Universal algorithms for solving discrete stationary Bellman equations

2019 ◽  
pp. 393-431
Author(s):  
Grigory L. Litvinov ◽  
Аnatoliy Ya. Rodionov ◽  
Serge Sergeev ◽  
Andrei N. Sobolevsky
Keyword(s):  
Bellman Equations ◽  
Idempotent Semirings

This paper investigates algorithms for solving discrete stationary (or) matrix Bellman equations over semirings, in particular over tropical and idempotent semirings, Also there are presented some original algorithms, applications and programmed realization.

scholarly journals Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

2021 ◽  
Author(s):  
Sudeep Kundu ◽  
Karl Kunisch
Keyword(s):  
Linear Equations ◽  
Hjb Equation ◽  
Policy Iteration ◽  
Optimal Feedback Control ◽  
Iteration Step ◽  
Control Constraints ◽  
Hjb Equations ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Feedback Control Theory

AbstractPolicy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

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