A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines

Govindarajan, N.; De Visser, C.C.; Krishnakumar, K.

A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines

Title

A sparse collocation method for solving time-dependent HJB equations using multivariate B-splines

Author

Govindarajan, N.
De Visser, C.C.
Krishnakumar, K.

Faculty

Aerospace Engineering

Department

Control & Operations

Date

2014-08-20

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 timehorizon 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 timedependent 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.

Subject

optimal control
Hamilton-Jacobi-Bellman equation
multivariate splines
collocation method
adaptive dynamic programming

To reference this document use:

http://resolver.tudelft.nl/uuid:1a702117-6668-4560-a80a-d2113905a6c5

Publisher

Elsevier / International Federation of Automatic Control (IFAC)

Embargo date

2014-12-20

ISSN

0005-1098

Source

Automatica, 50 (9), 2014