Abstract
Algebraic Riccati equations (ARE) of large dimension arise when using approximations to design controllers for systems modelled by partial differential equations. We use a modified Newton method to solve the ARE. Since the modified Newton method leads to a right-hand side of rank equal to the number of inputs, regardless of the weights, the resulting Lyapunov equation can be more efficiently solved. A low-rank Cholesky-ADI algorithm is used to solve the Lyapunov equation resulting at each step. The algorithm is straightforward to code. Performance is illustrated with an example of a beam, with different levels of damping. Results indicate that for weakly damped problems a low rank solution to the ARE may not exist. Further analysis supports this point.
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