engleski

Greedy algorithm for solving parameter dependent Lyapunov equations : Application to control problems

We adapt and apply greedy methods to approximate in an efficient way the solutions to parameter dependent, operator Algebraic Lyapunov equations. The algorithm identifies the most distinguished values of parameters (offline part) so to better describe or approximate the whole manifold of solutions (online part). The results are applied to control problems for dissipative PDE-s depending on a parameter, where the controllability Gramian is approximated by the solution to corresponding Lyapunov equation. The algorithm provides an approximating space for the Gramian operators which is independent of particular control data (initial and target state). This allows for a robust approach which is not datum sensitive. Both the computational cost and the numerical experiments confirm the efficiency of the method. Methodology and numerical results will be discussed.

Lyaounov equation ; greedy algorithm ; infinite dimensional setting ; Gramian operators

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