Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-Bounded Projection-Based Controllers
W.P.M.H. Heemels, Aneel Tanwani
Abstract
Projection-based control (PBC) systems have significant engineering impact and receive considerable scientific attention. To properly describe closed-loop PBC systems, extensions of classical projected dynamical systems are needed, because partial projection operators and irregular constraint sets (sectors) are crucial in PBC. These two features obstruct the application of existing results on existence and completeness of solutions. To establish a rigorous foundation for the analysis and design of PBC, we provide essential existence and completeness properties for this new class of discontinuous systems.
Topics & Concepts
Completeness (order theory)Projection (relational algebra)Dynamical systems theoryBounded functionConstraint (computer-aided design)MathematicsComputer scienceClass (philosophy)Mathematical optimizationApplied mathematicsCalculus (dental)Algebra over a fieldControl theory (sociology)Control (management)AlgorithmPure mathematicsArtificial intelligenceMathematical analysisMedicineQuantum mechanicsPhysicsGeometryDentistryFormal Methods in VerificationReal-Time Systems SchedulingLogic, programming, and type systems