Innovative Integrators for Computing the Optimal State in LQR Problems
We consider the numerical approximation of linear quadratic optimal control problems for partial differential equations where the dynamics is driven by a strongly continuous semigroup. For this problems, the optimal control is given in feedback form, i.e., it relies on solving the associated Riccati equation and the optimal state. We propose innovative integrators for solving the optimal state based on operator splitting procedures and exponential integrators and prove their convergence. We illustrate the performance of our approach in numerical experiments.
KeywordsAbstract LQR problems Optimal control Operator splitting procedures Exponential integrators Convergence analysis
P. Csomós acknowledges the support of the National Research, Development, and Innovation Office (NKFIH) under the grant PD121117. H. Mena was supported by the project Solution of large scale Lyapunov differential equations (P 27926) founded by the Austrian Science Foundation FWF.
- 2.Bagrinovskii, K.A., Godunov, S.K.: Difference schemes for multidimensional problems (in Russian). Dokl. Akad. Nauk. USSR 115, 431–433 (1957)Google Scholar
- 4.Benner, P., Mena, H.: Numerical solution of the infinite-dimensional LQR-problem and the associated differential Riccati equations. J. Numer. Math. (to appear)Google Scholar
- 6.Csomós, P., Mena, H., Schwaighofer, J.: Fourier-splitting method for solving hyperbolic LQR problems (2016, preprint)Google Scholar