Reserch On SPSA Algorithm And Its Applications In Function Optimazation And Control

In the large complicated nonlinear system, usually there are complexnonlinear mappings between the loss functions and the preparativeoptimization parameters, so we cannot establish their mathematicalmodels. Then the optimization algorithms based on gradient lost its effects,however, some optimization algorithms for large scale optimization have alow speed. It is particularly important that to research an optimizationalgorithm which is model free and can deal with complex problemsefficiently.This article focuses on the research of simultaneous perturbationstochastic approximation algorithm, and introduces it to the design of PDcontroller. The main contents and the innovations can be summed as follows:1. This paper summarizes the essence, the improvement and the useof simultaneous perturbation stochastic approximation algorithm, and alsoit introduces the latest research results both at home and abroad in the lasttwo years. In the article, the features of SPSA in control is pointed out,such as a mode-free method for control process (data-driven nature), goodat processing the control problem with large-scale variables, robustness tonoise and perturbation, easy to implement by computer; and combiningwith other control algorithm easily due to its natural iterative form.2. According to optimize the nonlinear function with large-scalevariables, the article do the research on a function optimization methodbased on SPSA.“Gradient approximation” is accepted to revise the searchdirection, so as to gradually approximate to the minimum. By thosecharacteristics it is able to solve the unconstrained optimization problemwith large number of parameters. This paper describes the basic steps ofthe method, and runs two simulation experiments. 3. According to the ship heading control problems, the articleproposes a PD control scheme based on SPSA, which using SPSAalgorithm to adjust the PD controller parameters online. The main idea isto approach the gradient of the performance index function of the PDcontroller efficiently with SPSA algorithm, and then to revise thecontroller parameters iteratively. Using the design of PD scheme based onSPSA to the control of the ship’s heading, and the simulation results verifythe effectiveness of the scheme.