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Optimal control of elliptic variational inequalities with bounded and unbounded operators Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Livia Betz, Irwin YouseptThis paper examines optimal control problems governed by elliptic variational inequalities of the second kind with bounded and unbounded operators. To tackle the bounded case, we employ the polyhedricity of the test set appearing in the dual formulation of the governing variational inequality. Based thereon, we are able to prove the directional differentiability of the associated solution operator

Tracking aircraft trajectories in the presence of wind disturbances Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Nikolai Botkin, Varvara Turova, Barzin Hosseini, Johannes Diepolder, Florian HolzapfelA method of path following, utilized in the theory of position differential games as a tool for establishing theoretical results, is adopted in this paper for tracking aircraft trajectories under windshear conditions. It is interesting to note that reference trajectories, obtained as solutions of optimal control problems with zero wind, can very often be tracked in the presence of rather severe wind

Optimal control of ODEs with state suprema Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Tobias Geiger, Daniel Wachsmuth, Gerd WachsmuthWe consider the optimal control of a differential equation that involves the suprema of the state over some part of the history. In many applications, this nonsmooth functional dependence is crucial for the successful modeling of realworld phenomena. We prove the existence of solutions and show that related problems may not possess optimal controls. Due to the nonsmoothness in the state equation

Performance estimates for economic model predictive control and their application in proper orthogonal decompositionbased implementations Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Lars Grüne, Luca Mechelli, Simon Pirkelmann, Stefan VolkweinIn this paper performance indices for economic model predictive controllers (MPC) are considered. Since existing relative performance measures, designed for stabilizing controllers, fail in the economic setting, we propose alternative absolute quantities. We show that these can be applied to assess the performance of the closed loop trajectories online while the controller is running. The advantages

A priori error estimates for the spacetime finite element discretization of an optimal control problem governed by a coupled linear PDEODE system Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Marita Holtmannspötter, Arnd Rösch, Boris VexlerIn this paper we investigate a priori error estimates for the spacetime Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a special structure as the state equation consists of an elliptic PDE which has to be fulfilled at almost all times coupled with an ODE that has to hold true in almost

External polyhedral estimates of reachable sets of discretetime systems with integral bounds on additive terms Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Elena K. KostousovaWe deal with the reachability problem for linear and bilinear discretetime uncertain systems under integral nonquadratic constraints on additive input terms and setvalued constraints on initial states. The bilinearity is caused by an interval type uncertainty in coefficients of the system. Algorithms for constructing external parallelepipedvalued (shorter, polyhedral) estimates of reachable sets

Modeling the pressure distribution in a spatially averaged cerebral capillary network Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Andrey Kovtanyuk, Alexander Chebotarev, Nikolai Botkin, Varvara Turova, Irina Sidorenko, Renée LampeA boundary value problem for the Poisson's equation with unknown intensities of sources is studied in context of mathematical modeling the pressure distribution in cerebral capillary networks. The problem is formulated as an inverse problem with finitedimensional overdetermination. The unique solvability of the problem is proven. A numerical algorithm is proposed and implemented.

Second order directional shape derivatives of integrals on submanifolds Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Anton Schiela, Julian OrtizWe compute first and second order shape sensitivities of integrals on smooth submanifolds using a variant of shape differentiation. The result is a quadratic form in terms of one perturbation vector field that yields a second order quadratic model of the perturbed functional. We discuss the structure of this derivative, derive domain expressions and Hadamard forms in a general geometric framework,

Uncertainty damping in kinetic traffic models by driverassist controls Math. Control Relat. Fields (IF 1.284) Pub Date : 20210304
Andrea Tosin, Mattia ZanellaIn this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover, we design control strategies at the level of the microscopic interactions among the

Optimal control of a nonsmooth quasilinear elliptic equation Math. Control Relat. Fields (IF 1.284) Pub Date : 20201217
Christian Clason, Vu Huu Nhu, Arnd RöschThis work is concerned with an optimal control problem governed by a nonsmooth quasilinear elliptic equation with a nonlinear coefficient in the principal part that is locally Lipschitz continuous and directionally but not Gâteaux differentiable. This leads to a controltostate operator that is directionally but not Gâteaux differentiable as well. Based on a suitable regularization scheme, we derive

