On the mixed sensitivity l1 optimal control

In this paper it is shown how discrete-time, mixed-sensitivity l ₁-optimal control problems can be converted via polynomial techniques to linear “least absolute data fitting” problems and solved via very efficient and stable numerical methods. In particular new sub/super-optimization schemes are introduced by expressing the impulse responses of the sensitivity and complementary sensitivity closed-loop maps in terms of the free parameter of a stabilizing deadbeat controller parameterization and exploiting the underlying algebraic structure of the above maps. This approach induces the application of a consistent truncation strategy and a redundancy-free constraints formulation that leads, as a consequence, to linear programming problems less affected by degeneracy. Further, the paper provides more insight on the algebraic structure of the problem and of the solution, allowing the development of a simple and conceptually attractive theory