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Constructive exact control of semilinear 1D heat equations Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-26 Jérôme Lemoine, Arnaud Münch
The exact distributed controllability of the semilinear heat equation \begin{document}$ \partial_{t}y-\Delta y + g(y) = f \,1_{\omega} $\end{document} posed over multi-dimensional and bounded domains, assuming that \begin{document}$ g\in C^1(\mathbb{R}) $\end{document} satisfies the growth condition \begin{document}$ \limsup_{r\to \infty} g(r)/ (\vert r\vert \ln^{3/2}\vert r\vert) = 0 $\end{document}
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On the controllability of the BBM equation Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-25 Melek Jellouli
In this article, we consider the nonlinear BBM equation on the torus. We use controls taking values in a finite dimensional space to show that the equation is approximately controllable in \begin{document}$ H^1(\mathbb{T}) $\end{document}. We also show that the equation is not exactly controllable in \begin{document}$ H^s(\mathbb{T}) $\end{document} for \begin{document}$ s\in[1,2[ $\end{document}.
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Identifying a space-dependent source term in distributed order time-fractional diffusion equations Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Dinh Nguyen Duy Hai
The aim of this paper is to investigate an inverse problem of recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such a problem is ill-posed and has important practical applications. For this problem, we propose a general regularization method based on the idea of the filter method. With a suitable source condition, we prove
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Time-consistent lifetime portfolio selection under smooth ambiguity Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Luyang Yu,Liyuan Lin,Guohui Guan,Jingzhen Liu
This paper studies the optimal consumption, life insurance and investment problem for an income earner with uncertain lifetime under smooth ambiguity model. We assume that risky assets have unknown market prices that result in ambiguity. The individual forms his belief, that is, the distribution of market prices, according to available information. His ambiguity attitude, which is similar to the risk
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Lifespan estimates of solutions to quasilinear wave equations with damping and negative mass term Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Jie Yang,Sen Ming,Wei Han,Xiongmei Fan
The main goal of this work is to investigate formation of singularities for solutions to the quasilinear wave equations with damping terms, negative mass terms and divergence form nonlinearities in the critical and sub-critical cases. Upper bound lifespan estimates of solutions are derived by applying the rescaled test function method and iteration technique. The results are the same as corresponding
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Second-order problems involving time-dependent subdifferential operators and application to control Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Soumia Saïdi,Fatima Fennour
The paper provides a new result concerning the existence of solutions for second-order evolution problems associated with time-dependent subdifferential operators involving both single-valued and mixed semi-continuous set-valued perturbations. Optimal control problems corresponding to such differential inclusions using relaxation theorems with Young measures are investigated. The existence of solutions
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Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Shivam Dhama,Chetan D. Pahlajani
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency \begin{document}$ 1/\delta $\end{document} (\begin{document}$ 0 < \delta \ll 1 $\end{document}), together with small white noise perturbations of size \begin{document}$ \varepsilon $\end{document} (\begin{document}$ 0< \varepsilon \ll
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Averaged turnpike property for differential equations with random constant coefficients Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Martín Hernández,Rodrigo Lecaros,Sebastián Zamorano
This paper studies the integral turnpike and turnpike in average for a class of random ordinary differential equations. We prove that, under suitable assumptions on the matrices that define the system, the optimal solutions for an optimal distributed control tracking problem remain, in an averaged sense, sufficiently close to the associated random stationary optimal solution for the majority of the
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Dynamical estimation of a noisy input in a system with a Caputo fractional derivative. The case of continuous measurements of a part of phase coordinates Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Platon Surkov
The problem of estimating (reconstructing) an unknown input for a system of nonlinear differential equations with the Caputo fractional derivative is considered. Information on the position of the system is available for observations and only a part of system's parameters can be measured. The case of measuring all phase coordinates is also presented. The measurements are continuous and the data obtained