On switching properties of time optimal controls for linear ODEs Math. Control Relat. Fields (IF 1.284) Pub Date : 20201021
Shulin Qin, Gengsheng Wang, Huaiqiang YuIn this paper, we present some properties of time optimal controls for linear ODEs with the balltype control constraint. More precisely, given an optimal control, we build up an upper bound for the number of its switching points; show that it jumps from one direction to the reverse direction at each switching point; give its dynamic behaviour between two consecutive switching points; and study its

General stability of abstract thermoelastic system with infinite memory and delay Math. Control Relat. Fields (IF 1.284) Pub Date : 20201021
Jianghao Hao, Junna ZhangIn this paper we study an abstract thermoelastic system in Hilbert space with infinite memory and time delay. Under some suitable conditions, we prove the wellposedness by invoking semigroup theory. Since the damping may stabilize the system while the delay may destabilize it, we discuss the interaction between the damping and the delay term, and obtain that the system is uniformly stable when the

Local contact subFinslerian geometry for maximum norms in dimension 3 Math. Control Relat. Fields (IF 1.284) Pub Date : 20201021
Entisar A.L. Ali, G. CharlotThe local geometry of subFinslerian structures in dimension 3 associated with a maximum norm is studied in the contact case. A normal form is given. The short extremals, the local switching, conjugate and cut loci, and the small spheres are described in the generic case.

Stable determination of a vector field in a nonSelfAdjoint dynamical Schrödinger equation on Riemannian manifolds Math. Control Relat. Fields (IF 1.284) Pub Date : 20201021
Mourad Bellassoued, Ibtissem Ben Aïcha, Zouhour RezigThis paper deals with an inverse problem for a nonselfadjoint Schrödinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical DirichlettoNeumann map. We establish in dimension $ n\geq2 $, an Hölder type stability estimate for the inverse problem under study. The proof is mainly based on the reduction to an equivalent problem for an electromagnetic

Extended backward stochastic Volterra integral equations and their applications to timeInconsistent stochastic recursive control problems Math. Control Relat. Fields (IF 1.284) Pub Date : 20201021
Yushi HamaguchiIn this paper, we study extended backward stochastic Volterra integral equations (EBSVIEs, for short). We establish the wellposedness under weaker assumptions than the literature, and prove a new kind of regularity property for the solutions. As an application, we investigate, in the openloop framework, a timeinconsistent stochastic recursive control problem where the cost functional is defined

Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension Math. Control Relat. Fields (IF 1.284) Pub Date : 20200813
Vahagn NersesyanIn this paper, we consider a parabolic PDE on a torus of arbitrary dimension. The nonlinear term is a smooth function of polynomial growth of any degree. In this general setting, the Cauchy problem is not necessarily well posed. We show that the equation in question is approximately controllable by only a finite number of Fourier modes. This result is proved by using some ideas from the geometric control

Optimal control problems governed by 1D Kobayashi–Warren–Carter type systems Math. Control Relat. Fields (IF 1.284) Pub Date : 20200813
Harbir Antil, Shodai Kubota, Ken Shirakawa, Noriaki YamazakiThis paper is devoted to the study of a class of optimal control problems governed by 1–D Kobayashi–Warren–Carter type systems, which are based on a phasefield model of grain boundary motion, proposed by [Kobayashi et al, Physica D, 140, 141–150, 2000]. The class consists of an optimal control problem for a physically realistic statesystem of Kobayashi–Warren–Carter type, and its regularized approximating

A stochastic optimal control problem governed by SPDEs via a spatialtemporal interaction operator Math. Control Relat. Fields (IF 1.284) Pub Date : 20200813
Zhun Gou, Nanjing Huang, Minghui Wang, Yaojia ZhangIn this paper, we first introduce a new spatialtemporal interaction operator to describe the spacetime dependent phenomena. Then we consider the stochastic optimal control of a new system governed by a stochastic partial differential equation with the spatialtemporal interaction operator. To solve such a stochastic optimal control problem, we derive an adjoint backward stochastic partial differential

Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions Math. Control Relat. Fields (IF 1.284) Pub Date : 20200813
Niklas BehringerThis work is motivated by recent interest in the topic of pointwise tracking type optimal control problems for the Stokes problem. Pointwise tracking consists of point evaluations in the objective functional which lead to Dirac measures appearing as source terms of the adjoint problem. Considering bounds for the control allows for improved regularity results for the exact solution and improved approximation

