| 1. |
- Agram, Nacira, Associate professor, 1987-, et al.
(author)
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Stochastic Fokker-Planck equations for conditional McKean-Vlasov jump diffusions and applications to optimal control
- 2023
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In: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 61:3, s. 1472-1493
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Journal article (peer-reviewed)abstract
- The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffu-sions, for short). To this end, we first prove a stochastic Fokker-Planck equation for the conditional law of the solution of such equations. Combining this equation with the original state equation, we obtain a Markovian system for the state and its conditional law. Furthermore, we apply this to formulate a Hamilton-Jacobi-Bellman equation for the optimal control of conditional McKean-Vlasov jump diffusions. Then we study the situation when the law is absolutely continuous with respect to Lebesgue measure. In that case the Fokker-Planck equation reduces to a stochastic par-tial differential equation for the Radon-Nikodym derivative of the conditional law. Finally we apply these results to solve explicitly the linear-quadratic optimal control problem of conditional stochastic McKean-Vlasov jump diffusions, and optimal consumption from a cash flow.
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| 2. |
- Bodnariu, Andi, et al.
(author)
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Local Time Pushed Mixed Equilibrium Strategies for Time-Inconsistent Stopping Problems
- 2024
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In: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 62:2, s. 1261-1290
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Journal article (peer-reviewed)abstract
- We consider the game-theoretic approach to time-inconsistent stopping of a onedimensional diffusion where the time-inconsistency is due to the presence of a nonexponential (weighted) discount function. In particular, we study (weak) equilibria for this problem in a novel class of mixed (i.e., randomized) stopping times based on a local time construction of the stopping intensity. For a general formulation of the problem we provide a verification theorem giving sufficient conditions for mixed (and pure) equilibria in terms of a set of variational inequalities, including a smooth fit condition. We apply the theory to prove the existence of (mixed) equilibria in a recently studied real options problem in which no pure equilibria exist.
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| 3. |
- Chen, Jianqi, et al.
(author)
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Geometrical Characterization Of Sensor Placement For Cone-Invariant And Multi-Agent Systems Against Undetectable Zero-Dynamics Attacks\Ast
- 2022
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In: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 60:2, s. 890-916
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Journal article (peer-reviewed)abstract
- Undetectable attacks are an important class of malicious attacks threatening the security of cyber-physical systems, which can modify a system's state but leave the system output measurements unaffected and hence cannot be detected from the output. This paper studies undetectable attacks on cone-invariant systems and multi-agent systems. We first provide a general characterization of zero-dynamics attacks, which characterizes fully undetectable attacks targeting the nonminimum phase zeros of a system. This geometrical characterization makes it possible to develop a defense strategy seeking to place a minimal number of sensors to detect and counter the zero-dynamics attacks on the system's actuators. The detect and defense scheme amounts to computing a set containing potentially vulnerable actuator locations and nodes and a defense union for feasible placement of sensors based on the geometrical properties of the cones under consideration.
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| 4. |
- Chen, Wei, et al.
(author)
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A Phase Theory Of Multi-Input Multi-Output Linear Time-Invariant Systems
- 2024
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In: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 62:2, s. 1235-1260
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Journal article (peer-reviewed)abstract
- In this paper, we define the phase response for a class of multi -input multi -output (MIMO) linear time -invariant (LTI) systems whose frequency responses are (semi -)sectorial at all frequencies. The newly defined phase subsumes the well-known notion of positive real systems and is closely related to the notion of negative imaginary systems. We formulate a small phase theorem for feedback stability, which complements the small gain theorem. The small phase theorem lays the foundation of a phase theory of MIMO systems. We also discuss time -domain interpretations of phase -bounded systems via both energy signal analysis and power signal analysis.
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| 5. |
- De Angelis, Tiziano, et al.
(author)
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The maximality principle in singular control with absorption and its applications to the dividend problem
- 2024
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In: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 62:1, s. 91-117
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Journal article (peer-reviewed)abstract
- Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with twodimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm's (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
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| 6. |
- Ekström, Erik, 1977-, et al.
(author)
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How To Detect A Salami Slicer : A Stochastic Controller-And-Stopper Game With Unknown Competition
- 2022
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In: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics Publications. - 0363-0129 .- 1095-7138. ; 60:1, s. 545-574
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Journal article (peer-reviewed)abstract
- We consider a stochastic game of control and stopping specified in terms of a process $X_t=-\theta \Lambda_t+W_t$, representing the holdings of Player 1, where $W$ is a Brownian motion, $\theta$ is a Bernoulli random variable indicating whether Player 2 is active or not, and $\Lambda$ is a nondecreasing continuous process representing the accumulated "theft" or "fraud" performed by Player 2 (if active) against Player 1. Player 1 cannot observe $\theta$ or $\Lambda$ directly but can merely observe the path of the process $X$ and may choose a stopping rule $\tau$ to deactivate Player 2 at a cost $M$. Player 1 thus does not know if she is the victim of fraud or not and operates in this sense under unknown competition. Player 2 can observe both $\theta$ and $W$ and seeks to choose a fraud strategy $\Lambda$ that maximizes the expected discounted amount ${\mathbb E} \left [ \left. \int _0^{\tau} e^{-rs} d\Lambda_s \right \vert \theta=1\right ],$ whereas Player 1 seeks to choose the stopping strategy $\tau$ so as to minimize the expected discounted cost ${\mathbb E} \left [\theta \int _0^{\tau} e^{-rs} d\Lambda_s + e^{-r\tau}M\I{\tau<\infty} \right ].$ This non-zero-sum game belongs to a class of stochastic dynamic games with unknown competition and continuous controls and is motivated by applications in fraud detection; it combines filtering (detection), stochastic control, optimal stopping, strategic features (games), and asymmetric information. We derive Nash equilibria for this game; for some parameter values we find an equilibrium in pure strategies, and for other parameter values we find an equilibrium by allowing for randomized stopping strategies.
