Thematische Bibliographien / Optimal control problems involving partial differential equations

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Auswahl der wissenschaftlichen Literatur zum Thema „Optimal control problems involving partial differential equations“

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Veröffentlicht am 17. September 2021

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Zeitschriftenartikel zum Thema "Optimal control problems involving partial differential equations"

Wong, Kar Hung. „On the computational algorithms for time-lag optimal control problems“. Bulletin of the Australian Mathematical Society 32, Nr. 2 (Oktober 1985): 309–11. http://dx.doi.org/10.1017/s0004972700009989.

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In this thesis we study the following two types of hereditary optimal control problems: (i) problems governed by systems of ordinary differential equations with discrete time-delayed arguments appearing in both the state and the control variables; (ii) problems governed by parabolic partial differential equations with Neumann boundary conditions involving time-delays.

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Rehbock, V., S. Wang und K. L. Teo. „Computing optimal control With a hyperbolic partial differential equation“. Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, Nr. 2 (Oktober 1998): 266–87. http://dx.doi.org/10.1017/s0334270000012510.

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AbstractWe present a method for solving a class of optimal control problems involving hyperbolic partial differential equations. A numerical integration method for the solution of a general linear second-order hyperbolic partial differential equation representing the type of dynamics under consideration is given. The method, based on the piecewise bilinear finite element approximation on a rectangular mesh, is explicit. The optimal control problem is thus discretized and reduced to an ordinary optimization problem. Fast automatic differentiation is applied to calculate the exact gradient of the discretized problem so that existing optimization algorithms may be applied. Various types of constraints may be imposed on the problem. A practical application arising from the process of gas absorption is solved using the proposed method.

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Beyko, Ivan, Olesya Furtel und Julia Spivak. „Generalized solutions of optimal control problems“. System research and information technologies, Nr. 4 (29.12.2020): 104–14. http://dx.doi.org/10.20535/srit.2308-8893.2020.4.08.

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The problems of optimal control of systems of algebraic-integro-differential equations and partial differential equations are considered, which describe controlled processes with concentrated and distributed parameters. Generalized optimal solutions that exist for a wide range of optimal control applications are identified. Methods for constructing approximate generalized solutions are considered.

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de Pinho, M. do R., und R. B. Vinter. „Necessary Conditions for Optimal Control Problems Involving Nonlinear Differential Algebraic Equations“. Journal of Mathematical Analysis and Applications 212, Nr. 2 (August 1997): 493–516. http://dx.doi.org/10.1006/jmaa.1997.5523.

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Wong, K. H., und N. Lock. „Optimal control of a chemical reactor“. Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, Nr. 1 (Juli 1997): 61–76. http://dx.doi.org/10.1017/s0334270000009218.

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AbstractA chemical reactor problem is considered governed by partial differential equations. We wish to control the input temperature and the input oxygen concentration so that the actual output temperature can be as close to the desired output temperature as possible. By linearizing the differential equations around a nominal equation and then applying a finite-element Galerkin Scheme to the resulting system, the original problem can be converted into a sequence of linearly-constrained quadratic programming problems.

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Khurshudyan, Asatur Zh. „On optimal boundary and distributed control of partial integro–differential equations“. Archives of Control Sciences 24, Nr. 1 (01.03.2014): 5–25. http://dx.doi.org/10.2478/acsc-2014-0001.

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Abstract A method of optimal control problems investigation for linear partial integro-differential equations of convolution type is proposed, when control process is carried out by boundary functions and right hand side of equation. Using Fourier real generalized integral transform control problem solution is reduced to minimization procedure of chosen optimality criterion under constraints of equality type on desired control function. Optimality of control impacts is obtained for two criteria, evaluating their linear momentum and total energy. Necessary and sufficient conditions of control problem solvability are obtained for both criteria. Numerical calculations are done and control functions are plotted for both cases of control process realization.

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Plekhanova, Marina, und Guzel Baybulatova. „Multi-Term Fractional Degenerate Evolution Equations and Optimal Control Problems“. Mathematics 8, Nr. 4 (01.04.2020): 483. http://dx.doi.org/10.3390/math8040483.

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A theorem on unique solvability in the sense of the strong solutions is proved for a class of degenerate multi-term fractional equations in Banach spaces. It applies to the deriving of the conditions on unique solution existence for an optimal control problem to the corresponding equation. Obtained results are used to an optimal control problem study for a model system which is described by an initial-boundary value problem for a partial differential equation.

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Nagase, Noriaki. „On the existence of optimal control for controlled stochastic partial differential equations“. Nagoya Mathematical Journal 115 (September 1989): 73–85. http://dx.doi.org/10.1017/s0027763000001549.