Controllability problems for the heat equation on a halfaxis with a bounded control in the Neumann boundary condition Math. Control Relat. Fields (IF 1.284) Pub Date : 20200813
Larissa Fardigola, Kateryna KhalinaIn the paper, the problems of controllability and approximate controllability are studied for the control system $ w_t = w_{xx} $, $ w_x(0,\cdot) = u $, $ x>0 $, $ t\in(0,T) $, where $ u\in L^\infty(0,T) $ is a control. It is proved that each initial state of the system is approximately controllable to each target state in a given time $ T $. A necessary and sufficient condition for controllability

Optimal design problems governed by the nonlocal \begin{document}$ p $\end{document}Laplacian equation Math. Control Relat. Fields (IF 1.284) Pub Date : 20200613
Fuensanta Andrés, Julio Muñoz, Jesús RosadoIn the present work, a nonlocal optimal design model has been considered as an approximation of the corresponding classical or local optimal design problem. The new model is driven by the nonlocal $ p $Laplacian equation, the design is the diffusion coefficient and the cost functional belongs to a broad class of nonlocal functional integrals. The purpose of this paper is to prove the existence of

Errorbased control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport Math. Control Relat. Fields (IF 1.284) Pub Date : 20200613
Simone FioriThe objective of the paper is to contribute to the theory of errorbased control systems on Riemannian manifolds. The present study focuses on system where the control field influences the covariant derivative of a control path. In order to define error terms in such systems, it is necessary to compare tangent vectors at different points using parallel transport and to understand how the covariant

On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems Math. Control Relat. Fields (IF 1.284) Pub Date : 20200613
Lars Grüne, Roberto GuglielmiThe paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuoustime finite dimensional linear quadratic optimal control problems. We characterize strict dissipativity properties of the dynamics in terms of the system matrices related to the linear quadratic problem. These characterizations then lead to new necessary conditions for the turnpike

Fractional optimal control problems on a star graph: Optimality system and numerical solution Math. Control Relat. Fields (IF 1.284) Pub Date : 20200613
Vaibhav Mehandiratta, Mani Mehra, Günter LeugeringIn this paper, we study optimal control problems for nonlinear fractional order boundary value problems on a star graph, where the fractional derivative is described in the Caputo sense. The adjoint state and the optimality system are derived for fractional optimal control problem (FOCP) by using the Lagrange multiplier method. Then, the existence and uniqueness of solution of the adjoint equation

Meanfield stochastic linearquadratic optimal control problems: Weak closedloop solvability Math. Control Relat. Fields (IF 1.284) Pub Date : 20200601
Jingrui Sun, Hanxiao WangThis paper is concerned with meanfield stochastic linearquadratic (MFSLQ, for short) optimal control problems with deterministic coefficients. The notion of weak closedloop optimal strategy is introduced. It is shown that the openloop solvability is equivalent to the existence of a weak closedloop optimal strategy. Moreover, when openloop optimal controls exist, there is at least one of them

Nonzerosum differential game of backward doubly stochastic systems with delay and applications Math. Control Relat. Fields (IF 1.284) Pub Date : 20200601
Qingfeng Zhu, Yufeng ShiThis paper is concerned with a kind of nonzerosum differential game of backward doubly stochastic system with delay, in which the state dynamics follows a delayed backward doubly stochastic differential equation (SDE). To deal with the above game problem, it is natural to involve the adjoint equation, which is a kind of anticipated forward doubly SDE. We give the existence and uniqueness of solutions

Finitedimensional controllers for robust regulation of boundary control systems Math. Control Relat. Fields (IF 1.284) Pub Date : 20200601
Duy Phan, Lassi PaunonenWe study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the abstract setting and present finitedimensional reduced order controllers. The controller design is then used for particular PDE models: highdimensional parabolic

LinearquadraticGaussian meanfieldgame with partial observation and common noise Math. Control Relat. Fields (IF 1.284) Pub Date : 20200531
Alain Bensoussan, Xinwei Feng, Jianhui HuangThis paper considers a class of linearquadraticGaussian (LQG) meanfield games (MFGs) with partial observation structure for individual agents. Unlike other literature, there are some special features in our formulation. First, the individual state is driven by some commonnoise due to the external factor and the stateaverage thus becomes a random process instead of a deterministic quantity. Second

Optimal dividend policy in an insurance company with contagious arrivals of claims Math. Control Relat. Fields (IF 1.284) Pub Date : 20200322
Yiling Chen, Baojun BianIn this paper we consider the optimal dividend problem for an insurance company whose surplus follows a classical CramérLundberg process with a feature of selfexciting. A Hawkes process is applied so that the occurrence of a jump in the claims triggers more sequent jumps. We show that the optimal value function is a unique viscosity solution of the associated HamiltonJacobiBellman equation with

