Regularity and Singularity in Linear-Quadratic Control Subject to Implicit Continuous-Time Systems.

摘要

A linear-quadratic (LQ) control problem subject to a standard continuous-time system is called regular if the input weighting matrix is invertible and singular if this is not the case. Consequently, optimal inputs for regular LQ problems are ordinary functions (state feedbacks), whereas optimal controls for singular problems are in general distributions, e.g. impulses. The author shows that regularity and singularity in LQ problems subject to general (implicit) systems depends not so much on the input weighting matrix, as on the property that the integrand of the cost criterion is a function only if inputs and state trajectories are, as is the case for LQ problems subject to standard systems. In particular, he provides a simple criterion for distinguishing between regularity and singularity in LQ problems subject to general systems. The criterion is expressed in the system coefficients only and reduces to the classical one if the underlying systems are standard.