Robust Control for Hybrid, Nonlinear Systems

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dc.contributor.authorChudoung, Jerawanen
dc.contributor.committeechairBall, Joseph A.en
dc.contributor.committeememberKing, Belinda B.en
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberKachroo, Pushkinen
dc.contributor.committeememberDay, Martin V.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:09:59Zen
dc.date.adate2000-04-20en
dc.date.available2014-03-14T20:09:59Zen
dc.date.issued2000-04-06en
dc.date.rdate2001-04-20en
dc.date.sdate2000-04-19en
dc.description.abstractWe develop the robust control theories of stopping-time nonlinear systems and switching-control nonlinear systems. We formulate a robust optimal stopping-time control problem for a state-space nonlinear system and give the connection between various notions of lower value function for the associated game (and storage function for the associated dissipative system) with solutions of the appropriate variational inequality (VI). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense. It also happens that a positive definite supersolution of the VI can be used for stability analysis. We also show how to solve the VI for some prototype examples with one-dimensional state space. For the robust optimal switching-control problem, we establish the Dynamic Programming Principle (DPP) for the lower value function of the associated game and employ it to derive the appropriate system of quasivariational inequalities (SQVI) for the lower value vector function. Moreover we formulate the problem in the <I>L</I>₂-gain/dissipative system framework. We show that, under appropriate assumptions, continuous switching-storage (vector) functions are characterized as viscosity supersolutions of the SQVI, and that the minimal such storage function is equal to the lower value function for the game. We show that the control strategy achieving the dissipative inequality is obtained by solving the SQVI in the viscosity sense; in fact this solution is also used to address stability analysis of the switching system. In addition we prove the comparison principle between a viscosity subsolution and a viscosity supersolution of the SQVI satisfying a boundary condition and use it to give an alternative derivation of the characterization of the lower value function. Finally we solve the SQVI for a simple one-dimensional example by a direct geometric construction.en
dc.description.degreePh. D.en
dc.identifier.otheretd-04192000-14240007en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04192000-14240007/en
dc.identifier.urihttp://hdl.handle.net/10919/26983en
dc.publisherVirginia Techen
dc.relation.haspartrobusthybrid.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectoptimal stoppingen
dc.subjectdissipative systemsen
dc.subjectviscosity solutionsen
dc.subjectH<sub>∞</sub> controlen
dc.subjecthybrid systemsen
dc.subjectstorage functionsen
dc.subjectdifferential gamesen
dc.subjectoptimal switchingen
dc.titleRobust Control for Hybrid, Nonlinear Systemsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en
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