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Showing 1 to 7 of 7 for “"control of partial differential equations"”.
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NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS
<p>Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Optimal control of partial differential equations (PDEs) has tremendous applications in engineering and science, such as shape optimization, image processing, fluid …
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Proper Orthogonal Decomposition for Reduced Order Control of Partial Differential Equations
Numerical models of PDE systems can involve very large matrix equations, but feedback controllers for these systems must be computable in real time to be implemented on physical systems. Classical control design methods produce controllers of the same order as the numerical models. Therefore, …
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Methods of Computing Functional Gains for LQR Control of Partial Differential Equations
This work focuses on a comparison of numerical methods for linear quadratic regulator (LQR) problems defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require …
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Model Predictive Control for Partial Differential Equations
… thesis we are concerned with model predictive control (MPC) of partial differential equations. The idea is to approximate an infinite time horizon optimal control problem by a sequence of finite horizon optimal control problems. The optimization horizon plays a crucial role in the stability …
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Multilevel-in-Time Methods for Optimal Control of PDEs and Training of Recurrent Neural Networks
… systems arising in discretized linear-quadratic Partial Differential Equation (PDE)-constrained optimization problems and Recurrent Neural Network (RNN) training problems. While these two problem classes seem different, they share a time-like structure. The proposed methods exploit decompositions …
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Shape Calculus Applied to State-Constrained Elliptic Optimal Control Problems
This thesis is devoted to the analysis of a very simple, pointwisely state-constrained optimal control problem of an elliptic partial differential equation. The transfer of an idea from the field of optimal control of ordinary differential equations, which proved fruitful with respect to both …
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Control of Periodic Systems Governed by Partial Differential Equations Using Averaging
… is a mathematical tool for dynamic analysis of time-periodic and space-periodic dynamical systems, including those governed by partial differential equations. The control design procedure presented in this work uses averaging techniques, the well-developed linear control strategies, and …