Design of nonlinear optimal control for chaotic synchronization of coupled stochastic neural networks via Hamilton–Jacobi–Bellman equation

2018 ◽  
Vol 99 ◽  
pp. 166-177 ◽  
Author(s):  
Ziqian Liu
Keyword(s):  
Neural Networks ◽  
Optimal Control ◽  
Bellman Equation ◽  
Nonlinear Optimal Control ◽  
Chaotic Synchronization ◽  
Stochastic Neural Networks ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

scholarly journals Entropic Dynamics in Neural Networks, the Renormalization Group and the Hamilton-Jacobi-Bellman Equation

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 587
Author(s):  
Nestor Caticha
Keyword(s):  
Neural Networks ◽  
Renormalization Group ◽  
Bayesian Learning ◽  
Bellman Equation ◽  
Depth Limit ◽  
Feed Forward ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Continuum ◽  
Entropic Dynamics

We study the dynamics of information processing in the continuum depth limit of deep feed-forward Neural Networks (NN) and find that it can be described in language similar to the Renormalization Group (RG). The association of concepts to patterns by a NN is analogous to the identification of the few variables that characterize the thermodynamic state obtained by the RG from microstates. To see this, we encode the information about the weights of a NN in a Maxent family of distributions. The location hyper-parameters represent the weights estimates. Bayesian learning of a new example determine new constraints on the generators of the family, yielding a new probability distribution which can be seen as an entropic dynamics of learning, yielding a learning dynamics where the hyper-parameters change along the gradient of the evidence. For a feed-forward architecture the evidence can be written recursively from the evidence up to the previous layer convoluted with an aggregation kernel. The continuum limit leads to a diffusion-like PDE analogous to Wilson’s RG but with an aggregation kernel that depends on the weights of the NN, different from those that integrate out ultraviolet degrees of freedom. This can be recast in the language of dynamical programming with an associated Hamilton–Jacobi–Bellman equation for the evidence, where the control is the set of weights of the neural network.

scholarly journals Optimal Control Strategy of Companies: Inheriting Period and Carbon Emission Reduction

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jin Liang ◽  
Wenlin Huang
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Emission Reduction ◽  
Carbon Emission ◽  
Bellman Equation ◽  
Control Model ◽  
Policy Implications ◽  
Optimal Control Strategy ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman

In this paper, we develop an optimal control model of companies for the inheriting period, during which interphase banking and borrowing of allowances are allowable. By considering the emission reduction policy and the initial auction amount, we optimize the problem in two steps. The model is then converted into a two-dimensional Hamilton–Jacobi–Bellman equation. The numerical results, analysis, and comparisons are presented. Finally, we highlight several policy implications from the perspectives of companies and governments.

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