The scaled-Q method for solving l1 optimization problems

We explore the scaled-Q approach for solving MIMO l₁ optimal control problems. This method was introduced by the author in order to alleviate many of the difficulties facing the numerical solution of optimal l₁ control problems. In particular, this approach does not require computations of multivariable zeros and their directions. It also avoids the pole-zero cancellation difficulties that existing methods based on zero-interpolation face when attempting to recover the optimal controller from an optimal closed-loop map. Since the scaled-Q approach is based on solving a regularized auxiliary problem for which the solution is always guaranteed to exist, it can be used no-matter where the system zeros are (including the stability boundary). Upper and lower bounds which converge to the optimal cost are provided, and all solutions are based on finite dimensional linear programming for which efficient software exists