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Boundary control for transport equations Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Guillaume Bal,Alexandre Jollivet
This paper considers two types of boundary control problems for linear transport equations. The first one shows that transport solutions on a subdomain of a domain \begin{document}$ X $\end{document} can be controlled exactly from incoming boundary conditions for \begin{document}$ X $\end{document} under appropriate convexity assumptions. This is in contrast with the only approximate control one typically
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Variational discretization of one-dimensional elliptic optimal control problems with BV functions based on the mixed formulation Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Evelyn Herberg,Michael Hinze
We consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for the state and the BV-seminorm of the control. We use the mixed formulation for the state equation together with the variational discretization approach, where we use the classical lowest order Raviart-Thomas finite elements
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Existence and cost of boundary controls for a degenerate/singular parabolic equation Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 U. Biccari,V. Hernández-Santamaría,J. Vancostenoble
In this paper, we consider the following degenerate/singular parabolic equation \begin{document}$ \begin{align*} u_t -(x^\alpha u_{x})_x - \frac{\mu}{x^{2-\alpha}} u = 0, \qquad x\in (0,1), \ t \in (0,T), \end{align*} $\end{document} where \begin{document}$ 0\leq \alpha <1 $\end{document} and \begin{document}$ \mu\leq (1-\alpha)^2/4 $\end{document} are two real parameters. We prove the boundary null
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Solvable approximations of 3-dimensional almost-Riemannian structures Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Philippe Jouan,Ronald Manríquez
In some cases, the nilpotent approximation of an almost-Riemannian structure can degenerate into a constant rank sub-Riemannian one. In those cases, the nilpotent approximation can be replaced by a solvable one that turns out to be a linear ARS on a nilpotent Lie group or a homogeneous space. The distance defined by the solvable approximation is analyzed in the 3D-generic cases. It is shown that it
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Feedback stabilization of parabolic systems with input delay Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Imene Aicha Djebour,Takéo Takahashi,Julie Valein
This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in the case of stabilization without delay. The proof consists in splitting the system into a finite dimensional unstable part and a stable infinite-dimensional part
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A semigroup approach to stochastic systems with input delay at the boundary Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 S. Hadd,F.Z. Lahbiri
This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces and a semigroup approach to reformulate such delay systems into free-delay distributed stochastic systems with unbounded control and observation operators. This gives us the opportunity to use the concept of admissible control and observation
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Uniqueness for inverse problem of determining fractional orders for time-fractional advection-diffusion equations Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Masahiro Yamamoto
We consider initial boundary value problems of time-fractional advection-diffusion equations with the zero Dirichlet boundary value \begin{document}$ \partial_t^{\alpha} u(x, t) = -Au(x, t) $\end{document}, where \begin{document}$ -A = \sum_{i, j = 1}^d \partial_i(a_{ij}(x) \partial_j) + \sum_{j = 1}^d b_j(x) \partial_j + c(x) $\end{document}. We establish the uniqueness for an inverse problem of determining
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A geometric approach of gradient descent algorithms in linear neural networks Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Yacine Chitour,Zhenyu Liao,Romain Couillet
In this paper, we propose a geometric framework to analyze the convergence properties of gradient descent trajectories in the context of linear neural networks. We translate a well-known empirical observation of linear neural nets into a conjecture that we call the overfitting conjecture which states that, for almost all training data and initial conditions, the trajectory of the corresponding gradient
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Analysis of exponential stabilization for Rao-Nakra sandwich beam with time-varying weight and time-varying delay: Multiplier method versus observability Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Baowei Feng,Carlos Alberto Raposo,Carlos Alberto Nonato,Abdelaziz Soufyane
In this paper, we study the global well-posedness and exponential stability for a Rao-Nakra sandwich beam equation with time-varying weight and time-varying delay. The system consists of one Euler-Bernoulli beam equation for the transversal displacement, and two wave equations for the longitudinal displacements of the top and bottom layers. By using the semigroup theory, we show that the system is
