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FEEDBACK CONTROL FOR RANDOM, LINEAR HYPERBOLIC BALANCE LAWS

卷 12, 册 2, 2022, pp. 81-104
DOI: 10.1615/Int.J.UncertaintyQuantification.2021037183
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Markus Bambach
Institut für virtuelle Produktion, Zürich, Switzerland
Stephan Gerster
Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany
Michael Herty
Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany
Muhammad Imran
Lehrstuhl Konstruktion und Fertigung, BTU Cottbus-Senftenberg, Cottbus, Germany

摘要

We design boundary controls of physical systems that are faced by uncertainties. The system dynamics are described by random hyperbolic balance laws. The control aims to steer the system to a desired state under uncertainties. We propose a control based on Lyapunov stability analysis of a suitable series expansion of the random dynamics. The control damps the impact of uncertainties exponentially fast in time. The presented approach can be applied to a large class of physical systems and random perturbations (e.g., Gaussian processes). We illustrate the boundary control effect on a stochastic viscoplastic material model.

键词: systems of hyperbolic balance laws, feedback stabilization, Lyapunov function, stochastic Galerkin, viscoplastic deformations
参考文献

  1. Bastin, G. and Coron, J.M., Stability and Boundary Stabilization of 1-D Hyperbolic Systems, lst ed., Basel, Switzerland: Birkhauser, 2016.

  2. Coron, J.M., Bastin, G., and d'Andrea-Novel, B., Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems, SIAMJ. Control Opt, 47(3):1460-1498, 2008.

  3. Coron, J.M., Bastin, G., and d'Andrea-Novel, B., Boundary Feedback Control and Lyapunov Stability Analysis for Physical Networks of 2x2 Hyperbolic Balance Laws, Proc. of 47th IEEE Conf. on Decision and Control, IEEE, New York, pp. 1454-1458, 2008.

  4. Coron, J.M. and Bastin, G., Dissipative Boundary Conditions for One-Dimensional Quasilinear Hyperbolic Systems: Lyapunov Stability for the C1-Norm, SIAMJ. Control Opt., 53(3):1464-1483, 2015.

  5. Gugat, M., Leugering, G., Tamasoiu, S., and Wang, K., H2-Stabilization of the Isothermal Euler Equations: A Lyapunov Function Approach, Chin. Ann. Math., 4:479-500,2012.

  6. Banda, M.K. and Herty, M., Numerical Discretization of Stabilization Problems with Boundary Controls for Systems of Hyperbolic Conservation Laws, Math. Control Relat. Fields, 3(2):121-142, 2013.

  7. Schillen, P. and Gottlich, S., Numerical Discretization of Boundary Control Problems for Systems of Balance Laws: Feedback Stabilization, Eur. j. Control, 35:11-18, 2017.

  8. Gerster, S. and Herty, M., Discretized Feedback Control for Systems of Linearized Hyperbolic Balance Laws, Math. Control Relat. Fields, 9(3):517-539,2019.

  9. Baumgartner, V., Gottlich, S., and Knapp, S., Feedback Stabilization for a Coupled PDE-ODE Production System, Math. Control Relat. Fields, 10(2):405-424, 2020.

  10. Banda, M. and Weldegiyorgis, G., Numerical Boundary Feedback Stabilisation of Non-Uniform Hyperbolic Systems of Balance Laws, Int. J. Control, 93(6):1428-1441, 2020.

  11. Gotzes, C., Heitsch, H., Henrion, R., and Schultz, R., On the Quantification of Nomination Feasibility in Stationary Gas Networks with Random Load, Math. Methods Oper. Res., 84(2):427-457, 2016.

  12. Gugat, M. and Schuster, M., Stationary Gas Networks with Compressor Control and Random Loads: Optimization with Probabilistic Constraints, Math. Problems Eng., 2018:7984079, 2019.

  13. Wiener, N., The Homogeneous Chaos, Am. J. Math, 60(4):897-936, 1938.

  14. Cameron, R.H. and Martin, W.T., The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals, Ann. Math, 48(2):385-392, 1947.

  15. Xiu, D. and Karniadakis, G.E., The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations, SIAM J. Sci. Comput., 24:619-644, 2002.

