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| Content Provider | Springer Nature Link |
|---|---|
| Author | Rossomakhine, Sergey Gaitsgory, Vladimir |
| Copyright Year | 2014 |
| Abstract | The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples. |
| Ending Page | 276 |
| Page Count | 82 |
| Starting Page | 195 |
| File Format | |
| ISSN | 00954616 |
| e-ISSN | 14320606 |
| Journal | Applied Mathematics and Optimization |
| Issue Number | 2 |
| Volume Number | 71 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2014-06-11 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Time-scale analysis and singular perturbations Averaging method Systems Theory, Control Theoretical, Mathematical and Computational Physics Averaging and linear programming Occupational measures Mathematical Methods in Physics Differential inclusions Numerical solution Calculus of Variations and Optimal Control; Optimization Singularly perturbed optimal control problems Numerical and Computational Physics Singular perturbations, general theory |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Control and Optimization |
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