Maximal discrete sparsity in parabolic optimal control with measures Math. Control Relat. Fields (IF 1.284) Pub Date : 20200322
Evelyn Herberg, Michael Hinze, Henrik SchumacherWe consider variational discretization [18] of a parabolic optimal control problem governed by spacetime measure controls. For the state discretization we use a PetrovGalerkin method employing piecewise constant states and piecewise linear and continuous test functions in time. For the space discretization we use piecewise linear and continuous functions. As a result the controls are composed of

Nonexponential discounting portfolio management with habit formation Math. Control Relat. Fields (IF 1.284) Pub Date : 20200322
Jingzhen Liu, Liyuan Lin, Ka Fai Cedric Yiu, Jiaqin WeiThis paper studies the portfolio management problem for an individual with a nonexponential discount function and habit formation in finite time. The investor receives a deterministic income, invests in risky assets, buys insurance and consumes continuously. The objective is to maximize the utility of excessive consumption, heritage and terminal wealth. The nonexponential discounting makes the optimal

Timeinconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach Math. Control Relat. Fields (IF 1.284) Pub Date : 20200322
Ishak AliaIn this paper, we investigate a class of timeinconsistent stochastic control problems for stochastic differential equations with deterministic coefficients. We study these problems within the game theoretic framework, and look for openloop Nash equilibrium controls. Under suitable conditions, we derive a verification theorem for equilibrium controls via a flow of forwardbackward stochastic partial

On optimal \begin{document}$ L^1 $\end{document}control in coefficients for quasilinear Dirichlet boundary value problems with \begin{document}$ BMO $\end{document}anisotropic \begin{document}$ p $\end{document}Laplacian Math. Control Relat. Fields (IF 1.284) Pub Date : 20200322
Umberto De Maio, Peter I. Kogut, Gabriella ZeccaWe study an optimal control problem for a quasilinear elliptic equation with anisotropic pLaplace operator in its principal part and $ L^1 $control in coefficient of the loworder term. We assume that the matrix of anisotropy belongs to BMOspace. Since we cannot expect to have a solution of the state equation in the classical Sobolev space, we introduce a suitable functional class in which we look

Stochastic impulse control Problem with state and time dependent cost functions Math. Control Relat. Fields (IF 1.284) Pub Date : 20200322
Brahim El Asri, Sehail MazidWe consider stochastic impulse control problems when the impulses cost functions depend on $ t $ and $ x $. We use the approximation scheme and viscosity solutions approach to show that the value function is a unique viscosity solution for the associated HamiltonJacobiBellman equation (HJB) partial differential equation (PDE) of stochastic impulse control problems.

Semiconical eigenvalue intersections and the ensemble controllability problem for quantum systems Math. Control Relat. Fields (IF 1.284) Pub Date : 20200322
Nicolas Augier, Ugo Boscain, Mario SigalottiWe study oneparametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semiconical intersections of eigenvalues. Then, through the use of normal forms, we study the problem of ensemble controllability between the eigenstates of a generic Hamiltonian

Uniform indirect boundary controllability of semidiscrete \begin{document}$ 1 $\end{document}\begin{document}$ d $\end{document} coupled wave equations Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Abdeladim El Akri, Lahcen ManiarIn this paper, we treat the problem of uniform exact boundary controllability for the finitedifference space semidiscretization of the $ 1 $$ d $ coupled wave equations with a control acting only in one equation. First, we show how, after filtering the high frequencies of the discrete initial data in an appropriate way, we can construct a sequence of uniformly (with respect to the mesh size) bounded

The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Lassaad Aloui, Imen El Khal El TaiefWe establish Strichartz estimates for the regularized Schrödinger equation on a two dimensional compact Riemannian manifold without boundary. As a consequence we deduce global existence and uniqueness results for the Cauchy problem for the nonlinear regularized Schrödinger equation and we prove under the geometric control condition the Kato smoothing effect for solutions of this equation in this particular

Asymptotic stabilization of continuoustime periodic stochastic systems by feedback control based on periodic discretetime observations Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Ran Dong, Xuerong MaoIn 2013, Mao initiated the study of stabilization of continuoustime hybrid stochastic differential equations (SDEs) by feedback control based on discretetime state observations. In recent years, this study has been further developed while using a constant observation interval. However, timevarying observation frequencies have not been discussed for this study. Particularly for nonautonomous periodic