  16. Shu, R., Hu, J., and Jin, S., A Stochastic Galerkin Method for the Boltzmann Equation with Multi-Dimensional Random Inputs Using Sparse Wavelet Bases, Numer. Math.: Theory, Methods Appl., 10(2):465-488, 2017.

  17. Hu, J. and Jin, S., A Stochastic Galerkin Method for the Boltzmann Equation with Uncertainty, J. Comput. Phys., 315:150-168,2016.

  18. Carrillo, J., Pareschi, L., and Zanella, M., Particle Based GPC Methods for Mean-Field Models of Swarming with Uncertainty, Commun. Comput. Phys, 25:508-531,2019.

  19. Zhu, Y. and Jin, S., The Vlasov-Poisson-Fokker-Planck System with Uncertainty and a One-Dimensional Asymptotic Preserving Method, Multiscale Model. Simul., 15:1502-1529,2017.

  20. Jin, S. and Zhu, Y., Hypocoercivity and Uniform Regularity for the Vlasov-Poisson-Fokker-Planck System with Uncertainty and Multiple Scales, SIAMJ. Math. Anal., 50(2):1790-1816, 2018.

  21. Carrillo, J. and Zanella, M., Monte Carlo GPC Methods for Diffusive Kinetic Flocking Models with Uncertainties, Vietnam J. Math, 47:931-954, 2019.

  22. Zanella, M., Structure Preserving Stochastic Galerkin Methods for Fokker-Planck Equations with Background Interactions, Math. Comput. Simul, 168:28-47, 2020.

  23. Despres, B., Poette, G., and Lucor, D., Uncertainty Quantification for Systems of Conservation Laws, J. Comput. Phys, 228:2443-2467, 2009.

  24. Chen, Q.Y., Gottlieb, D., and Hesthaven, J.S., Uncertainty Analysis for the Steady-State Flows in a Dual Throat Nozzle, J. Comput. Phys, 204:378-398, 2005.

  25. Gottlieb, D. and Xiu, D., Galerkin Method for Wave Equations with Uncertain Coefficients, Commun. Comput. Phys, 3(2):505-518, 2008.

  26. Pulch, R. and Xiu, D., Generalised Polynomial Chaos for a Class of Linear Conservation Laws, J. Sci. Comput., 51:293-312, 2012.

  27. Pettersson, P., Iaccarino, G., and Nordstrom, J., A Stochastic Galerkin Method for the Euler Equations with Roe Variable Transformation, J. Comput. Phys, 257:481-500,2014.

  28. Gerster, S., Herty, M., and Sikstel, A., Hyperbolic Stochastic Galerkin Formulation for the p-System, J. Comput. Phys, 395:186-204,2019.

  29. Gerster, S. and Herty, M., Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations, Commun. Comput. Phys, 27:639-671,2020.

  30. Kusch, J., Alldredge, G., and Frank, M., Maximum-Principle-Satisfying Second-Order Intrusive Polynomial Moment Scheme, SMAIJ. Comput. Math., 5:23-51, 2017.

  31. Li, Q. and Wang, L., Uniform Regularity for Linear Kinetic Equations with Random Input Based on Hypocoercivity, SIAMJ. Uncertainty Quantif., 5:1193-1219, 2017.

  32. Liu, L. and Shi, J., Hypocoercivity Based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs, Multiscale Model. Simul., 16(3):1085-1114, 2018.

  33. Gerster, S., Herty, M., and Yu, H., Hypocoercivity of Stochastic Galerkin Formulations for Stabilization of Kinetic Equations, Commun. Math. Sci., 19(3):787-806,2021.

  34. Herau, F., Hypocoercivity and Exponential Time Decay for the Linear Inhomogeneous Relaxation Boltzmann Equation, Asymptot. Anal, 46:349-359, 2006.

  35. Herau, F., Introduction to Hypocoercive Methods and Applications for Simple Linear Inhomogeneous Kinetic Models, in Lectures on the Analysis of Nonlinear Partial Differential Equations, CCSD, Lyon, France, pp. 119-147, 2017.

  36. Villani, C., Hypocoercivity, Providence, RI: Memoirs of the American Mathematical Society, 2009.

  37. Dolbeault, J., Mouhot, C., and Schmeiser, C., Hypocoercivity for Kinetic Equations with Linear Relaxation Terms, Comptes RendusMath, 347:511-516, 2009.

