Approximating the Solution to LQR Problems with Bounded Controls
New equations involving the unknown final states and initial costates corresponding to families of LQR problems are shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2011 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/13105 |
| Online Access: | http://hdl.handle.net/11336/13105 |
| Access Level: | Open access |
| Keyword: | Optimal Control Constrained Control Lqr First Order Pdes https://purl.org/becyt/ford/2.11 https://purl.org/becyt/ford/2 |
| Summary: | New equations involving the unknown final states and initial costates corresponding to families of LQR problems are shown to be useful in calculating optimal strategies when bounded control restrictions are present, and in approximating the solution to fixed-end problems. The missing boundary values of the Hamiltonian equations are obtained by (off-line) solving two uncoupled, first-order, linear partial differential equations for two auxiliary n×n matrices, whose independent variables are the time-horizon duration T and the eigenvalues of the final-penalty matrix S. The solutions to these PDEs give information on the behavior of the whole (T,S)-family of control problems. Illustrations of numerical results are provided and checked against analytical solutions of ´the cheapest stop of a train´ problem. |
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