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Controllability problems for the heat equation on a half-axis with a bounded control in the Neumann boundary condition Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-08-13 Larissa Fardigola; Kateryna Khalina
In 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 $. A necessary and sufficient condition for controllability
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Optimal design problems governed by the nonlocal \begin{document}$ p $\end{document}-Laplacian equation Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-06-13 Fuensanta Andrés; Julio Muñoz; Jesús Rosado
In 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
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Error-based control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-06-13 Simone Fiori
The objective of the paper is to contribute to the theory of error-based 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
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On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-06-13 Lars Grüne; Roberto Guglielmi
The paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuous-time 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
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Fractional optimal control problems on a star graph: Optimality system and numerical solution Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-06-13 Vaibhav Mehandiratta; Mani Mehra; Günter Leugering
In 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
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Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-06-01 Jingrui Sun; Hanxiao Wang
This paper is concerned with mean-field stochastic linear-quadratic (MF-SLQ, for short) optimal control problems with deterministic coefficients. The notion of weak closed-loop optimal strategy is introduced. It is shown that the open-loop solvability is equivalent to the existence of a weak closed-loop optimal strategy. Moreover, when open-loop optimal controls exist, there is at least one of them
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Nonzero-sum differential game of backward doubly stochastic systems with delay and applications Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-06-01 Qingfeng Zhu; Yufeng Shi
This paper is concerned with a kind of nonzero-sum 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
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Finite-dimensional controllers for robust regulation of boundary control systems Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-06-01 Duy Phan; Lassi Paunonen
We 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 finite-dimensional reduced order controllers. The controller design is then used for particular PDE models: high-dimensional parabolic
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Linear-quadratic-Gaussian mean-field-game with partial observation and common noise Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-05-31 Alain Bensoussan; Xinwei Feng; Jianhui Huang
This paper considers a class of linear-quadratic-Gaussian (LQG) mean-field 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 common-noise due to the external factor and the state-average thus becomes a random process instead of a deterministic quantity. Second
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Optimal dividend policy in an insurance company with contagious arrivals of claims Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-03-22 Yiling Chen; Baojun Bian
In this paper we consider the optimal dividend problem for an insurance company whose surplus follows a classical Cramér-Lundberg process with a feature of self-exciting. 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 Hamilton-Jacobi-Bellman equation with
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Maximal discrete sparsity in parabolic optimal control with measures Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-03-22 Evelyn Herberg; Michael Hinze; Henrik Schumacher
We consider variational discretization [18] of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin 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
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Non-exponential discounting portfolio management with habit formation Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-03-22 Jingzhen Liu; Liyuan Lin; Ka Fai Cedric Yiu; Jiaqin Wei
This paper studies the portfolio management problem for an individual with a non-exponential 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 non-exponential discounting makes the optimal
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Time-inconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-03-22 Ishak Alia
In this paper, we investigate a class of time-inconsistent stochastic control problems for stochastic differential equations with deterministic coefficients. We study these problems within the game theoretic framework, and look for open-loop Nash equilibrium controls. Under suitable conditions, we derive a verification theorem for equilibrium controls via a flow of forward-backward stochastic partial
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On optimal \begin{document}$ L^1 $\end{document}-control in coefficients for quasi-linear Dirichlet boundary value problems with \begin{document}$ BMO $\end{document}-anisotropic \begin{document}$ p $\end{document}-Laplacian Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-03-22 Umberto De Maio; Peter I. Kogut; Gabriella Zecca
We study an optimal control problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principal part and $ L^1 $-control in coefficient of the low-order term. We assume that the matrix of anisotropy belongs to BMO-space. 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
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Stochastic impulse control Problem with state and time dependent cost functions Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-03-22 Brahim El Asri; Sehail Mazid
We consider stochastic impulse control problems when the impulses cost functions depend on $ t $ and $ x $. We use the approximation scheme and viscosity solutions approach to show that the value function is a unique viscosity solution for the associated Hamilton-Jacobi-Bellman equation (HJB) partial differential equation (PDE) of stochastic impulse control problems.
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Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems Math. Control Relat. Fields (IF 0.857) Pub Date : 2020-03-22 Nicolas Augier; Ugo Boscain; Mario Sigalotti
We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical intersections of eigenvalues. Then, through the use of normal forms, we study the problem of ensemble controllability between the eigenstates of a generic Hamiltonian
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Uniform indirect boundary controllability of semi-discrete \begin{document}$ 1 $\end{document}-\begin{document}$ d $\end{document} coupled wave equations Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Abdeladim El Akri; Lahcen Maniar
In this paper, we treat the problem of uniform exact boundary controllability for the finite-difference space semi-discretization 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
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The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Lassaad Aloui; Imen El Khal El Taief
We 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
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Asymptotic stabilization of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Ran Dong; Xuerong Mao
In 2013, Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback control based on discrete-time state observations. In recent years, this study has been further developed while using a constant observation interval. However, time-varying observation frequencies have not been discussed for this study. Particularly for non-autonomous periodic
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Implicit parametrizations and applications in optimization and control Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Dan Tiba
We 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
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Sparse optimal control for the heat equation with mixed control-state constraints Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Eduardo Casas; Fredi Tröltzsch
A problem of sparse optimal control for the heat equation is considered, where pointwise bounds on the control and mixed pointwise control-state 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
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Optimality conditions in variational form for non-linear constrained stochastic control problems Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Laurent Pfeiffer
Optimality 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
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State-constrained semilinear elliptic optimization problems with unrestricted sparse controls Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Eduardo Casas; Fredi Tröltzsch
In 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
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Optimal periodic control for scalar dynamics under integral constraint on the input Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Térence Bayen; Alain Rapaport; Fatima-Zahra Tani
This paper studies a periodic optimal control problem governed by a one-dimensional 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 so-called
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A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matrices Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Stéphane Gaubert; Nikolas Stott
We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive 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
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Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 El Mustapha Ait Ben Hassi; Mohamed Fadili; Lahcen Maniar
In 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.
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Lipschitz stability for some coupled degenerate parabolic systems with locally distributed observations of one component Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-27 Brahim Allal; Abdelkarim Hajjaj; Lahcen Maniar; Jawad Salhi
This 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
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Optimal control of the linear wave equation by time-depending BV-controls: A semi-smooth Newton approach Math. Control Relat. Fields (IF 0.857) Pub Date : 2019-12-23 Sebastian Engel; Karl Kunisch
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm 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
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