| 摘要: |
| In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-Isaacs equations (HJBIEs) arising in both deterministic and stochastic optimal control for affine nonlinear systems are developed. Convergence of the methods are established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the methods. However, the results presented in the paper are preliminary, and do not yet imply in anyway that the solutions computed will be stabilizing. More improvements and experimentation will be required before a satisfactory algorithm is developed. |
| 关键词: Hamilton-Jacobi-Bellman-Isaac equation, vector identity, fixed-point theory, successive approximation method, bounded continuous functions, convergence, Riccati equation |
| DOI： |
|
| 基金项目: |
|
| Iterative computational approach to the solution of the Hamilton-Jacobi-Bellman-Isaacs equation in nonlinear optimal control |
| M. D. S. Aliyu |
| (Department of Electrical Engineering, King Faisal University, Al Ahsa, 31982, Saudi Arabia) |
| Abstract: |
| In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-Isaacs equations (HJBIEs) arising in both deterministic and stochastic optimal control for affine nonlinear systems are developed. Convergence of the methods are established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the methods. However, the results presented in the paper are preliminary, and do not yet imply in anyway that the solutions computed will be stabilizing. More improvements and experimentation will be required before a satisfactory algorithm is developed. |
| Key words: Hamilton-Jacobi-Bellman-Isaac equation, vector identity, fixed-point theory, successive approximation method, bounded continuous functions, convergence, Riccati equation |
