Proceedings of the London Mathematical Society · 2005 · 79 citations · 0 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsStochastic ProcessesControl Of Dynamical SystemsControl TheoryDifferential SystemsOperator TheoryOptimal ControlSystems Of Differential EquationsInfinite-dimensional Optimal ControlLinear Time-invariant SystemsLinear-quadratic ControlNonlinear Partial Differential EquationsOperator SemigroupsParabolic Partial Differential EquationsResolvent OperatorsResolvent Theory
We introduce the concept of a distributional resolvent linear system and solve the linear quadratic optimal control problem for this class of systems. The class of distributional resolvent linear systems includes all linear time-invariant systems that have been studied in the control literature. We show connections with integrated semigroups and distribution semigroups and we consider some examples of systems described by partial differential equations that could not be handled by the existing theory. 2000 Mathematics Subject Classification 47A48, 47D62, 49N10, 93C20.