engleski

Greedy Algorithm for Parameter Dependent Operator Lyapunov Equations. Application to Control Problems

We provide an efficient method for solving a family of parameter dependent, algebraic Lyapunov equations in an infinite dimensional setting. Our analysis is based on previous work on reduced modeling and (weak) greedy algorithms for parameter dependent PDEs and abstract equations in Banach spaces. The major contribution is threefold. Firstly, the problem is resolved in an infinite dimensional setting, thus enabling applications to PDEs and equations governed by unbounded operators. Secondly, we demonstrate the boundedness and coercive properties of the Lyapunov operator in appropriate functional spaces. Lastly, the method is applied to the control theory, enabling rapid construction of approximate control functions for a wide range of control problems.

Greedy methods ; Lyapunov operator ; PDE control ; Infinite-dimensional setting

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