Discrete and Continuous Dynamical Systems - B · 2010 · 58 citations · 19 references
EngineeringIndustrial EngineeringManufacturing EngineeringDynamical SystemsManufacturing SystemsProcess ControlControl SystemsControl TheoryNonlinear Process ControlOptimal ControlProduction OptimizationProduction TheoryConservation Law ModelsConservation LawsEquilibrium StatesFinite-time Optimal ControlOptimal Control Existence TheoremsOptimal Control ModelsOutput RegulationTime-optimal Control
This article studies a hyperbolic conservation law that modelsa highly re-entrant manufacturing system as encountered insemi-conductor production.Characteristic features are the nonlocal character of the velocityand that the influx and outflux constitute the control and outputsignal, respectively.We prove the existence and uniqueness of solutions for $L^1$-data,and study their regularity properties.We also prove the existence of optimal controlsthat minimizes in the $L^2$-sense the mismatch between the actualand a desired output signal.Finally, the time-optimal control for a step between equilibrium states isidentified and proven to be optimal.
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