Geodesic
Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods
Kybernetika, Tome 54 (2018) no. 4, pp. 629-647.

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This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem is computed. In addition, to get more efficient and accurate method, the domain decomposition strategy is proposed with the pseudospectral spatial discretization. Five numerical examples are presented to demonstrate the efficiency and accuracy of the proposed hybrid method.
DOI : 10.14736/kyb-2018-4-0629
Classification : 35F21, 49J20, 65M70
Keywords: nonlinear optimal control; pseudospectral method; Hamilton–Jacobi–Bellman equation 
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     title = {Solving a class of {Hamilton-Jacobi-Bellman} equations using pseudospectral methods},
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Mehrali-Varjani, Mohsen; Shamsi, Mostafa; Malek, Alaeddin. Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods. Kybernetika, Tome 54 (2018) no. 4, pp. 629-647. doi : 10.14736/kyb-2018-4-0629. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-4-0629/

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