scholarly journals A Patchy Dynamic Programming Scheme for a Class of Hamilton--Jacobi--Bellman Equations

2012 ◽  
Vol 34 (5) ◽  
pp. A2625-A2649 ◽  
Author(s):  
Simone Cacace ◽  
Emiliano Cristiani ◽  
Maurizio Falcone ◽  
Athena Picarelli
Keyword(s):  
Dynamic Programming ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Dynamic Programming Scheme

scholarly journals Dynamic Programming and Hamilton–Jacobi–Bellman Equations on Time Scales

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yingjun Zhu ◽  
Guangyan Jia
Keyword(s):  
Dynamic Programming ◽  
Dynamic System ◽  
Time Scales ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Dynamic ◽  
Optimality Principle ◽  
Bellman Equations ◽  
Special Cases ◽  
Hamilton Jacobi Bellman

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman (HJB) equation on time scales is obtained. Finally, an example is employed to illustrate our main results.

Minimizing Power-Consumption of a Generalized Convective Law Multistage Heat Pump System via Hamilton-Jacobi-Bellman Equations and Dynamic Programming

2017 ◽  
Author(s):  
Shaojun Xia ◽  
Lingen Chen
Keyword(s):  
Dynamic Programming ◽  
Power Consumption ◽  
Heat Pump ◽  
Heat Sink ◽  
Heat Engine ◽  
Control Variable ◽  
Pump System ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Chp System

A multistage endoreversible Carnot heat pump (CHP) system with a finite heat sink and generalized convective heat transfer law (HTL) [q ∝ (AT)m] is investigated. For the given initial sink temperature, the minimum power consumption (MPC) is chosen to be optimization objective, the sink temperature is the control variable, and the corresponding continuous Hamilton-Jacobi-Bellman (HJB) equation is established. The detailed expressions of the MPC and the corresponding heat sink temperature for Newtonian HTL (m = 1) are further obtained based on the universal results. While for the cases with other HTLs (m ≠ 1), there exists no analytical solution, so numerical algorithm of dynamic programming (DP) is used, and the difference between the MPC optimization of the multistage endoreversible CHP system and the maximum power output (MPO) of the multistage endoreversible Carnot heat engine (CHE) system is also indicated. The obtained results in this paper could help an engineer in better evaluation of energy limits in practical power-consumption processes.

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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