Implicit parametrizations and applications in optimization and control Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Dan TibaWe discuss necessary conditions (with less Lagrange multipliers), perturbations and general algorithms in non convex optimization problems. Optimal control problems with mixed constraints, governed by ordinary differential equations, are also studied in this context. Our treatment is based on a recent approach to implicit systems, constructing parametrizations of the corresponding manifold, via iterated

Sparse optimal control for the heat equation with mixed controlstate constraints Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Eduardo Casas, Fredi TröltzschA problem of sparse optimal control for the heat equation is considered, where pointwise bounds on the control and mixed pointwise controlstate constraints are given. A standard quadratic tracking type functional is to be minimized that includes a Tikhonov regularization term and the $ L^1 $norm of the control accounting for the sparsity. Special emphasis is laid on existence and regularity of Lagrange

Optimality conditions in variational form for nonlinear constrained stochastic control problems Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Laurent PfeifferOptimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the probability distribution of the state variable at the final time. The analysis uses in an essential manner a convexity property of the set of reachable probability distributions

Stateconstrained semilinear elliptic optimization problems with unrestricted sparse controls Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Eduardo Casas, Fredi TröltzschIn this paper, we consider optimal control problems associated with semilinear elliptic equation equations, where the states are subject to pointwise constraints but there are no explicit constraints on the controls. A term is included in the cost functional promoting the sparsity of the optimal control. We prove existence of optimal controls and derive first and second order optimality conditions

Optimal periodic control for scalar dynamics under integral constraint on the input Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Térence Bayen, Alain Rapaport, FatimaZahra TaniThis paper studies a periodic optimal control problem governed by a onedimensional system, linear with respect to the control $ u $, under an integral constraint on $ u $. We give conditions for which the value of the cost function at steady state with a constant control $ \bar u $ can be improved by considering periodic control $ u $ with average value equal to $ \bar u $. This leads to the socalled

A convergent hierarchy of nonlinear eigenproblems to compute the joint spectral radius of nonnegative matrices Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Stéphane Gaubert, Nikolas StottWe show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a nonlinear operator. This eigenvalue coincides with the ergodic constant of a risksensitive control problem, or of an entropy game, in which the state space consists of all switching sequences of a given length. We show that, by increasing this length, we arrive at a convergent

Controllability of a system of degenerate parabolic equations with nondiagonalizable diffusion matrix Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
El Mustapha Ait Ben Hassi, Mohamed Fadili, Lahcen ManiarIn this paper we study the null controllability of some non diagonalizable degenerate parabolic systems of PDEs, we assume that the diffusion, coupling and controls matrices are constant and we characterize the null controllability by an algebraic condition so called Kalman's rank condition.

Lipschitz stability for some coupled degenerate parabolic systems with locally distributed observations of one component Math. Control Relat. Fields (IF 1.284) Pub Date : 20191227
Brahim Allal, Abdelkarim Hajjaj, Lahcen Maniar, Jawad SalhiThis article presents an inverse source problem for a cascade system of $ n $ coupled degenerate parabolic equations. In particular, we prove stability and uniqueness results for the inverse problem of determining the source terms by observations in an arbitrary subdomain over a time interval of only one component and data of the $ n $ components at a fixed positive time $ T' $ over the whole spatial

Optimal control of the linear wave equation by timedepending BVcontrols: A semismooth Newton approach Math. Control Relat. Fields (IF 1.284) Pub Date : 20191223
Sebastian Engel, Karl KunischAn optimal control problem for the linear wave equation with control cost chosen as the BV seminorm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal solutions and necessary optimality conditions are derived. With numerical realisation in mind, the regularization by $ H^1 $ functionals is investigated, and the

An infinite time horizon portfolio optimization model with delays Math. Control Relat. Fields (IF 1.284) Pub Date : 20161001
Tao Pang, Azmat HussainIn this paper we consider a portfolio optimization problem of the Merton's type over an infinite time horizon. Unlike the classical Markov model, we consider a system with delays. The problem is formulated as a stochastic control problem on an infinite time horizon and the state evolves according to a process governed by a stochastic process with delay. The goal is to choose investment and consumption

Optimal $L^2$control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions Math. Control Relat. Fields (IF 1.284) Pub Date : 20161001
Thierry Horsin, Peter I. Kogut, Olivier WilkIn this paper we study we study a Dirichlet optimal control prob lem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The characteristic feature of this control object is the fact that the skewsymmetric part of matrixvalued control A(x) belongs to L2space (rather than Linfinty). In spite of the fact that the equations

