Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation

2021 ◽  
Vol 34 (5) ◽  
pp. 1681-1702
Author(s):  
Shuhang Chen ◽  
Adithya Devraj ◽  
Andrey Berstein ◽  
Sean Meyn
Keyword(s):  
Stochastic Approximation ◽  
Fast Convergence ◽  
Recursive Algorithms ◽  
Ode Method

scholarly journals An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 174
Author(s):  
Wenxiao Zhao
Keyword(s):  
Approximation Algorithm ◽  
Stochastic Approximation ◽  
Probabilistic Method ◽  
Principal Component ◽  
Stochastic Approximation Algorithm ◽  
The Past ◽  
Systems And Control ◽  
Ode Method ◽  
Centralized Algorithm ◽  
And Control

The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).

scholarly journals Robust Optimal Tracking Control of a Full-Bridge DC-AC Converter

2021 ◽  
Vol 11 (3) ◽  
pp. 1211
Author(s):  
En-Chih Chang ◽  
Chun-An Cheng ◽  
Rong-Ching Wu
Keyword(s):  
Steady State ◽  
Digital Signal Processor ◽  
Tracking Control ◽  
Harmonic Distortion ◽  
Digital Signal ◽  
Fast Convergence ◽  
Solution Quality ◽  
Hybrid Strategy ◽  
Optimal Tracking ◽  
Optimal Tracking Control

This paper develops a full-bridge DC-AC converter, which uses a robust optimal tracking control strategy to procure a high-quality sine output waveshape even in the presence of unpredictable intermissions. The proposed strategy brings out the advantages of non-singular fast convergent terminal attractor (NFCTA) and chaos particle swarm optimization (CPSO). Compared with a typical TA, the NFCTA affords fast convergence within a limited time to the steady-state situation, and keeps away from the possibility of singularity through its sliding surface design. It is worth noting that once the NFCTA-controlled DC-AC converter encounters drastic changes in internal parameters or the influence of external non-linear loads, the trembling with low-control precision will occur and the aggravation of transient and steady-state performance yields. Although the traditional PSO algorithm has the characteristics of simple implementation and fast convergence, the search process lacks diversity and converges prematurely. So, it is impossible to deviate from the local extreme value, resulting in poor solution quality or search stagnation. Thereby, an improved version of traditional PSO called CPSO is used to discover global optimal NFCTA parameters, which can preclude precocious convergence to local solutions, mitigating the tremor as well as enhancing DC-AC converter performance. By using the proposed stable closed-loop full-bridge DC-AC converter with a hybrid strategy integrating NFCTA and CPSO, low total harmonic distortion (THD) output-voltage and fast dynamic load response are generated under nonlinear rectifier-type load situations and during sudden load changes, respectively. Simulation results are done by the Matlab/Simulink environment, and experimental results of a digital signal processor (DSP) controlled full-bridge DC-AC converter prototype confirm the usefulness of the proposed strategy.

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