ℓ 1-optimal control of multivariable systems with output norm constraints

Abstract

In this paper, we consider the ℓ 1-optimal control problem for general rational plants. It is shown that for plants with no poles or zeros on the unit circle an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs. Exactly or approximately optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed loop transfer function. No assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators. It is shown that constrained problems in which a set of outputs is regulated subject to ℓ ∞-norm constraints on another set of outputs can be solved using a slight modification of the same algorithm.