Galerkin spectral approximation for optimal control problem of a fourth-order equation with L 2-norm control constraint
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[1] Jie Shen,et al. Spectral and High-Order Methods with Applications , 2006 .
[2] Wenbin Liu,et al. Adaptive Finite Element Methods for Optimal Control Governed by PDEs: C Series in Information and Computational Science 41 , 2008 .
[3] Danping Yang,et al. Ciarlet-Raviart mixed finite element approximation for an optimal control problem governed by the first bi-harmonic equation , 2009, J. Comput. Appl. Math..
[4] R. Rannacher,et al. A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator , 2012, Calcolo.
[5] Liu San-yang,et al. On gradient-type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi-harmonic equation , 2007 .
[6] J. Lions. Optimal Control of Systems Governed by Partial Differential Equations , 1971 .
[7] Yvon Maday,et al. Some spectral approximations of two-dimensional fourth-order problems , 1989 .
[8] Wei,et al. A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM , 2009 .
[9] F. Tröltzsch. Optimal Control of Partial Differential Equations: Theory, Methods and Applications , 2010 .
[10] Jie Shen,et al. Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials , 1994, SIAM J. Sci. Comput..
[11] C. Canuto. Spectral methods in fluid dynamics , 1991 .
[12] Thirupathi Gudi,et al. An interior penalty method for distributed optimal control problems governed by the biharmonic operator , 2014, Comput. Math. Appl..
[13] Kunibert G. Siebert,et al. A Posteriori Error Analysis of Optimal Control Problems with Control Constraints , 2014, SIAM J. Control. Optim..
[14] Arnd Rösch,et al. Finite Element Discretization of State-Constrained Elliptic Optimal Control Problems with Semilinear State Equation , 2015, SIAM J. Control. Optim..
[15] Stefan Ulbrich,et al. Optimization with PDE Constraints , 2008, Mathematical modelling.
[16] Simone Cacace,et al. Modeling and Optimal Control of an Octopus Tentacle , 2018, SIAM J. Control. Optim..
[17] D. Gottlieb,et al. Numerical analysis of spectral methods : theory and applications , 1977 .
[18] Maïtine Bergounioux,et al. General Optimality Conditions for Constrained Convex Control Problems , 1996 .
[19] Juan Zhang,et al. Galerkin spectral approximations for optimal control problems governed by the fourth order equation with an integral constraint on state , 2016, Comput. Math. Appl..
[20] Bing Sun,et al. Dynamic Programming Viscosity Solution Approach and Its Applications to Optimal Control Problems , 2019, Studies in Systems, Decision and Control.
[21] Yildirim Hurmuzlu,et al. Active Vibration Control of a Clamped Square Plate , 2002 .
[22] Lixin Zhou. A priori error estimates for optimal control problems with state and control constraints , 2018 .
[23] Yanping Chen,et al. Galerkin Spectral Approximation of Elliptic Optimal Control Problems with $$H^1$$H1-Norm State Constraint , 2016, J. Sci. Comput..
[24] Nianyu Yi,et al. A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations , 2008, SIAM J. Numer. Anal..
[25] Michael Hinze,et al. Convergence of a Finite Element Approximation to a State-Constrained Elliptic Control Problem , 2007, SIAM J. Numer. Anal..
[26] Fenglin Huang,et al. A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Stokes Equations , 2011, SIAM J. Numer. Anal..
[27] Fredi Tröltzsch,et al. NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR OPTIMIZATION PROBLEMS IN FUNCTION SPACES AND APPLICATIONS TO CONTROL THEORY , 2003 .
[28] Karl Kunisch,et al. A Semi-smooth Newton Method for Regularized State-constrained Optimal Control of the Navier-Stokes Equations , 2006, Computing.
[29] P. Prakash,et al. Mixed Finite Element Methods for Fourth Order Elliptic Optimal Control Problems , 2016 .
[30] Michael Hinze,et al. A Variational Discretization Concept in Control Constrained Optimization: The Linear-Quadratic Case , 2005, Comput. Optim. Appl..
[31] Yanping Chen,et al. Error estimates for spectral approximation of elliptic control problems with integral state and control constraints , 2014, Comput. Math. Appl..
[32] Karl Kunisch,et al. Augemented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems , 1997 .
[33] Ahmed Naji,et al. Solving biharmonic equation as an optimal control problem using localized radial basis functions collocation method , 2019, Engineering Analysis with Boundary Elements.
[34] Yanping Chen,et al. Spectral Method Approximation of Flow Optimal Control Problems withH1-Norm State Constraint , 2017 .
[35] Lei Yuan,et al. Finite Element Approximations of an Optimal Control Problem with Integral State Constraint , 2010, SIAM J. Numer. Anal..
[36] Zhong Zheng,et al. Error estimates of the space-time spectral method for parabolic control problems , 2017, Comput. Math. Appl..
[37] Danping Yang,et al. International Journal of Computer Mathematics Spectral Mixed Galerkin Method for State Constrained Optimal Control Problem Governed by the First Bi- Harmonic Equation Spectral Mixed Galerkin Method for State Constrained Optimal Control Problem Governed by the First Bi-harmonic Equation , 2022 .
[38] Bao-Zhu Guo,et al. Convergence of an Upwind Finite-Difference Scheme for Hamilton–Jacobi–Bellman Equation in Optimal Control , 2015, IEEE Transactions on Automatic Control.
[39] Danping Yang,et al. Legendre–Galerkin spectral methods for optimal control problems with integral constraint for state in one dimension , 2015, Comput. Optim. Appl..
[40] Enrique Zuazua,et al. Generic Simplicity of the Spectrum and Stabilization for a Plate Equation , 2000, SIAM J. Control. Optim..