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Optimal control of a global model of climate change with adaptation and mitigation Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Manoj Atolia,Prakash Loungani,Helmut Maurer,Willi Semmler
The economy-climate interaction and an appropriate mitigation policy for climate protection have been treated in various types of scientific modeling. Here, we specifically focus on the seminal work by Nordhaus [14, 15] on the economy-climate link. We extend the Nordhaus type model to include optimal policies for mitigation, adaptation and infrastructure investment studying the dynamics of the transition
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A differential game control problem with state constraints Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Nidhal Gammoudi,Hasnaa Zidani
We study the Hamilton-Jacobi (HJ) approach for a two-person zero-sum differential game with state constraints and where controls of the two players are coupled within the dynamics, the state constraints and the cost functions. It is known for such problems that the value function may be discontinuous and its characterization by means of an HJ equation requires some controllability assumptions involving
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The discretized backstepping method: An application to a general system of $ 2\times 2 $ linear balance laws Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Mathias Dus
In this paper, we introduce the numerical backstepping method by applying it to a problem of finite-time stabilization for a system of \begin{document}$ 2 \times 2 $\end{document} balance laws discretized thanks to the upwind scheme. On the one hand, we illustrate on an example that the scheme used to compute the feedback control cannot be chosen arbitrarily. On the other hand, an algorithm is given
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Local well-posedness for a class of 1D Boussinesq systems Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Alex M. Montes,Ricardo Córdoba
In this paper we study the local well-posedness for the Cauchy problem associated with a special class of one-dimensional Boussinesq systems that model the evolution of long water waves with small amplitude in the presence of surface tension.
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Optimal control problems of parabolic fractional Sturm-Liouville equations in a star graph Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Günter Leugering,Gisèle Mophou,Maryse Moutamal,Mahamadi Warma
In the present paper we deal with parabolic fractional initial-boundary value problems of Sturm–Liouville type in an interval and in a general star graph. We first give several existence, uniqueness and regularity results of weak and very-weak solutions. We prove the existence and uniqueness of solutions to a quadratic boundary optimal control problem and provide a characterization of the optimal contol
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A general maximum principle for partially observed mean-field stochastic system with random jumps in progressive structure Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Tian Chen,Zhen Wu
We study the progressive optimal control for partially observed stochastic system of mean-field type with random jumps. The cost function and the observation are also of mean-field type. The control is allowed to enter the diffusion, jump coefficient and the observation. The control domain need not be convex. We obtain the maximum principle for the partially observable progressive optimal control by
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Theoretical and computational decay results for a memory type wave equation with variable-exponent nonlinearity Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Adel M. Al-Mahdi,Mohammad M. Al-Gharabli,Mostafa Zahri
In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally
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Stability and instability of standing waves for Gross-Pitaevskii equations with double power nonlinearities Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Yue Zhang,Jian Zhang
In this paper, we investigate Gross-Pitaevskii equations with double power nonlinearities. Firstly, due to the defocusing effect from the lower power order nonlinearity, Gross-Pitaevskii equations still have standing waves when the frequency \begin{document}$ \omega $\end{document} is the negative of the first eigenvalue of the linear operator \begin{document}$ - \Delta + \gamma|x{|^2} $\end{document}
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Carleman estimates for a magnetohydrodynamics system and application to inverse source problems Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Xinchi Huang,Masahiro Yamamoto
In this article, we consider a linearized magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. We first prove two kinds of Carleman estimates. This is done by combining the Carleman estimates for the parabolic and the elliptic equations. Then we apply the Carleman estimates to prove Hölder type stability results for some inverse source problems.
