Multiple solutions to the l1-optimal control problem andits dual linear programming problem

摘要

This paper explores the consequences for the l1-optimal controller of the dual linear programming problem having multiple solutions, for linear time-invariant single-input/single-output systems. When the dual problem has multiple solutions, all solutions yield the same set of optimal controllers. If these multiple solutions comprise an entire face of the constraint region, there is a single optimal controller. Thus, if the constraint region is two-dimensional, the primal and dual problems cannot both have multiple solutions. An example is given with a three dimensional constraint region where both problems have multiple solutions