On optimal peak regulation

Control systems which minimize a sum of mean-square control effort and peak trajectory error for linear plants are considered. These systems are shown to obey generalized Hamilton-Jacobi necessary (and sufficient) conditions. Closed loop control laws, which require feedback of worst error-to-date as well as state, can be computed through a series of related linear optimizations. Examples suggest the peak regulator may save considerable peak trajectory error with respect to the linear-quadratic regulator, but at the cost of slower return to the origin and more complex implementation.