Approximate dynamic programming for stochastic systems with additive and multiplicative noise

2011 ◽  
Author(s):  
Yu Jiang ◽  
Zhong-Ping Jiang
Keyword(s):  
Dynamic Programming ◽  
Multiplicative Noise ◽  
Stochastic Systems ◽  
Approximate Dynamic Programming ◽  
Additive And Multiplicative Noise

scholarly journals Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva
Keyword(s):  
Multiplicative Noise ◽  
Nonlinear Dynamical Systems ◽  
Stochastic Theory ◽  
Slow Variable ◽  
Theoretical Description ◽  
Mathematical Study ◽  
Stochastic Generation ◽  
Nonlinear Dynamical ◽  
Additive And Multiplicative Noise ◽  
And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

scholarly journals Robust-adaptive dynamic programming-based time-delay control of autonomous ships under stochastic disturbances using an actor-critic learning algorithm

2021 ◽  
Author(s):  
Hossein Nejatbakhsh Esfahani ◽  
Rafal Szlapczynski
Keyword(s):  
Dynamic Programming ◽  
Time Delay ◽  
Control Algorithm ◽  
Approximate Dynamic Programming ◽  
Robust Adaptive Control ◽  
Stochastic Disturbances ◽  
Time Delay Control ◽  
Model Free ◽  
Delay Control ◽  
Robust Adaptive

AbstractThis paper proposes a hybrid robust-adaptive learning-based control scheme based on Approximate Dynamic Programming (ADP) for the tracking control of autonomous ship maneuvering. We adopt a Time-Delay Control (TDC) approach, which is known as a simple, practical, model free and roughly robust strategy, combined with an Actor-Critic Approximate Dynamic Programming (ACADP) algorithm as an adaptive part in the proposed hybrid control algorithm. Based on this integration, Actor-Critic Time-Delay Control (AC-TDC) is proposed. It offers a high-performance robust-adaptive control approach for path following of autonomous ships under deterministic and stochastic disturbances induced by the winds, waves, and ocean currents. Computer simulations have been conducted under two different conditions in terms of the deterministic and stochastic disturbances and all simulation results indicate an acceptable performance in tracking of paths for the proposed control algorithm in comparison with the conventional TDC approach.

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