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| 7. |
- Ekström, Erik, 1977-, et al.
(author)
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The de Finetti problem with uncertain competition
- 2023
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In: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 61:5, s. 2997-3017
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Journal article (peer-reviewed)abstract
- We consider a resource extraction problem which extends the classical de Finetti problem for a Wiener process to include the case when a competitor, who is equipped with the ability to extract all the remaining resources in one piece, may exist. This situation is modeled as a nonzero-sum controller-and-stopper game with incomplete information. For this stochastic game we provide a Nash equilibrium with an explicit structure. In equilibrium, the agent and the competitor use singular strategies in such a way that a two-dimensional process, which represents available resources and the filtering estimate of active competition, reflects in a specific direction along a given boundary.
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| 8. |
- Haasler, Isabel, et al.
(author)
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Multimarginal optimal transport with a tree-structured cost and the schrödinger bridge problem
- 2021
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In: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 59:4, s. 2428-2453
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Journal article (peer-reviewed)abstract
- The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the problem with an entropy term, which connects it to the Schrodinger bridge problem and thus to stochastic optimal control. Moreover, the entropy regularization makes the otherwise computationally demanding optimal transport problem feasible even for large scale settings. This has led to an accelerated development of optimal transport based methods in a broad range of fields. Many of these applications have an underlying graph structure, for instance, information fusion and tracking problems can be described by trees. In this work we consider multimarginal optimal transport problems with a cost function that decouples according to a tree structure. The entropy regularized multimarginal optimal transport problem can be viewed as a generalization of the Schrodinger bridge problem with the same tree-structure, and by utilizing these connections we extend the computational methods for the classical optimal transport problem in order to solve structured multimarginal optimal transport problems in an efficient manner. In particular, the algorithm requires only matrix-vector multiplications of relatively small dimensions. We show that the multimarginal regularization introduces less diffusion, compared to the commonly used pairwise regularization, and is therefore more suitable for many applications. Numerical examples illustrate this, and we finally apply the proposed framework for the tracking of an ensemble of indistinguishable agents.
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| 9. |
- He, Xingkang, et al.
(author)
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EVENT-TRIGGERED DISTRIBUTED ESTIMATION WITH DECAYING COMMUNICATION RATE
- 2022
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In: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 60:2, s. 992-1017
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Journal article (peer-reviewed)abstract
- We study distributed estimation of a high-dimensional static parameter vector through a group of sensors whose communication network is modeled by a fixed directed graph. Different from existing time-triggered communication schemes, an event-triggered asynchronous scheme is investigated in order to reduce communication while preserving estimation convergence. A distributed estimation algorithm with a single step size is first proposed based on an event-triggered communication scheme with a time-dependent decaying threshold. With the event-triggered scheme, each sensor sends its estimate to neighbor sensors only when the difference between the current estimate and the last sent-out estimate is larger than the triggering threshold. Different sensors can have different step sizes and triggering thresholds, enabling the parameter estimation process to be conducted in a fully distributed way. We prove that the proposed algorithm has mean-square and almost-sure convergence, respectively, under an integrated condition of sensor network topology and sensor measurement matrices. The condition is satisfied if the topology is a balanced digraph containing a spanning tree and the system is collectively observable. The collective observability is the possibly mildest condition, since it is a spatially and temporally collective condition of all sensors and allows sensor measurement matrices to be time-varying, stochastic, and nonstationary. Moreover, we provide estimates for the convergence rates, which are related to the step size as well as the triggering threshold. Furthermore, as an essential metric of sensor communication intensity in the event-triggered distributed algorithms, the communication rate is proved to decay to zero with a certain speed almost surely as time goes to infinity. In addition, we show that it is feasible to tune the threshold and the step size such that requirements of algorithm convergence and communication rate decay are satisfied simultaneously. We also show that given the step size, adjusting the decay speed of the triggering threshold can lead to a tradeoff between the convergence rate of the estimation error and the decay speed of the communication rate. Specifically, increasing the decay speed of the threshold would make the communication rate decay faster but reduce the convergence rate of the estimation error. Numerical simulations are provided to illustrate the developed results.
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| 10. |
- Jönsson, Johan, et al.
(author)
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Finite Horizon Impulse control of Stochastic Functional Differential Equations
- 2023
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In: SIAM Journal of Control and Optimization. - : SIAM Publications. - 0363-0129 .- 1095-7138. ; 61:2, s. 924-948
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Journal article (peer-reviewed)abstract
- 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.
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