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This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…

Optimization and Control · Mathematics 2016-12-07 Qingxin Meng , Yang Shen , Peng Shi

In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…

Probability · Mathematics 2026-03-09 Liangying Chen , Wilhelm Stannat

This paper is concerned with an optimal control problem governed by a non-smooth semilinear elliptic equation. We show that the control-to-state mapping is directionally differentiable and precisely characterize its Bouligand…

Optimization and Control · Mathematics 2018-01-29 Constantin Christof , Christian Clason , Christian Meyer , Stephan Walther

The considered optimal control problem of a stochastic power system, is to select the set of power supply vectors which infimizes the probability that the phase-angle differences of any power flow of the network, endangers the transient…

Optimization and Control · Mathematics 2024-01-31 Zhen Wang , Kaihua Xi , Aijie Cheng , Hai Xiang Lin , Jan H. van Schuppen

The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in…

Optimization and Control · Mathematics 2023-03-23 Jin W. Kim , Prashant G. Mehta

The path-integral control, which stems from the stochastic Hamilton-Jacobi-Bellman equation, is one of the methods to control stochastic nonlinear systems. This paper gives a new insight into nonlinear stochastic optimal control problems…

Optimization and Control · Mathematics 2021-09-14 Jun Ohkubo

We consider the PDE-constrained optimal control of a leader-follower kinetic opinion formation model, with a Fokker-Planck-type system of partial differential equations as a state constraint. We derive the Boltzmann-type and…

Optimization and Control · Mathematics 2025-09-11 Bertram Düring , Oliver Wright

This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…

Optimization and Control · Mathematics 2015-01-23 Liangquan Zhang , Jianhui Huang , Xun Li

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…

Probability · Mathematics 2008-07-23 Seid Bahlali

This paper focuses on the analysis of an optimal control problem governed by a nonsmooth quasilinear partial differential equation that models a stationary incompressible shear-thickening fluid. We start by studying the directional…

Optimization and Control · Mathematics 2023-03-07 Juan Carlos De los Reyes , Paola Quiloango

We study the optimal control of a rate-independent system that is driven by a convex, quadratic energy. Since the associated solution mapping is non-smooth, the analysis of such control problems is challenging. In order to derive optimality…

Optimization and Control · Mathematics 2016-11-04 Ulisse Stefanelli , Gerd Wachsmuth , Daniel Wachsmuth

The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…

Optimization and Control · Mathematics 2025-01-30 Nikolay Pogodaev , Maxim Staritsyn

In this note, we consider the existence and uniqueness of the solution of a time-dependent optimal control problem constrained by a partial differential equation with uncertain inputs. Relying on the Lions' Lemma for deterministic problems,…

Optimization and Control · Mathematics 2018-10-04 Peter Benner , Akwum Onwunta , Martin Stoll

This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…

Optimization and Control · Mathematics 2025-04-01 Chuanzhi Lv , Xunmin Yin , Hongdan Li , Huanshui Zhang

This paper is devoted to an optimal control problem of fully coupled forward-backward stochastic differential equations driven by sub-diffusion, whose solutions are not Markov processes. The stochastic maximum principle is obtained, where…

Optimization and Control · Mathematics 2025-03-11 Chenhui Hao , Jingtao Shi , Shuaiqi Zhang

In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…

Optimization and Control · Mathematics 2018-09-07 AbdulRahman Al-Hussein , Boulakhras Gherbal

This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…

Optimization and Control · Mathematics 2021-07-02 Johannes N. Hendriks , James R. Z. Holdsworth , Adrian G. Wills , Thomas B. Schon , Brett Ninness

The solution to a stochastic optimal control problem can be determined by computing the value function from a discretization of the associated Hamilton-Jacobi-Bellman equation. Alternatively, the problem can be reformulated in terms of a…

Optimization and Control · Mathematics 2024-02-29 Sebastian Reich

A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…

Optimization and Control · Mathematics 2019-11-20 Christian Clason , Yu Deng , Patrick Mehlitz , Uwe Prüfert

We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are…

Optimization and Control · Mathematics 2017-01-31 Fouzia Baghery , Nabil Khelfallah , Brahim Mezerdi , Isabelle Turpin