addition to unbounded coefficients. Using the dynamic programming principle we deduce that the upper and lower value functions are both solutions (in viscosity sense) to the same Hamilton-Jacobi-Bellman-Isaacs obstacle problem. By showing uniqueness of solutions to this partial differential inequality we conclude that the game has a value.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

sted, utgiver, år, opplag, sider
Elsevier, 2023
Emneord
Forward-backward stochastic, differential equations, Impulse control, Quasi-variational inequalities, Viscosity solutions, Zero-sum stochastic differential games
HSV kategori
Forskningsprogram
Fysik, Elektroteknik alt Electrical engineering
Identifikatorer
urn:nbn:se:lnu:diva-123525 (URN)10.1016/j.jmaa.2023.127403 (DOI)001011079500001 ()2-s2.0-85160086851 (Scopus ID)
Tilgjengelig fra: 2023-08-09 Laget: 2023-08-09 Sist oppdatert: 2023-08-24bibliografisk kontrollert
Organisasjoner
Identifikatorer
ORCID-id: ORCID iD iconorcid.org/0000-0003-3111-4820