Laguerre Bases for Youla-Parametrized Optimal-Controller Design: Numerical Issues and Solutions

This thesis concerns the evaluation of cost functionals on H2 when designing optimal controllers using finite Youla parameterizations and convex optimization. We propose to compute inner products of stable, strictly proper systems via solving Sylvester equations. The properties of different state space realizations of Laguerre filters, when performing Ritz expansions of the optimal controller are discussed, and a closed form expression of the output orthogonal realization is presented. An algorithm to exploit Toeplitz substructure when solving Lyapunov equations is discussed, and a method to extend SISO results to MIMO systems using the vectorization operator is proposed. Finally the methods are evaluated on example systems from the industry, where it is shown that properly selecting the cutoff frequency of the filters is an important problem that should be discussed when Laguerre bases are used to parametrize the optimal controller