  38. Dolbeault, J., Mouhot, C., and Schmeiser, C., Hypocoercivity for Linear Kinetic Equations Conserving Mass, Trans. Am. Mathe. Soc., 367:3807-3828,2015.

  39. Dafermos, C.M., Hyperbolic Conservation Laws in Continuum Physics, 3rd ed., Berlin: Springer-Verlag, 2010.

  40. Khalil, H.K., Nonlinear Control, Boston: Pearson Education, 2015.

  41. Bastin, G. and Coron, J.M., On Boundary Feedback Stabilization of Non-Uniform Linear 2x2 hyperbolic Systems over a Bounded Interval, Syst. Control Lett., 60(11):900-906, 2011.

  42. Gugat, M. and Gerster, S., On the Limits of Stabilizability for Networks of Strings, Syst. Control Lett., 131:1-10, 2019.

  43. Nordstrom, J. and Wahlsten, M., Variance Reduction through Robust Design of Boundary Conditions for Stochastic Hyperbolic Systems of Equations, J. Comput. Phys., 282:1-22,2015.

  44. Rasmussen, C.E. and Williams, C.K.I., Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning), 2nd ed., Cambridge, London: The MIT Press, 2005.

  45. Le Maitre, O.P. and Knio, O.M., Spectral Methods for Uncertainty Quantification, lst ed., Netherlands: Springer, 2010.

  46. Funaro, D., Polynomial Approximation of Differential Equations, Vol. 8, Berlin, Heidelberg: Springer, 2008.

  47. Courant, R. andHilbert, D., Methods of Mathematical Physics, Vol. l,New York: Wiley, 1989.

  48. Ernst, O.G., Mugler, A., Starkloff, H.J., and Ullmann, E., On the Convergence of Generalized Polynomial Chaos Expansions, ESAIM: M2AN, 46(2):317-339,2012.

  49. Sonday, B., Berry, R., Najm, H., and Debusschere, B., Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System, J. Sci. Comput, 33:1212-1233,2011.

  50. Xiu, D., Numerical Methods for Stochastic Computations, Princeton, NJ: Princeton University Press, 2010.

  51. Xiu, D. and Karniadakis, G.E., Supersensitivity Due to Uncertain Boundary Conditions, Int. J. Numer. Methods Eng., 61:2114-2138, 2004.

  52. Riemann, B., Uber Die Fortpflanzung Ebener Luftwellen VonEndlicher Schwingungsweite, Abh. Kdnig. Ges. Wiss. Gottingen, 8:43-66, 1860.

  53. Dai, D., Epshteyn, Y., andNarayan, A., Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations, SIAMJ. Sci. Comput., 43(2):A929-A952, 2021.

  54. Despres, B., Poette, G., and Lucor, D., Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method, Cham, Switzerland: Springer, 2013.

  55. Lax, P.D., Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, 1973.

  56. Ta-Tsien, L., Yi, Z., and De-Xing, K., Global Classical Solutions for General Quasilinear Hyperbolic Systems with Decay Initial Data, Nonlinear Anal, 28(8):1299-1332, 1997.

  57. Jin, S., Xiu, D., and Zhu, X., A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs, J. Sci. Comput., 67:1198-1218, 2016.

  58. Leveque, R.J., Finite Volume Methods for Hyperbolic Problems, lst ed., Cambridge: Cambridge University Press, 2002.

  59. Simo, J.C. and Hughes, T.J.R., Computational Inelasticity, lst ed., New York: Springer, 2016.

  60. Bergstrom, Y., A Dislocation Model for the Stress-Strain Behaviour of Polycrystalline a-FE with Special Emphasis on the Variation of the Densities of Mobile and Immobile Dislocations, Mater. Sci. Eng., 5(4):193-200, 1970.

  61. Bambach, M., Implications from the Poliak-Jonas Criterion for the Construction of Flow Stress Models Incorporating Dynamic Recrystallization, Acta Mater., 61(16):6222-6233,2013.

  62. Driscoll, T.A., Hale, N., and Trefethen, L.N., Chebfun Guide, Oxford: Pafnuty Publications, 2014.

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