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In this paper we are concerned with stochastic control problems of the following kind. Let Y(t) be a d’-dimensional Brownian motion defined on a probability space (Ω, F, Ft, P) and u(t) an admissible control. We consider the Cauchy problem of stochastic partial differential equations (SPDE in short)where L(y, u) is the 2nd order elliptic differential operator and M(y) the 1st order differential operator.

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Pörner, Frank, und Daniel Wachsmuth. „Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations“. Mathematical Control & Related Fields 8, Nr. 1 (2018): 315–35. http://dx.doi.org/10.3934/mcrf.2018013.

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Alia, Ishak. „Time-inconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach“. Mathematical Control & Related Fields 10, Nr. 4 (2020): 785–826. http://dx.doi.org/10.3934/mcrf.2020020.

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Dissertationen zum Thema "Optimal control problems involving partial differential equations"

Tsang, Siu Chung. „Preconditioners for linear parabolic optimal control problems“. HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/464.

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In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and All-time problems. Our major contribution in this research is that we developed a preconditioner for each kind of problems, so our iterative method is accelerated. In chapter 1, we gave a brief introduction to our problems with a literature review. In chapter 2, we demonstrated how to derive the first-order optimality conditions from the parabolic optimal control problems. Afterwards, we showed how to use the shooting method along with the flexible generalized minimal residual to find the solution. In chapter 3, we offered three preconditioners to enhance our shooting method for the problems with symmetric differential operator. Next, in chapter 4, we proposed another three preconditioners to speed up our scheme for the problems with non-symmetric differential operator. Lastly, we have the conclusion and the future development in chapter 5.

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Yousept, Irwin. „Optimal control of partial differential equations involving pointwise state constraints: regularization and applications“. Göttingen Cuvillier, 2008. http://d-nb.info/990426513/04.

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Flaig, Thomas G. [Verfasser]. „Discretization strategies for optimal control problems with parabolic partial differential equations / Thomas G. Flaig“. München : Verlag Dr. Hut, 2013. http://d-nb.info/103729176X/34.

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Trautwein, Christoph [Verfasser], und Peter [Gutachter] Benner. „Optimal control problems constrained by stochastic partial differential equations / Christoph Trautwein ; Gutachter: Peter Benner“. Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2019. http://d-nb.info/1220034959/34.

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Lee, Jangwoon. „Analysis and finite element approximations of stochastic optimal control problems constrained by stochastic elliptic partial differential equations“. [Ames, Iowa : Iowa State University], 2008.

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Qi, Meiyu [Verfasser], und Ronald H. W. [Akademischer Betreuer] Hoppe. „Adaptive Mixed Finite Element Approximations of Distributed Optimal Control Problems for Elliptic Partial Differential Equations / Meiyu Qi. Betreuer: Ronald H. W. Hoppe“. Augsburg : Universität Augsburg, 2012. http://d-nb.info/1077700849/34.

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Pearson, John W. „Fast iterative solvers for PDE-constrained optimization problems“. Thesis, University of Oxford, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405.

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In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we exploit saddle point theory, as this is the form of the matrix systems we wish to solve. We utilize well-known results on saddle point systems to motivate preconditioners based on effective approximations of the (1,1)-block and Schur complement of the matrices involved. These preconditioners are used in conjunction with suitable iterative solvers, which include MINRES, non-standard Conjugate Gradients, GMRES and BiCG. The solvers we use are selected based on the particular problem and preconditioning strategy employed. We consider the numerical solution of a range of PDE-constrained optimization problems, namely the distributed control, Neumann boundary control and subdomain control of Poisson's equation, convection-diffusion control, Stokes and Navier-Stokes control, the optimal control of the heat equation, and the optimal control of reaction-diffusion problems arising in chemical processes. Each of these problems has a special structure which we make use of when developing our preconditioners, and specific techniques and approximations are required for each problem. In each case, we motivate and derive our preconditioners, obtain eigenvalue bounds for the preconditioners where relevant, and demonstrate the effectiveness of our strategies through numerical experiments. The goal throughout this work is for our iterative solvers to be feasible and reliable, but also robust with respect to the parameters involved in the problems we consider.

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Bénézet, Cyril. „Study of numerical methods for partial hedging and switching problems with costs uncertainty“. Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7079.

