Numerical Discretization Methods for the Discounted Linear Quadratic Control Problem
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911969089421312 |
|---|---|
| author | Zhang, Zhanhao Hørsholt, Steen Jørgensen, John Bagterp |
| author_facet | Zhang, Zhanhao Hørsholt, Steen Jørgensen, John Bagterp |
| contents | This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system matrices of the discounted LQ-OCPs into systems of differential equations. Subsequently, we derive the discrete-time equivalent of the discounted LQ-OCP by solving these systems. This paper presents three numerical methods for solving the proposed differential equations systems: the fixed-time-step ordinary differential equation (ODE) method, the step-doubling method, and the matrix exponential method. Our numerical experiment demonstrates that all three methods accurately solve the differential equation systems. Interestingly, the step-doubling method emerges as the fastest among them while maintaining the same level of accuracy as the fixed-time-step ODE method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Discretization Methods for the Discounted Linear Quadratic Control Problem Zhang, Zhanhao Hørsholt, Steen Jørgensen, John Bagterp Optimization and Control This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system matrices of the discounted LQ-OCPs into systems of differential equations. Subsequently, we derive the discrete-time equivalent of the discounted LQ-OCP by solving these systems. This paper presents three numerical methods for solving the proposed differential equations systems: the fixed-time-step ordinary differential equation (ODE) method, the step-doubling method, and the matrix exponential method. Our numerical experiment demonstrates that all three methods accurately solve the differential equation systems. Interestingly, the step-doubling method emerges as the fastest among them while maintaining the same level of accuracy as the fixed-time-step ODE method. |
| title | Numerical Discretization Methods for the Discounted Linear Quadratic Control Problem |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2407.18769 |