Neuro-Optimal Control for Discrete Stochastic Processes via a Novel Policy Iteration Algorithm

2020 ◽  
Vol 50 (11) ◽  
pp. 3972-3985 ◽  
Author(s):  
Mingming Liang ◽  
Ding Wang ◽  
Derong Liu
Keyword(s):  
Optimal Control ◽  
Stochastic Processes ◽  
Policy Iteration ◽  
Iteration Algorithm ◽  
Policy Iteration Algorithm

Approximate Solution for Optimal Control of Continuous-Time Switched Systems

2016 ◽  
Author(s):  
Tohid Sardarmehni ◽  
Ali Heydari
Keyword(s):  
Optimal Control ◽  
Continuous Time ◽  
Switched Systems ◽  
Online Training ◽  
Policy Iteration ◽  
Recursive Least Squares ◽  
Iteration Algorithm ◽  
Computational Burden ◽  
Time Dynamics ◽  
Policy Iteration Algorithm

Two approximate solutions for optimal control of switched systems with autonomous subsystems and continuous-time dynamics are developed. The proposed solutions consist of online training algorithms with recursive least squares training laws. The first solution is the classic policy iteration algorithm which imposes heavy computational burden (full back-up). In order to relax the computational burden in the policy iteration algorithm, the second algorithm is presented. The convergence of the proposed algorithms to the optimal solution in online training is investigated. Simulation results are presented to illustrate the effectiveness of the discussed algorithms.

scholarly journals A policy iteration algorithm for nonzero-sum stochastic impulse games

2019 ◽  
Vol 65 ◽  
pp. 27-45
Author(s):  
René Aïd ◽  
Francisco Bernal ◽  
Mohamed Mnif ◽  
Diego Zabaljauregui ◽  
Jorge P. Zubelli
Keyword(s):  
Nash Equilibrium ◽  
Numerical Methods ◽  
Variational Inequalities ◽  
Convergence Analysis ◽  
Policy Iteration ◽  
Iteration Algorithm ◽  
Value Functions ◽  
Numerical Tests ◽  
Wide Range ◽  
Policy Iteration Algorithm

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods available, to the best of our knowledge. Our method relies on the recently introduced characterisation of the value functions and Nash equilibrium via a system of quasi-variational inequalities. While our algorithm is heuristic and we do not provide a convergence analysis, numerical tests show that it performs convincingly in a wide range of situations, including the only analytically solvable example available in the literature at the time of writing.

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