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- W2143340660 abstract "This paper presents a sparse collocation method for solving the time-dependent Hamilton–Jacobi–Bellman (HJB) equation associated with the continuous-time optimal control problem on a fixed, finite time-horizon with integral cost functional. Through casting the problem in a recursive framework using the value-iteration procedure, the value functions of every iteration step is approximated with a time-varying multivariate simplex B-spline on a certain state domain of interest. In the collocation scheme, the time-dependent coefficients of the spline function are further approximated with ordinary univariate B-splines to yield a discretization for the value function fully in terms of piece-wise polynomials. The B-spline coefficients are determined by solving a sequence of highly sparse quadratic programming problems . The proposed algorithm is demonstrated on a pair of benchmark example problems. Simulation results indicate that the method can yield increasingly more accurate approximations of the value function by refinement of the triangulation." @default.
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- W2143340660 date "2014-09-01" @default.
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- W2143340660 title "A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines" @default.
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- W2143340660 doi "https://doi.org/10.1016/j.automatica.2014.07.012" @default.
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