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Controllability under positive constraints for quasilinear parabolic PDEs Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Miguel R. Nuñez-Chávez
This paper deals with the analysis of the internal controllability with constraint of positive kind of a quasilinear parabolic PDE. We prove two results about this PDE: First, we prove a global steady state constrained controllability result. For this purpose, we employ the called "stair-case method". And second, we prove a global trajectory constrained controllability result. For this purpose, we
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Optimal investment and reinsurance of insurers with lognormal stochastic factor model Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Hiroaki Hata,Li-Hsien Sun
We propose the stochastic factor model of optimal investment and reinsurance of insurers where the wealth processes are described by a bank account and a risk asset for investment and a Cramér-Lundberg process for reinsurance. The optimization is obtained through maximizing the exponential utility. Owing to the claims driven by a Poisson process, the proposed optimization problem is naturally treated
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Optimal control of perfect plasticity part I: Stress tracking Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Christian Meyer,Stephan Walther
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of the boundary. The control thus enters the system in the Dirichlet boundary conditions. Therefore, the safe load condition is automatically fulfilled so that the system
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Local Kalman rank condition for linear time varying systems Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Hamid Maarouf
In this paper, we study some non-negative integers related to a linear time varying system and to some Krylov sub-spaces associated to this system. Such integers are similar to the controllability indices and have been used in the literature to derive results on the controllability of linear systems. The purpose of this paper goes in the same direction by studying the local behavior of these integers
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Maximum principle for discrete-time stochastic optimal control problem and stochastic game Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Zhen Wu,Feng Zhang
This paper is first concerned with one kind of discrete-time stochastic optimal control problem with convex control domains, for which necessary condition in the form of Pontryagin's maximum principle and sufficient condition of optimality are derived. The results are then extended to two kinds of discrete-time stochastic games. Two illustrative examples are studied, for which the explicit optimal
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Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Jun Moon
In this paper, we consider linear-quadratic (LQ) leader-follower Stackelberg differential games for mean-field type stochastic systems with jump diffusions, where the system includes mean-field variables, i.e., the expected value of state and control variables. We first solve the LQ mean-field type control problem of the follower using the stochastic maximum principle and obtain the state-feedback
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A nonzero-sum risk-sensitive stochastic differential game in the orthant Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Mrinal K. Ghosh,Somnath Pradhan
We study a nonzero-sum risk-sensitive stochastic differential game for controlled reflecting diffusion processes in the nonnegative orthant. We treat two cost evaluation criteria, namely, discounted cost and ergodic cost. Under certain assumptions, we establish the existence of Nash equilibria. Also, we completely characterize a Nash equilibrium for the ergodic cost criterion in the space of stationary
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On the nonuniqueness and instability of solutions of tracking-type optimal control problems Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Constantin Christof,Dominik Hafemeyer
We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state \begin{document}$ y_d $\end{document}, and a desired control \begin{document}$ u_d $\end{document}. It is proved that such problems are always nonuniquely solvable for certain choices of the tuple \begin{document}$ (y_d, u_d) $\end{document} and instable in the
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Optimal control of parameterized stationary Maxwell's system: Reduced basis, convergence analysis, and a posteriori error estimates Math. Control Relat. Fields (IF 1.2) Pub Date : 2022-01-01 Quyen Tran,Harbir Antil,Hugo Díaz
We consider an optimal control problem governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter set is assumed to be compact. We discretize the electric field by a finite element method and use variational discretization concept for the control. We present a reduced basis method
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Stability and asymptotic properties of dissipative evolution equations coupled with ordinary differential equations Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-12-17 Serge Nicaise
In this paper, we obtain some stability results of systems corresponding to the coupling between a dissipative evolution equation (set in an infinite dimensional space) and an ordinary differential equation. Many problems from physics enter in this framework, let us mention dispersive medium models, generalized telegraph equations, Volterra integro-differential equations, and cascades of ODE-hyperbolic
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Piezoelectric beams with magnetic effect and localized damping Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-12-17 Mounir Afilal, Abdelaziz Soufyane, Mauro de Lima Santos
In this work we are considering a one-dimensional dissipative system of piezoelectric beams with magnetic effect and localized damping. We prove that the system is exponential stable using a damping mechanism acting only on one component and on a small part of the beam.
