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Volume 5 Issue 1
Jan.  2018

IEEE/CAA Journal of Automatica Sinica

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M. D. S. Aliyu, "An Iterative Relaxation Approach to the Solution of the Hamilton-Jacobi-Bellman-Isaacs Equation in Nonlinear Optimal Control," IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 360-366, Jan. 2018. doi: 10.1109/JAS.2017.7510682
Citation: M. D. S. Aliyu, "An Iterative Relaxation Approach to the Solution of the Hamilton-Jacobi-Bellman-Isaacs Equation in Nonlinear Optimal Control," IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 360-366, Jan. 2018. doi: 10.1109/JAS.2017.7510682

An Iterative Relaxation Approach to the Solution of the Hamilton-Jacobi-Bellman-Isaacs Equation in Nonlinear Optimal Control

doi: 10.1109/JAS.2017.7510682
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  • In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation (HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.

     

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