کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
696103 890323 2014 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Automatica - Volume 50, Issue 9, September 2014, Pages 2234–2244
نویسندگان
, , ,