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Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-12-17 Mohammad Akil, Ibtissam Issa, Ali Wehbe
In this paper, we investigate the energy decay of hyperbolic systems of wave-wave, wave-Euler-Bernoulli beam and beam-beam types. The two equations are coupled through boundary connection with only one localized non-smooth fractional Kelvin-Voigt damping. First, we reformulate each system into an augmented model and using a general criteria of Arendt-Batty, we prove that our models are strongly stable
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Eigenvalues of stochastic Hamiltonian systems with boundary conditions and its application Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-12-17 Guangdong Jing, Penghui Wang
In this paper we solve the eigenvalue problem of stochastic Hamiltonian system with boundary conditions. Firstly, we extend the results in Peng [12] from time-invariant case to time-dependent case, proving the existence of a series of eigenvalues \begin{document}$ \{\lambda_m\} $\end{document} and construct corresponding eigenfunctions. Moreover, the order of growth for these \begin{document}$ \{\lambda_m\}
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General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-12-17 Mengxian Lv, Jianghao Hao
In this paper we consider a system of viscoelastic wave equations of Kirchhoff type with dynamic boundary conditions. Supposing the relaxation functions \begin{document}$ g_i $\end{document} \begin{document}$ (i = 1, 2, \cdots, l) $\end{document} satisfy \begin{document}$ g_i(t)\leq-\xi_i(t)G(g_i(t)) $\end{document} where \begin{document}$ G $\end{document} is an increasing and convex function near
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Open-loop equilibriums for a general class of time-inconsistent stochastic optimal control problems Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-11-01 Ishak Alia
This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward stochastic differential equations with jumps (FBSDEJs, for short), we derive two systems of integro-partial differential equations (IPDEs, for short). Then, we rigorously
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Commutative properties for conservative space-time DG discretizations of optimal control problems involving the viscous Burgers equation Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-11-01 Xenia Kerkhoff, Sandra May
We consider one-dimensional distributed optimal control problems with the state equation being given by the viscous Burgers equation. We discretize using a space-time discontinuous Galerkin approach. We use upwind flux in time and the symmetric interior penalty approach for discretizing the viscous term. Our focus is on the discretization of the convection terms. We aim for using conservative discretizations
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Null controllability of a nonlinear age, space and two-sex structured population dynamics model Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-10-14 Yacouba Simporé, Oumar Traoré
In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males and females and we are dealing with two cases of null controllability problems. The first problem is related to the total extinction, which means that, we estimate
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Existence and uniqueness for variational data assimilation in continuous time Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-10-11 Jochen Bröcker
A variant of the optimal control problem is considered which is nonstandard in that the performance index contains "stochastic" integrals, that is, integrals against very irregular functions. The motivation for considering such performance indices comes from dynamical estimation problems where observed time series need to be "fitted" with trajectories of dynamical models. The observations may be contaminated
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Controllability to rest of the Gurtin-Pipkin model Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-10-11 Xiuxiang Zhou, Shu Luan
This paper is devoted to analyzing the controllability to rest of the Gurtin-Pipkin model, which is a class of differential equations with memory terms. The goal is not only to derive the state to vanish at some time but also to require the memory term to vanish at the same time, ensuring that the controlled system is controllable to rest. In order to get rid of the influence of memory, the controllability
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Continuity with respect to the speed for optimal ship forms based on Michell's formula Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-10-11 Julien Dambrine, Morgan Pierre
We consider a ship hull design problem based on Michell's wave resistance. The half hull is represented by a nonnegative function and we seek the function whose domain of definition has a given area and which minimizes the total resistance for a given speed and a given volume. We show that the optimal hull depends only on two parameters without dimension, the viscous drag coefficient and the Froude
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Parameter learning and fractional differential operators: Applications in regularized image denoising and decomposition problems Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-14 Sören Bartels, Nico Weber
In this paper, we focus on learning optimal parameters for PDE-based image denoising and decomposition models. First, we learn the regularization parameter and the differential operator for gray-scale image denoising using the fractional Laplacian in combination with a bilevel optimization problem. In our setting the fractional Laplacian allows the use of Fourier transform, which enables the optimization
