Direct method to solve linear-quadratic optimal control problems
| Autor: | Nacima Moussouni, Mohand Bentobache, Mohamed Aliane, Philippe Marthon |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
021103 operations research Control and Optimization Algebra and Number Theory Discretization Applied Mathematics Direct method 0211 other engineering and technologies Cauchy distribution 02 engineering and technology Quadratic function Optimal control 020901 industrial engineering & automation Maximum principle Applied mathematics Quadratic programming Active set method Mathematics |
| Zdroj: | Numerical Algebra, Control & Optimization. 11:645 |
| ISSN: | 2155-3297 2155-3289 |
| DOI: | 10.3934/naco.2021002 |
| Popis: | In this work, we have proposed a new approach for solving the linear-quadratic optimal control problem, where the quality criterion is a quadratic function, which can be convex or non-convex. In this approach, we transform the continuous optimal control problem into a quadratic optimization problem using the Cauchy discretization technique, then we solve it with the active-set method. In order to study the efficiency and the accuracy of the proposed approach, we developed an implementation with MATLAB, and we performed numerical experiments on several convex and non-convex linear-quadratic optimal control problems. The obtained simulation results show that our method is more accurate and more efficient than the method using the classical Euler discretization technique. Furthermore, it was shown that our method fastly converges to the optimal control of the continuous problem found analytically using the Pontryagin's maximum principle. |
| Databáze: | OpenAIRE |
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