Construction of nonlinear feedback for l1-optimal control

This paper considers the l¹-optimal control problem, i.e., minimization of the effects of disturbances as measured by the l ^∞-induced norm. Earlier work showed that even in the case of full state feedback, optimal and near-optimal linear controllers may be dynamic and of arbitrarily high order. However, previous work by the author derived the existence of near-optimal nonlinear controllers which are static. This paper presents a constructive algorithm for such nonlinear controllers. The main idea is to construct a certain subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. A computationally efficient construction of this subset requires the solution of several finite linear programs with the number of variables being at least the number of states but less than the number of states plus the number of controls. Concepts from viability theory play a central role throughout