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

8902811 拉谢茨卡 这个项目是调查一个连贯的边界集 波型描述的系统的控制问题， 板型偏微分方程，定义在有界 在更高的维度空间中。 线性和非线性 动力学被认为。 调查的问题包括： 精确能控性;通过以下任一方法的一致镇定 显式耗散反馈算子或 基于代数Riccati的非耗散反馈算子 最优二次费用问题及相关Riccati 方程;非线性系统;渐近稳定性 渐近稳定性的鲁棒性 非线性结构扰动;非线性结构扰动的适定性 Neumann非单调非线性波动方程 边界条件 贯穿始终的重点是最佳的 设置解决方案及其相关属性的位置 在最佳规律性的空间中进行研究，或者， 在有限能量的空间里。 理论上有很多应用 上述发展。 例如，控制 机器人手臂和减少破坏性的振荡， 地球上或轨道上的柔性结构，是 这一工作带来的实际好处。

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.