Paper Info
Title
Linear Hamilton Jacobi Bellman Equations in high dimensions
Abstract
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than moderate state space size due to the curse of dimensionality. This work combines recent results in the structure of the HJB, and its reduction to a linear Partial Differential Equation (PDE), with methods based on low rank tensor representations, known as a separated representations, to address the curse of dimensionality. The result is an algorithm to solve optimal control problems which scales linearly with the number of states in a system, and is applicable to systems that are nonlinear with stochastic forcing in finite-horizon, average cost, and first-exit settings. The method is demonstrated on inverted pendulum, VTOL aircraft, and quadcopter models, with system dimension two, six, and twelve respectively.
Year
DOI
Venue
2014
10.1109/CDC.2014.7040310
Decision and Control
Keywords
Field
DocType
nonlinear control systems,optimal control,partial differential equations,stochastic systems,tensors,HJB equation,PDE,VTOL aircraft,curse-of-dimensionality,finite-horizon,globally optimal solution,inverted pendulum,linear Hamilton Jacobi Bellman equation,linear partial differential equation,low rank tensor representations,nonlinear system,optimal control problems,quadcopter models,stochastic forcing
Hamilton–Jacobi–Bellman equation,Applied mathematics,Mathematical optimization,Inverted pendulum,Nonlinear system,Optimal control,Computer science,Curse of dimensionality,Bellman equation,Partial differential equation,State space
Conference
Volume
ISSN
Citations 
abs/1404.1089
0743-1546
12
PageRank 
References 
Authors
0.76
24
3
Name
Order
Citations
PageRank
Matanya B. Horowitz1464.79
Anil Damle2120.76
Burdick, J.W.32988516.87