An algorithm for solving the "peak-to-peak" optimal control problem

The peak-to-peak or l(1) performance objective can be used to capture many desirable closed-loop specifications, in particular when hard bounds on signals are imposed. However, few applications of the criterion have been reported, probably because the algorithms for computing a solution to the el problem were hard to implement. The purpose of this note is to review briefly the peak-to-peak criterion, and to describe an algorithm for computing optimal and sub-optimal el controllers using sequential H-2 projections. As opposed to previous approaches, the algorithm does not use interpolations constraints nor attempts to solve an infinite optimization problem via finite approximation. Instead, sequential projections onto convex sets are performed to decide whether a given sub-optimal l(1)-norm level can be achieved or not.