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Nous apportons dans cette thèse quelques contributions à l’étude théorique et numérique de certains problèmes de contrôle stochastique, ainsi que leurs applications aux mathématiques financières et à la gestion des risques financiers. Ces applications portent sur des problématiques de valorisation et de couverture faibles de produits financiers, ainsi que sur des problématiques réglementaires. Nous proposons des méthodes numériques afin de calculer efficacement ces quantités pour lesquelles il n’existe pas de formule explicite. Enfin, nous étudions les équations différentielles stochastiques rétrogrades liées à de nouveaux problèmes de switching, avec incertitude sur les coûts
In this thesis, we give some contributions to the theoretical and numerical study to some stochastic optimal control problems, and their applications to financial mathematics and risk management. These applications are related to weak pricing and hedging of financial products and to regulation issues. We develop numerical methods in order to compute efficiently these quantities, when no closed formulae are available. We also study backward stochastic differential equations linked to some new switching problems, with costs uncertainty

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Flaig, Thomas Gerhard [Verfasser], Thomas [Akademischer Betreuer] Apel, Fredi [Akademischer Betreuer] Tröltzsch und Boris [Akademischer Betreuer] Vexler. „Discretization strategies for optimal control problems with parabolic partial differential equations / Thomas Gerhard Flaig. Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften. Gutachter: Thomas Apel ; Fredi Tröltzsch ; Boris Vexler. Betreuer: Thomas Apel“. Neubiberg : Universitätsbibliothek der Universität der Bundeswehr, 2013. http://d-nb.info/1037118820/34.

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Flaig, Thomas G. [Verfasser], Thomas [Akademischer Betreuer] Apel, Fredi [Akademischer Betreuer] Tröltzsch und Boris [Akademischer Betreuer] Vexler. „Discretization strategies for optimal control problems with parabolic partial differential equations / Thomas Gerhard Flaig. Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften. Gutachter: Thomas Apel ; Fredi Tröltzsch ; Boris Vexler. Betreuer: Thomas Apel“. Neubiberg : Universitätsbibliothek der Universität der Bundeswehr, 2013. http://d-nb.info/1037118820/34.

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Bücher zum Thema "Optimal control problems involving partial differential equations"

Kogut, Peter I., und Günter R. Leugering. Optimal Control Problems for Partial Differential Equations on Reticulated Domains. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8149-4.

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Kogut, Peter I. Optimal control problems for partial differential equations on reticulated domains: Approximation and asymptotic analysis. New York: Birkhäuser, 2011.

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1952-, Kunisch K. (Karl), und SpringerLink (Online service), Hrsg. Optimal control of coupled systems of partial differential equations. Basel, Switzerland: Birkhäuser Verlag, 2009.

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service), SpringerLink (Online, Hrsg. Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE. New York, NY: Springer New York, 2013.

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Infinite dimensional linear control systems: The time optimal and norm optimal problems. Amsterdam: Elsevier, 2005.

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Variational and optimal control problems on unbounded domains: A workshop in memory of Arie Leizarowitz, January 9-12, 2012, Technion, Haifa, Israel. Providence, Rhode Island: American Mathematical Society, 2014.

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1943-, Gossez J. P., und Bonheure Denis, Hrsg. Nonlinear elliptic partial differential equations: Workshop in celebration of Jean-Pierre Gossez's 65th birthday, September 2-4, 2009, Université libre de Bruxelles, Belgium. Providence, R.I: American Mathematical Society, 2011.

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Harmonic maps and differential geometry: A harmonic map fest in honour of John C. Wood's 60th birthday, September 7-10, 2009, Cagliari, Italy. Providence, R.I: American Mathematical Society, 2011.

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1966-, Pérez Joaquín, und Galvez José A. 1972-, Hrsg. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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P, Minicozzi William, Hrsg. A course in minimal surfaces. Providence, R.I: American Mathematical Society, 2011.

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Buchteile zum Thema "Optimal control problems involving partial differential equations"

Quarteroni, Alfio. „Optimal control of partial differential equations“. In Numerical Models for Differential Problems, 483–525. Milano: Springer Milan, 2014. http://dx.doi.org/10.1007/978-88-470-5522-3_17.

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Quarteroni, Alfio. „Optimal control of partial differential equations“. In Numerical Models for Differential Problems, 511–53. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49316-9_18.

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Cagnol, John, und Jean-Paul Zolésio. „Shape Control in Hyperbolic Problems“. In Optimal Control of Partial Differential Equations, 77–88. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8691-8_7.

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Tröltzsch, Fredi. „Linear-quadratic elliptic control problems“. In Optimal Control of Partial Differential Equations, 21–118. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/gsm/112/02.

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Tröltzsch, Fredi. „Linear-quadratic parabolic control problems“. In Optimal Control of Partial Differential Equations, 119–79. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/gsm/112/03.

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Puel, Jean-Pierre. „Some results on optimal control for unilateral problems“. In Control of Partial Differential Equations, 225–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0002596.

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Tröltzsch, Fredi. „Optimization problems in Banach spaces“. In Optimal Control of Partial Differential Equations, 323–53. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/gsm/112/06.

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Díaz, J. I., und J. L. Lions. „On the Approximate Controllability for some Explosive Parabolic Problems“. In Optimal Control of Partial Differential Equations, 115–32. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8691-8_10.

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Avdonin, Sergei A., Sergei A. Ivanov und David L. Russell. „Exponential Bases in Sobolev Spaces in Control and Observation Problems“. In Optimal Control of Partial Differential Equations, 33–42. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8691-8_3.