An optimal control model of carbon reduction and trading Math. Control Relat. Fields (IF 1.284) Pub Date : 20161001
Huaying Guo, Jin LiangIn this study, a stochastic control model is established for a country to formulate a carbon abatement policy to minimize the total carbon reduction costs. Under Merton's consumption framework, by considering carbon trading, carbon abatement and penalties in a synthetic manner, the model is converted into a twodimensional HamiltonJacobiBellman equation. We rigorously prove the existence and uniqueness

Forwardbackward evolution equations and applications Math. Control Relat. Fields (IF 1.284) Pub Date : 20161001
Jiongmin YongWellposedness is studied for a special system of twopoint boundary value problem for evolution equations which is called a forwardbackward evolution equation (FBEE, for short). Two approaches are introduced: A decoupling method with some brief discussions, and a method of continuation with some substantial discussions. For the latter, we have introduced Lyapunov operators for FBEEs, whose existence

Concentrating solitary waves for a class of singularly perturbed quasilinear Schrödinger equations with a general nonlinearity Math. Control Relat. Fields (IF 1.284) Pub Date : 20161001
Yi He, Gongbao LiWe are concerned with a class of singularly perturbed quasilinear Schrodinger equations of the following form: \[  {\varepsilon ^2}\Delta u  {\varepsilon ^2}\Delta ({u^2})u + V(x)u = h(u),{\text{ }}u > 0{\text{ in }}{\mathbb{R}^N}, \] where $\varepsilon $ is a small positive parameter, $N \ge 3$ and the nonlinearity $h$ is of critical growth. We construct a family of positive solutions ${u_\varepsilon

A sparse Markov chain approximation of LQtype stochastic control problems Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
Ralf Banisch, Carsten HartmannWe propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linearquadratic in the controls, but possibly nonlinear in the state variables, and the discretization is based on the fact that problems of this kind admit a dual formulation in terms of linear boundary value problems. We show that the discretized linear

Asymptotic stability of wave equations coupled by velocities Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
Yan Cui, Zhiqiang WangThis paper is devoted to study the asymptotic stability of wave equations with constant coefficients coupled by velocities. By using Riesz basis approach, multiplier method and frequency domain approach respectively, we find the sufficient and necessary condition, that the coefficients satisfy, leading to the exponential stability of the system. In addition, we give the optimal decay rate in one dimensional

Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
Michel Cristofol, Shumin Li, Eric SoccorsiWe consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove H{\"o}lder stability with the aid of a Carleman estimate specifically designed for hyperbolic waveguides.

An optimal meanreversion trading rule under a Markov chain model Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
Jingzhi Tie, Qing ZhangThis paper is concerned with a meanreversion trading rule. In contrast to most market models treated in the literature, the underlying market is solely determined by a twostate Markov chain. The major advantage of such Markov chain model is its striking simplicity and yet its capability of capturing various market movements. The purpose of this paper is to study an optimal trading rule under such

A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
Yanqing WangIn this paper, we present a numerical scheme to solve the initialboundary value problem for backward stochastic partial differential equations of parabolic type. Based on the Galerkin method, we approximate the original equation by a family of backward stochastic differential equations (BSDEs, for short), and then solve these BSDEs by the time discretization. Combining the truncation with respect

An optimal consumptioninvestment model with constraint on consumption Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
Zuo Quan Xu, Fahuai YiA continuoustime consumptioninvestment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a riskfree and a risky asset with logarithmic Brownian motion fluctuations. The consumption rate is subject to an upper bound constraint which linearly depends on the investor's wealth and bankruptcy is prohibited. The investor's

On the convergence of the SakawaShindo algorithm in stochastic control Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
J. Frédéric Bonnans, Justina Gianatti, Francisco J. SilvaWe analyze an algorithm for solving stochastic control problems, based on Pontryagin's maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of the cost functions as well as, in the convex case, the fact

Characterizations of integral inputtostate stability for bilinear systems in infinite dimensions Math. Control Relat. Fields (IF 1.284) Pub Date : 20160801
Andrii Mironchenko, Hiroshi ItoFor bilinear infinitedimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral inputtostate stability. We provide two proofs of this fact. One applies to general systems over Banach spaces. The other is restricted to Hilbert spaces, but is more constructive and results in an explicit form of iISS Lyapunov functions.