A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering
SIAM Journal on Control and Optimization
Max-Plus Eigenvector Methods for Nonlinear H$_\infty$ Problems: Error Analysis
SIAM Journal on Control and Optimization
A Curse-of-Dimensionality-Free Numerical Method for Solution of Certain HJB PDEs
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
An Iterative Procedure for Constructing Subsolutions of Discrete-Time Optimal Control Problems
SIAM Journal on Control and Optimization
Hi-index | 22.14 |
Idempotent methods have been found to be extremely fast for the solution of dynamic programming equations associated with deterministic control problems. The original methods exploited the idempotent (e.g., max-plus) linearity of the associated semigroup operator. It is now known that curse-of-dimensionality-free idempotent methods do not require this linearity. Instead, it is sufficient that certain solution forms are retained through application of the associated semigroup operator. Here, we see that idempotent methods may be used to solve some classes of stochastic control problems. The key is the use of the idempotent distributive property. We demonstrate this approach for a class of nonlinear, discrete-time stochastic control problems.