Centering on a distributed optimal control problem governed by elliptic equations with a unilateral integral constraint on the state, we recall the first-order optimality conditions to explore variational formulations...
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Centering on a distributed optimal control problem governed by elliptic equations with a unilateral integral constraint on the state, we recall the first-order optimality conditions to explore variational formulations. The classical linear finite element method is employed to approximate the equivalent formulae. Taking into account the distinctive structural characteristics of discretized schemes, we divide the discretized optimal conditions into two equivalent matrix schemes. Subsequently, we introduce an efficient iterative algorithm designed to solve the approximation schemes. We demonstrate the convergence of our iterative algorithm and investigate its robustness and uniform optimality under a specified constraint, particularly focusing on small regularization parameters. Finally, numerical tests are conducted using various h and alpha to illustrate the efficiency of our proposed algorithm. These tests also validate a tremendous reduction in the number of required iterations.
We consider space-time tracking-type distributed optimal control problems for the wave equation in the space-time domain Q := \Omega x (0, T) \subset \BbbR n+1, where the control is assumed to be in 0;,0 (Q)]*, rather...
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We consider space-time tracking-type distributed optimal control problems for the wave equation in the space-time domain Q := \Omega x (0, T) \subset \BbbR n+1, where the control is assumed to be in 0;,0 (Q)]*, rather than in L2(Q), which is more common. While the latter ensures 0;0,(Q), this does not define a solution isomorphism. Hence, we use an appropriate state space X such that the wave operator becomes an isomorphism from X onto completely unstructured but shape regular simplicial meshes, we derive a priori estimates for the error II uwidetilde \\varrho h - uIIL2(Q) between the computed space-time finite element solution uwidetilde \\varrho h and the target function u with respect to the regularization parameter \varrho , and the space-time finite element mesh size h, depending on the regularity of the desired state u. These estimates lead to the optimal choice \varrho = h2 in order to define the regularization parameter \varrho for a given space-time finite element mesh size h or to determine the required mesh size h when \varrho is a given constant representing the costs of the control. The theoretical results will be supported by numerical examples with targets of different regularities, including discontinuous targets. Furthermore, an adaptive space-time finite element scheme is proposed and numerically analyzed.
In this paper, experimental results are presented for a distributed model predictive control ( DMPC) scheme applied to a laboratory-scale water distribution system consisting of connected water tanks. The setup is an ...
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ISBN:
(纸本)9781479974061
In this paper, experimental results are presented for a distributed model predictive control ( DMPC) scheme applied to a laboratory-scale water distribution system consisting of connected water tanks. The setup is an example of coupled dynamical systems whose modular structure makes them candidates for agent based distributedcontrol methods. A set of low cost Raspberry Pi microcomputers connected via a common Ethernet-network is used for the implementation of the DMPC. The DMPC algorithm employs an augmented Lagrangian approach to solve the distributed optimal control problem (OCP) subject to nonlinear system dynamics in continuous-time form and input constraints. In this way, the performance and modular character of the DMPC as well as the individual runtime footprints of the communication and computation with respect to the overall runtime of the distributed algorithm are studied.
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