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Avdonin, Sergei, und William Moran. „Sampling and Interpolation of Functions with Multi-Band Spectra and Controllability Problems“. In Optimal Control of Partial Differential Equations, 43–51. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8691-8_4.

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Konferenzberichte zum Thema "Optimal control problems involving partial differential equations"

Jiang, Canghua, Kun Xie, Zhiqiang Guo und Kok Lay Teo. „Implicit integration with adjoint sensitivity propagation for optimal control problems involving differential-algebraic equations“. In 2017 36th Chinese Control Conference (CCC). IEEE, 2017. http://dx.doi.org/10.23919/chicc.2017.8027734.

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Pesch, Hans Josef, Simon Bechmann und Jan-Eric Wurst. „Bang-bang and singular controls in optimal control problems with partial differential equations“. In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6426979.

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Shanshan, Zuo, und Min Hui. „Optimal control problems of mean-field forward-backward stochastic differential equations with partial information“. In 2013 25th Chinese Control and Decision Conference (CCDC). IEEE, 2013. http://dx.doi.org/10.1109/ccdc.2013.6561841.

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Chaturvedi, Nalin A., Jake F. Christensen, Reinhardt Klein und Aleksandar Kojic. „Approximations for Partial Differential Equations Appearing in Li-Ion Battery Models“. In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4072.

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Li-ion based batteries are believed to be the most promising battery system for HEV/PHEV/EV applications due to their high energy density, lack of hysteresis and low self-discharge currents. However, designing a battery, along with its Battery Management System (BMS), that can guarantee safe and reliable operation, is a challenge since aging and other mechanisms involving optimal charge and discharge of the battery are not sufficiently well understood. In a previous article [1], we presented a model that has been studied in [2]–[5] to understand the operation of a Li-ion battery. In this article, we continue our work and present an approximation technique that can be applied to a generic battery model. These approximation method is based on projecting solutions to a Hilbert subspace formed by taking the span of an countably infinite set of basis functions. In this article, we apply this method to the key diffusion equation in the battery model, thus providing a fast approximation for the single particle model (SPM) for both variable and constant diffusion case.

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Fabien, Brian C. „A Simple Continuation Method for the Solution of Optimal Control Problems With State Variable Inequality Constraints“. In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13617.

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This paper develops a simple continuation method for the approximate solution of optimal control problems with pure state variable inequality constraints. The method is based on transforming the inequality constraints into equality constraints using nonnegative slack variables. The resultant equality constraints are satisfied approximately using a quadratic loss penalty function. The solution of the original problem is obtained by solving the transformed problem with a sequence of penalty weights that tends to zero. The penalty weight is treated as the continuation parameter. The necessary conditions for a minimum are written as a boundary value problem involving index-1 differential-algebraic equations (BVP-DAE). The BVP-DAE include the complementarity conditions associated with the inequality constraints. The paper shows that the necessary conditions for optimality of the original problem and the transformed problems are remarkably similar. In particular, the BVP-DAE for each problem differ by a linear term related to the Lagrange multipliers associated with the state variable inequality constraints. Numerical examples are presented to illustrate the efficacy of the proposed technique. Specifically, the paper presents results for; (1) the optimal control of a simplified model of a gantry crane system, (2) the optimal control of a rigid body moving in the vertical plane, and (3) the trajectory optimization of a planar two-link robot. All problems include pure state variable inequality constraints.

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Nguyen, Ngoc-Hien, Karen Willcox und Boo Cheong Khoo. „Model Order Reduction for Stochastic Optimal Control“. In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82061.

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This work presents an approach to solve stochastic optimal control problems in the application of flow quality management in reservoir systems. These applications are challenging because they require real-time decision-making in the presence of uncertainties such as wind velocity. These uncertainties must be accounted for as stochastic variables in the mathematical model. In addition, computational costs and storage requirements increase rapidly due to the stochastic nature of the simulations and optimisation formulations. To overcome these challenges, an approach is developed that uses the combination of a reduced-order model and an adjoint-based method to compute the optimal solution rapidly. The system is modelled by a system of stochastic partial differential equations. The finite element method together with collocation in the stochastic space provide an approximate numerical solution—the “full model”, which cannot be solved in real-time. The proper orthogonal decomposition and Galerkin projection technique are applied to obtain a reduced-order model that approximates the full model. The conjugate-gradient method with Armijo line-search is then employed to find the solution of the optimal control problem under the uncertainty of input parameters. Numerical results show that the stochastic control yields solutions that are above the bound of the set solutions of the deterministic control. Applying the reduced model to the stochastic optimal control problem yields a speed-up in computational time by a factor of about 80 with acceptable accuracy in comparison with the full model. Application of the optimal control strategy shows the potential effectiveness of this computational modeling approach for managing flow quality.

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