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Linear-Quadratic-Gaussian mean-field controls of social optima Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-14 Zhenghong Qiu, Jianhui Huang, Tinghan Xie
This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be indefinite in cost functional. This setup is innovative
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Optimal control of transverse vibration of a moving string with time-varying lengths Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Bing Sun
In this article, we are concerned with optimal control for the transverse vibration of a moving string with time-varying lengths. In the fixed final time horizon case, the Pontryagin maximum principle is established for the investigational system with a moving boundary, owing to the Dubovitskii and Milyutin functional analytical approach. A remark then follows for discussing the utilization of obtained
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Computation of open-loop inputs for uniformly ensemble controllable systems Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Michael Schönlein
This paper presents computational methods for families of linear systems depending on a parameter. Such a family is called ensemble controllable if for any family of parameter-dependent target states and any neighborhood of it there is a parameter-independent input steering the origin into the neighborhood. Assuming that a family of systems is ensemble controllable we present methods to construct suitable
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Asymptotic gain results for attractors of semilinear systems Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Jochen Schmid, Oleksiy Kapustyan, Sergey Dashkovskiy
We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee–Infante equations, for example.
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A nonlinear version of Halanay's inequality for the uniform convergence to the origin Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Pierdomenico Pepe
A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and
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Convergence of coprime factor perturbations for robust stabilization of Oseen systems Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Jan Heiland
Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional system has to be linearized and discretized. The unavoidable consistency errors add a small but critical uncertainty to the controller model which will likely make it fail, especially when an observer is involved. Standard
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Stable invariant manifolds with application to control problems Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Alexey Gorshkov
In this article we develop the theory of stable invariant manifolds for evolution equations with application to control problem. We will construct invariant subspaces for linear equations which can be extended to the non-linear equations in the neighbourhood of the equilibrium with help of perturbation theory. Here will be considered both cases of the discrete and continuous spectrum of the generator
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A tracking problem for the state of charge in a electrochemical Li-ion battery model Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Esteban Hernández, Christophe Prieur, Eduardo Cerpa
In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has
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On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-09-08 Julie Valein
The aim of this work is to study the asymptotic stability of the nonlinear Korteweg-de Vries equation in the presence of a delayed term in the internal feedback. We first consider the case where the weight of the term with delay is smaller than the weight of the term without delay and we prove a semiglobal stability result for any lengths. Secondly we study the case where the support of the term without
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Local null controllability of the penalized Boussinesq system with a reduced number of controls Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-07-26 Jon Asier Bárcena-Petisco, Kévin Le Balc'h
In this paper we consider the Boussinesq system with homogeneous Dirichlet boundary conditions, defined in a regular domain \begin{document}$ \Omega\subset\mathbb R^N $\end{document} for \begin{document}$ N = 2 $\end{document} and \begin{document}$ N = 3 $\end{document}. The incompressibility condition of the fluid is replaced by its approximation by penalization with a small parameter \begin{document}$
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Numerical analysis and simulations of a frictional contact problem with damage and memory Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-07-13 Hailing Xuan, Xiaoliang Cheng
In this paper, we study a frictional contact model which takes into account the damage and the memory. The deformable body consists of a viscoelastic material and the process is assumed to be quasistatic. The mechanical damage of the material which caused by the tension or the compression is included in the constitutive law and the damage function is modelled by a nonlinear parabolic inclusion. Then
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Cross-constrained variational method and nonlinear Schrödinger equation with partial confinement Math. Control Relat. Fields (IF 1.2) Pub Date : 2021-07-13 Chenglin Wang, Jian Zhang
In this paper, we study the nonlinear Schrödinger equation with a partial confinement. By applying the cross-constrained variational arguments and invariant manifolds of the evolution flow, the sharp condition for global existence and blowup of the solution is derived.