\(Q\) domain optimization method for \(l_1\)-optimal controllers (Q1975558)

This paper presents an efficient approach for determining an \(\ell_1\) optimal controller. This problem has been solved in the past by means of linear programming using the finite-impulse response of the closed-loop system as optimization parameters. Here, the closed-loop system is expressed as \(\Phi= H-UQV\) with an arbitrary stable parameter \(Q\), where \(U\), \(V\) and \(H\) are defined by the Youla parametrization. The \(\ell_1\) optimal solution is characterized as: Among all internally stabilizing controllers, minimize the maximum peak-to-peak gain of \(\Phi\) operating on the space of bounded disturbances with unit norm. The \(Q\)-domain optimization method needs to solve a nonlinear optimization problem, but often it gives better results then the linear programming approach, because the number of parameters is small. As an example the position control of a flexible beam is considered (see Daleh, Diaz-Bobillo).