Mathematical Sciences: Boundary Control Problems for Higher Dimensional Wave-Type and Plate-Type Partial Differential Equations

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8902811 Lasiecka This project is to investigate a coherent set of boundary control problems for systems described by wave-type and plate-type partial differential equations, defined on a bounded domain in higher dimensional space. Both linear and nonlinear dynamics are considered. Problems for investigation include: exact controllability; uniform stabilization by means either of explicit dissipative feedback operators or else of nondissipative feedback operators based on algebraic Riccati operators; optimal quadratic cost problems and related Riccati equations; asymptotic stability properties for nonlinear models; robustness of asymptotic stability properties under nonlinear structural perturbations; well-posedness of nonlinear wave equations with nonmonotone nonlinearities in the Neumann boundary conditions. The emphasis throughout is on the optimal setting where the solutions and their relevant properties are studied in the spaces of optimal regularity, or, alternatively, in the spaces of finite energy. There are many applications for the theoretical developments described above. For instance, the control of robot arms and the reduction of damaging oscillations in large flexible structures on Earth or in orbit, are examples of practical benefits resulting from this work.